advanced corporate finance-2017 · advanced corporate finance-2017 chinhoyi university of finance...

ADVANCED

CORPORATE

FINANCE-2017

FINANCE MAKES SENSE

CHINHOYI UNIVERSITY OF TECHNOLOGY

T.J MABVURE (MR.)

[ADVANCED CORPORATE FINANCE-2017] This course is designed to develop an understanding of finance and corporate financial analytical tools at a higher level. The course is a continuation of Corporate Finance. By the end of the course, students should be able to determine the value of Equity and Firms, analyse Mergers and Acquisitions of Companies, and discuss Short term financial strategies of firms.

T.J MABVURE (Mr.)

Functional Strategy of a Company (Firm)

a) Marketing Strategy

b) Human Resources Strategy

c) Production Strategy

d) Financial Strategy

Financial Strategy

Issues to consider in crafting this strategy:

a) Sources of funds

b) Uses of funds

c) Capital structure(Debt/Equity structure)

d) Risk return(measured by ke,P0,g,β)

e) Dividend policy

Main Corporate Strategy issues: How financial strategy fits into it.

a) Market share and growth rate of the market

b) Product range(Product life cycle)-At what stage of the PLC is each product

c) Strategic Business Units (SBU)-every SBU is strongly related to each product in each

product range. For e.g. Chinhoyi University of Technology has the Farm and the Hotel

as its SBUs. Another example is Innscor Plc which has got food, battery

manufacturing, crocodile farming, and electronics, as its SBUs. Each SBU will follow

the PLC of its product or product range. The PLC of the product is the PLC of the SBU.

T.J MABVURE (Mr.)

Maturity Stage Decline stage

g

Growth stage

Introduction stage

t

Fig: Product Life Cycle (PLC)

Stage 1: Introduction

Profits are negative

Promotion of the product(Heavy expenditure on promotional activities resulting in low

profits)

Heavy expenditure on R&D

Cash floware negative

Stage 2: Growth

Profits are positive and are increasing

Advertising expenditure because of new competitors

Developing of Brands e.g. GTEL goat, Astro goat. Cash flows will be negative because

of brand building. If positive they are still low.

Stage 3: Maturity

Market growth rate has started to decline

Rebranding activities/brand transfer; Buddie to Libertie, and back to Buddie again;

Mazoe orange crush to raspberry, Granadilla, Blackberry.

T.J MABVURE (Mr.)

Large companies who have survived

Large market share

Growth rate of market stabilized

Cash flows now positive, now exploiting the characteristic of your brand

Stage 4: Decline

Cash flows now negative

Growth opportunities now small

Divesting from SBUse.g. Harvesting SBUs like gold mining where gold has run out.

Kamativi tin mine was divested long ago because of the increase in plastic.

Boston Consultant Group(BCG Matrix)

SBU

Star

High relative market share in a

high growth market

2.Growth

Dividend payments low

Listing or private placement

Option based borrowing

PE ratio high

Operating risk high

Gearing low

SBU

Question Mark

Low relative market share in a

high growth market

1.Introduction

Dividends nil

Equity finance-venture capital

Gearing nil

P/E ratio high

Operating risk high, financial

risk

low

SBU

Cash Cow

High relative market share in a

low growth market

3.Maturity

Dividend high because of

positive

SBU

Dog

Low relative market share in a

low growth market

4.Decline

T.J MABVURE (Mr.)

Cash flows

Net cash flows high

Rights issues

Operating risk now low

P/E ratio now low

Financial Strategic Issues

1. Net cash flows at each stage

2. P/E ratio at each stage

3. Dividend policy at each stage

4. Gearing ratio determined by the total risk

Introductory stage

Net cash flows will be negative or very low because revenues are still low and there

are outflows in concept development

Dividends are nil because profits still low and cash flows are negative. Retention ratio

is 100% in order to gain market share in the growing market.

P/E ratio will be very high. Market perception that the company will do well in the

future are very high. Price per share relative to earnings per share is high.

Total return(Dividend yield plus capital gain yield)

The investors are the promoters of the product concept and they are the sponsors.

The investors are venture capitalists using venture capital (venture capitalists have

different portfolios in different SBUs, i.e invest in a controlling stake. They will be

looking for capital gains and not dividends. They sell their equity holdings and as soon

as the company grows they pull out. Angel capitalists are an alternative to venture

capitalists.

Financing structure will be all equity finance. Therefore the gearing ratio will be Nill.

The Company cannot sustain loan obligations as they come due.

T.J MABVURE (Mr.)

Operating risk (business risk) will be very high so the required rate of return by debt

holders will be high and cannot be sustained. Total risk=Operating risk+Financail risk),

so financial risk has to be maintained at low levels.

Growth Stage

Still fighting competitors if the barriers to entry are very low. In the telecoms

industry POTRAZ and BAZ for broadcasting have artificially raised the barriers.

Net cash flows are still low because of the heavy expenditures incorporated in

strengthening the brand, e.g Netone, Telecel, and Econet.

Dividends payments are very low

P/E ratio still very high

Capital gains being sought for, other than dividends

Gearing low because at this stage the business risk is still relatively high, that’s why

there is need for reducing financial risk by reducing borrowings

Equity financing, but changed from venture because the company will be listed to

facilitate a new share issue (IPO) for expansion of the company. Equity is now

shareholders equity and the venture capitalists will pull out. At listing there will be a

price which will determine the price at which the venture will sell their share. Private

placements (approaching institutional investors such as the MIPF, PTC, NSSA, OLD

MUTUAL, etc) would also be considered when the company does not want to list.

Option based financing; financing with imbedded options such as convertible

debentures, convertible bonds will be considered. This are issued at a lower cost than

plain vanilla bonds. These will be converted after a period of time agreeable. The

option to convert is not obligatory, only exercised when it’s profitable to do so. Also

there can be debentures with warrants attached, i.e. the right to buy an agreed

number of the company’s ordinary equity at an agreed time and at an agreed price

(strike price/exercise price) .A convertible is known as a European option because it

can only be exercised at an expiration date. A bond with a warrant is an American

option because it can be exercised at any time before the expiration time. It gives an

option within an option. With a warrant you become a shareholder and also a bond

holder, the warrant can be detached from the bond,i.e it can have its own market

value. It’s a highly valued instrument compared to the convertible. At this stage the

T.J MABVURE (Mr.)

company has to take advantage of financial leverage because earnings are increasing

but can not borrow outright because business risk is still high and financial risk has to

be minimized. To go around this problem, option based instruments have to be used.

Option based bonds (sweeteners) are cheaper than plain vanilla bonds. They reduce

the total cost of borrowing. Option based bonds can be issued at low coupon rates

because they will gain value, that is they are participating in the growth of the

company. Ordinary bondholders have a fixed return and they don’t benefit from the

increase in the value of the share. After the exercise the equity base will increase and

the debt will decrease, that is the capital structure will shift, for the convertible

bonds. For the bond with warrants, the debt levels will remain the same and the

equity will increase, also with these bonds there will be a fresh injection of funds as

the shares have to be bought. With the options the company will be preparing for the

restructuring of the balance sheet, i.e restructuring at the initial public offer (IPO)

and then another restructuring at the exercise of the options.

Maturity

This is a stage at which the balance sheet will also be restructured.

Rights issue/seasoned issue; New shares to existing shareholders. The rationale is to

reward the shareholders for being loyal because they have made the company grow by

accepting low or no dividends for capital gains. The company does not want to dilute

the earnings of the shareholders.

Exercise of options if convertibles and warrants had been issued.

Net cash flows are now high, that is positive. High turnover with low cost of R&D.

Main expenditure is advertising rather than promotional because brand is now

established. Consolidating your position by tour brand. No need to reinvest as the

market opportunities for expansion is now low.

Dividends now high because growth opportunities now reduced, i.e retentions now

reduced

Cash cow because some of the cash flows can be used to finance new SBUs.

The returns now dividends yields rather than capital gains

Bond holders now interested in dividends rather than capital gains and also this holds

for all the former shareholders who the company started with.

T.J MABVURE (Mr.)

The P/E ratio now low

The operating risk now very low

Gearing ratio low, can now afford to have plain vanilla debt because the cash flows

are there.

Decline

Divesting/harvesting

Zero opportunities

Total dividend, that is 100% payout

Not able to increase borrowings because the required rate of return will be high. If

the company increase borrowings and the company is wound up the share of the debt

holders will increase in the company. Therefore the debt/equity ratio has to be

decreased.

The company will grow(g) at the same rate as the growth of the economy

Exercise

1. Production life cycles of companies can be related to the growth rate of the market and the

relative market share of the company. Use the following variables to explain how this

observation can be supported

a) The overall risk profile of the company [5]

b) Types of equity funding [4]

c) Dividend policy [4]

d) Growth rate in earnings [4]

e) Gearing ratio and type of debt funding [4]

f) P/E multiple [4]

g) Capital expenditure VS depreciation [4]

2. The functional strategy of a company consists of the Marketing Strategy, Human

Resources Strategy, Production Strategy, and Financial Strategy.

T.J MABVURE (Mr.)

Describe the company’s financial strategy at each stage of the Product life cycle in

terms of the overall risk of the company, Type of equity funding, Dividend policy,

growth rate in earnings, gearing ratio, P/E Multiple, Capital expenditure and

Depreciation [20 Marks]

3. The question mark, star, cash cow and dog are associated with the Boston Consultant

group. Describe the happenings in each of the SBU’s as relates to market share,

growth rate, dividend policy, type of equity financing risk, gearing ratio, cash flows,

profitability, liquidity, Capex and depreciation. [20 Marks]

APPROACHES TO VALUATION

The purpose is to arrive at the value of the company using its fundamentals. There are three

approaches to valuation.

Discounted cash flow Valuation

1. Value of equity-specifically the price per share(P0)

2. Value of the firm

How do we derive value of an Asset?

The value of an asset is the present value of the expected future cash flows, discounted

at the required rate of return that reflects the risk ness of these expected cash flows.

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 = ∑𝐶𝐹𝑡

(1 + 𝑖)𝑡

𝑛

𝑡=1

+𝑀

(1 + 𝑖)𝑛

n=Life of the asset

CFt= Cash flow in period t

i=required rate of return given the risk

The value of equity is found by discounting the expected cash flows to equity at the rate

of return required by equity investors.

T.J MABVURE (Mr.)

If we assume that the firm is in a stable growth period:

Value of equity=

1 1tt

t

ke

FCFE

Where t is starting from year 1 to infinity

CFE=Cash flow to equity

Ke= risk adjusted required rate of return [ke=Rf+β (Rm-Rf)]

Rf= Risk free rate, ie the average money market rate, TB rate is used

as proxy .Not that it is the only risk free rate, as all the securities

in the money market are risk free.

β= Beta coefficient, measure the volatility of the returns on the

security relative to the returns on the market. It’s a measure of

the systematic risk

rm-rf= risk premium on the market

[illustrate with a diagram the risk premium]

Value of firm=

1 1tt

t

WACC

FCFF

FCFF=Cash flow to the firm

WACC=Weighted average cost of capital

Value of firm is the cash flows to the firm discounted to the weighted

present value of the weighted average cost of capital(WACC)

Cash flows to the firm are the equity to the shareholders and debt to debt

holders, Cash flows to preference share holders.

WACC=Wd[kd(1-T)]+WeKe+WpKp

kd= cost of debt adjusted for tax(T) because interest is

Allowable for tax to make the debt cheaper.

Ke= cost of equity

Wd= weight of debt

Wk= weight of equity

Wp= weight of preference shares

T.J MABVURE (Mr.)

Applicability

Discounted cash flow valuation is based on expected future cash flows and discounts

rates.

The expected cash flows have to be estimated

Given these informational requirements the approach is easier for firms whose cash

flows can be reliably estimated for future periods.

The approach also requires the use of a proxy for risk to be applied to the discounted

rates and the proxy is the β coefficient

With other models other than CAPM the β is not a sufficient proxy however.

The discounted cash flow approach may be difficult to use because of the following:

1. Firms in trouble: A distressed firm generally has negative earnings and cash

flows. To estimate the future cash flows for such a firm may be difficult

because of the high probability of bankruptcy.

2. Cyclical firms: This is a firm whose earnings and cash flows tend to follow the

economic cycle, which is increasing during economic booms and falling during

recessions.

3. Firms with unutilized assets: Discounted cash flow valuation reflects the value

of all assets that produce cash flows. If a firm has assets that are not utilized

and therefore didn’t produce cash flows the value of these assets would not be

reflected in the total value. For example a firm with a piece of land, mining

claim not exploited.

4. Firms with Patents and Product options: Firms that have unutilized patents or

product options that are not currently producing Cash flows but can be

exploited are not also easy to value using this approach.

5. Firms in the process of restructuring: For example the firm maybe in the

process of selling some of its assets and acquiring others, e.g Delta disbanded

some of its subsidiaries like the hospitality, furniture and remained with the

beverages.

6. Firms involved in acquisitions: This causes the problem of synergy (expected

benefits of the merger and they are not easy to quantify.).

T.J MABVURE (Mr.)

2. Relative valuation approach

1. This approach says that the value of an asset is derived from the pricing of

comparable assets standardized using a common variable such as earnings,

cashflows, book values or revenues.

2. We can use the industry average P/E ratio assuming that the other firms in

industry are comparable to the firm being valued.

3. We can also use the price to book value (market price/book value). A firm selling

at a discount to its book value relative to other firms in the industry is considered

undervalued.

4. Also price to sales multiple is used in this valuation process.

5. To use these multiples we relate the multiple to the firm’s fundamentals such as;

the growth rate in earnings, and dividend payout ratio. This allows us to explore

how the multiple will change as the firms’ characteristics change for e.g.we would

want to know the effect of changing profit margins on the P/Sales ratio or the

effect of changes in the growth rates on the P/E ratio.

6. This approach is useful when there is large number of comparable firms being

traded on the financial markets and the market is on average pricing these firms

correctly.

3. The contingent valuation method

This approach uses option pricing models to measure the value of assets with option

characteristics (warrants and convertible bonds).

T.J MABVURE (Mr.)

Discounting cash flow approach

Estimating cash flows

I.Free cash flows to equity(FCFE)

Equity investors receive a residual claim on the cash flows to the firm, which is

they are entitled to any cash flow that is left over after meeting all the

financial obligations of the firm including debt repayments and the re-

investment needs of the firm.

The free cash flow to equity (FCFE) are the cash flows that remain after

operating expenses and principal repayments and any capital expenditures that

are required to maintain the growth rate in projected cash flows.

a) Free cash flows for an unlevered firm: An unlevered firm has no debt in its capital

structure, therefore there are no interest and principal Repayments, it finances all

capital expenditures and working capital needswith equity therefore the free cash

flow to equity will be as follows:

b)

Gross Profit xxx

Operating Expenses (xx)

EBITDA xxx

Depreciation and Amortization (xx)

EBIT xxx

Taxes (xx)

Net Income xxx

Depreciation and Amortisation xxx

Cash flow from operations xxx

Capital Expenditure (CAPEX) (xx)

Changes in Working capital (xx)

Free cash flow to Equity (FCFE) xxx

T.J MABVURE (Mr.)

Amortization is the w/o of intangible assets e.g. goodwill, pre-operations costs.

Assuming an increase in working capital. If there was a decrease we will add

changes in working capital.

The FCFE is the residual cash flow after meeting the entire firm’s financial

needs; it can be negative in which case the firm must raise new equity. If it’s

positive it could but is not always paid out as dividends to equity investors.

When we reach net income the amount we eventually deduct for dividends has

to take into consideration the CAPEX, and the change in working capital.

Depreciation and amortization are treated as tax deductible expenses in the

income statement but they are non-cash expenses and therefore they should be

added back.

Equity investors can not withdraw the entire cash flow from operations from

the firm’s since some or all of it will have to be re-invested to maintain

existing assets and to create new assets to generate future growth.

Funds tied up in working capital can’t be used elsewhere in the firm therefore

increases in working capital are cash outflows and decreases are cash

inflows(specifically non-cash working capital)

T.J MABVURE (Mr.)

Eg of the effect of a decrease in CAPEX

2013($m) 2014($m)

Net Income 150 40

Depreciation 50 55

Funds from operations 200 95

CAPEX (100) (20)

ΔWC (50) (10)

FCFE 50 65

The drop in the CAPEX and WC in 2014 resulted in increased FCFE though the net income was

much lower.

b) FCFE For a levered firm

In addition to making all of the outlays that an unlevered firm must make the

levered firm must also generate cash flows to cover interest expenses plus

principal repayments. It can also finance some of its capital expenditures and

working capital needs with debt thereby reducing the equity investments needed.

Gross Profit xxx

Operating Expenses (xx)

EBITDA xxx

Depreciation and Amortisation (xx)

EBIT xxx

Interest (xx)

EBT xxx

Taxes (xx)

Net Income xxx


Cash flow from operating Activities xxx

CAPEX (xx)

T.J MABVURE (Mr.)

ΔWC (xx)

Principal Repayments (debt repayments) (xx)

Proceeds from new debt issues xxx

FCFE xxx

The interest is tax deductible but the principal repayments are not tax

deductible.

i) A levered firm at its desired level of leverage

The desired leverage is the debt ratio that is viewed as acceptable for

future financing so there is no plan to change it:

Debt Ratio=equitydebt

Debt

If the debt ratio is regarded to be optimal the free cash flows to equity

(FCFE) will be: Net income-(1-d) (CAPEX-Depreciation)-(1-d) (ΔWC). d=Debt

ratio regarded as optimal.

For such a firm the proceeds from new debt issues will be given by the

following: Principal repayments+d (CAPEX+ ΔWC).

Since the firm is at its desired capital structure principal repayments are

made with proceeds from new debt issues. CAPEX and WC needs are

financed using the desired mix of debt and equity.

e.g. In 2013 a firm had $20million of debt outstanding and $40million in market value of

equity giving a debt ratio of 33.3%. This debt ratio is assumed to be stable (there is no

attempt to change it). The following information is available:

2013(Reported) 2014(Projected)

$ $

Net income 300 500

Depreciation 100 125

CAPEX 200 350

WC (2012=10) 50 -

Sales 1500 2000

T.J MABVURE (Mr.)

Question: calculate the Free Cash Flow to `Equity (FCFE)

Working capital in 2014 is projected to be at the same percentage of sales as in 2013

WC (2013) = %33.3100*1500

50

WC (2014) =3.33%*2000=$66.7million

2013 2014(Projected)

Net income 300 500

- (CAPEX-Dep)(1-d) 66.7 150.075

- (ΔWC) (1-d) 26.68 11.1389

FCFE 206.62 338.7861

The FCFE will increase as the amount of debt used by the firm increases, that is the

FCFE is an increasing function of‘d’.

Suppose we increase the debt ratio to 40%, the FCFE will be high.

d=40%

2013 2014

Net income 300 500

- (Capex-Depn) (1-d) 60 135

- (ΔWC) (1-d) 24 10.012

FCFE 216 354.98

This is tying up with the financial leverage effect

This increase in FCFE however comes at the price of increased risk to the equity

holders (financial risk), that is as we increase debt there is a probability that our

earnings would not be able to pay our interest and principal obligations.

T.J MABVURE (Mr.)

This risk will result in a higher β coefficient for the firm. The higher the β, the

higher the ke, that is investors, will penalize the firm’s equity by increasing the

required rate of return.

ii) A levered firm with a debt ratio below the optimal level

A levered firm that is operating at a debt ratio below its desired level can afford

to use more debt in financing its capital expenditures and working capital needs

until it reaches the target debt ratio(optimal level) and the FCFE for such a firm

will be as follows.

Net Income xxx


Cash flow from operations xxx

CAPEX (xx)

ΔWC (xx)

Principal Repayments (xx)

Proceeds from new debt issues xxx

FCFE xxx

If the firm decides to increase its leverage towards its targeted levels then the

proceeds from new debt issues would be greater than the principal repayments

plus the CAPEX and WC needs.

Cannot use the short cut method because debt levels not optimal

Proceeds from new debt>Principal repayments+d (CAPEX+ ΔWC)

During the period when the firm is financing its investment needs

disproportionately with debt, the FCFE for such a firm would exceed that of a firm

which does not have such financing slack. A firm with financial slack will have

more FCFE than a firm with no financial slack.

The principal repayments are still financed with new debt issues therefore don’t

affect the FCFE.

Suppose the company has reported the following:

T.J MABVURE (Mr.)


$ $

Net Income 1000 1600

CAPEX 500 700


ΔWC 150 155

Debt (mkt value) 350 -

Principal repayments 170 170

Equity (mkt value) 900 -

d= 100*350900

350

=28%

The company wants to increase this debt ratio to 45% which it

considers optimal, to achieve this target the company plans to

finance70% of its CAPEX and WC needs with debt between 2013 and

2014.

Calculate The FCFE in 2014:

We can’t use the short cut method since the debt ratio is not optimal.

Net Income 1600

Depreciation 200

Cash flow from operations 1800

ΔWC (155)

Principal Repayments (170)

Proceeds from new debt issues 768.5

Capex (700)

FCFE 1543.5

Proceeds from new debt issues=170+0.70(700+155) =768.5

70% should be debt and 30% equity if the company wants 100% capital injection.

Equity will not remain at $900; it will increase by 30%.

T.J MABVURE (Mr.)

iii) A levered firm with leverage above the optimal.

The ‘d’ is the desired level of debt

A firm will have to use disproportionately more equity in financing its

investments needs in order to reduce its debt ratio and may also have to generate

funds from equity in order to meet some or all of its principal repayments.

The FCFE will be as follows

Net income xxx


Cash flows from operations xxx

CAPEX (xx)

Principal Repayments (xx)

WC needs (xx)

Proceeds from new debt xxx

FCFE xxx

There is some short-term debt which needs to be refinanced as

they mature, we can’t live without them.

If the company decides to reduce its leverage towards the optimal level then

proceeds from new debt issues will be less than principal repayments + WC and

CAPEX.

In the period that the company is raising disproportionately more equity to finance

its investments needs and principal repayments the FCFE would be lower than the

FCFE for an otherwise similar firm which is operating at its desired leverage.

In Zimbabwe companies above leverage were (2007 and before) financing through

retained earnings to reduce debt levels but in the process they were reducing

FCFE.

T.J MABVURE (Mr.)

Question-levered firm below the optimal


Net income 500 950

CAPEX 220 340

Principal Repayments 120 120

ΔWC 150 160


Mkt value of debt 550

Market value equity 1300

Proceeds From new debt 190

d= %73.29100*1300550

550

The company plans to increase the debt ratio to 35% by 2014. To

reach this target it plans to finance 45% of its capital expenditures

and WC requirementsbetween 2013 and 2014 with debt. Calculate

the current FCFE and the projected FCFE for 2014.

Proceeds from new debt issues=Principal repayments+d(CAPEX+ ΔWC)

=120+0.45(340+160)

=345

2013 2014

Net income 500 950


Cash flow from operations 655 1120

CAPEX (220) (340)

ΔWC (150) (160)

Principal repayments (120) (120)

Proceeds from new debt issues 190 345

FCFE 355 845

T.J MABVURE (Mr.)

Question-levered firm above the optimal

2012 2013

Net income 15000 19500

CAPEX 1850 3700


ΔWC 1500 1950

Mkt value of debt 41000 -

Mkt value of equity 46000 -

Principal repayments 6000 8500

New Debt issues 11000 -

d= %13.47100*4100046000

41000

The company plans to reduce its debt ratio from 47% to 25% by 2013,

to achieve this only the short term debt which is currently standing

at $11000 will be refinanced. All CAPEX and any increases in WC

needs would be financed primarily with equity that is 80% and 20%

debt. Long term debt outstanding would be repaid with cash flows

from equity.

Calculate the FCFE for 2012 and the projections for 2013.

Proceeds from new debt issues=New debt issues+d (Capex+∆WC)

=11000+0.20(3700+1950) =12130

For 2013 the 11 000 which the company had in 2012will be refinanced and raise 20% in

the proportion of CAPEX and WC.

T.J MABVURE (Mr.)

2012 2013

Net income 15000 19500


Cash flow from operations 17000 23450

CAPEX (1850) (3700)

ΔWC (1500) (1800)

Principal repayments (6000) (8500)

New debt issues 11000 12130

FCFE 18650 21580

Exercise

1. The following data pertains to a well-diversified company trading on the Zimbabwe

stock exchange.

2013 (Reported) 2014(Projected)

Net Income 1 600 2000

CAPEX 1 300 1 400

Principal

Repayments 1 200 1 200

ΔWC 1 250 1 300

Depreciation 1 250 1 380

Market Value

Of Debt 1 600

Market Value

Of Equity 2 400

Proceeds from

New debt 1 290

The company plans to increase the debt ratio to 50% by 2012. To reach this target it

plans to finance 45% of its capital expenditures and Working Capital between 2011

and 2012 with debt. Calculate the current and projected FCFE. [10]

T.J MABVURE (Mr.)

II. Free cash flows to the firm

Value of the firm=ngWACC

FCFF

1

This is the value of the firm for a company in a stable growth model.

The firm can be valued more realistically when we use the above

model than the dividend growth model as some firms don’t offer dividends.

A firm is composed of all its claim holders(claim to the cash flows

Including equity investors, debt holders, and preferred stock holders).

The cash flows are the total cash flows to all these claimholders. The

cash flows to the firm are those left over after meeting operating expenses and

taxes but before making any payments to any claimholders.

Free cash flows to the Firm (FCFF)=FCFE+Interest expenses(1-T)+Principal

repayments+New debt issues+Preferred Dividends

Another approach will give the same result is where we start with

Operating earnings.

EBIT(1-T)[Pre-interest after tax EBIT]

+Depreciation

-CAPEX

- ΔWC

=FCFF

Suppose we have the following information.

2010 2011

EBIT 6000 11500


CAPEX 4000 5000

Tax rate 45% 45%

Increase in WC 1400 2600

T.J MABVURE (Mr.)

What is the FCF to the firm?

2010 2011

EBIT(1-0.45) 3300 6325


CAPEX (4000) (5000)

Increase in WC (1400) (2600)

FCFF (1800) (825)

1-T is the tax shield

Principal repayments are added back because they are payments to

debt holders.

Since cash flows to the firm are before debt payments they are not affected by

the amount of debt that the firm is using but this does not mean that the value of

the firm is not affected by the amount of leverage because as the amount of debt

increases the WACC will also increase because the cost of capital (ke) will

increase.

WACC=Wdkd(1-T)+Weke, as Wd increase the β will increase and the ke(cost of

equity) will increase.

The difference between FCFE and Net Income

FCFE differs from net income for the following reasons:

Non-cash charges are added back to net income to arrive at the cash flows from

operations therefore the earnings reported by firms that take significant non-

cash charges against current might be lower than cash flows.

FCFE are residual cash flows after meeting CAPEX and WC needs, whereas these

are not included in the calculation of net income, therefore high growth firms that

have significant CAPEX and WC needs might report positive growing earnings but

negative FCFE. Investors are however more interested in FCFE.

T.J MABVURE (Mr.)

Estimating Growth

In the formula,P0=nn gKe

FCFE

1 ;we discussed about the FCFE, Ke. Now we

desire to discuss about the g.

g is the expected growth rate in earnings and dividends assuming that earnings and

dividends grow at the same rate.

There are two approaches to estimating the growth rate in earnings.

1) Estimating using an average of past growth rates and assuming that this growth

rate reflects the expected growth rate.

The most common ones are the arithmetic average and the

geometric Mean.

The arithmetic average is the mean of past growth and the

geometric average takes into account the compounding effect.

The geometric mean is a more accurate measure of the growth of

the earnings especially when the year to year growth in the past

has been erratic.

The geometric mean will always be lower than the arithmetic average.

Year EPS %Δ

$

2005 0.76

2006 0.95 25

2007 0.97 2.11

2008 1.30 34.02

2009 1.15 -11.54

2010 1.30 13.04

T.J MABVURE (Mr.)

Arithmetic mean= 526.125

04.13)54.11(02.3411.225

𝐺𝑒𝑜𝑚𝑒𝑡𝑖𝑐 𝑀𝑒𝑎𝑛: 1 + 𝑔 = √𝐸𝑃𝑆 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑(𝐹𝑖𝑛𝑎𝑙 𝑦𝑒𝑎𝑟)

𝐸𝑃𝑆 𝑎𝑡 𝑡ℎ𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔(𝑆𝑡𝑎𝑟𝑡 𝑦𝑒𝑎𝑟)

𝑛

𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑀𝑒𝑎𝑛: 1 + 𝑔 = √1.30

0.76

5

𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑀𝑒𝑎𝑛; 𝑔 = √1.30

0.76

5 -1=11.33

or geometric mean(g)= %33.11176.0

30.1 5

1

Estimating Issues

The first problem is that the EPS must grow at the same rate as the

DPS.

The growth rate is sensitive to the starting and ending period for the

estimation, fore.g. the growth rate in earnings over the past five

years will be different from the growth rate over the past 6 years but

the length of the estimation period is subject to the judgment of the

analyst for e.g. if 2004 had EPS of $0.70 then the arithmetic average

will be 11.87% and the geometric mean will be 10.87%.

2) Using the fundamentals reported in the current year: what are the determinants of

earnings growth?

The growth rate in earnings is determined by the decisions that the firm makes

with regards to product lines, profit margins, leverage, and dividend policy.

T.J MABVURE (Mr.)

The retention ratio and the Return on Equity (ROE)

The ROE=fEquityBookValueo

NetIncome

1

1

t

tt

NI

NINIgt

NIt =Net income for this year

NIt-1 =Net income for last year

gt =Growth rate in the net income

ROE=fEquityBookValueo

NetIncome

Therefore NI =ROE*Book value of equity

NIt-1 =ROEt-1*Book value of equityt-1

Assuming that the ROE is unchanged, that is to say

ROEt =ROEt-1,

1

1

1

11 Re

t

tt

t

ttttt

NI

tainedROE

NI

BVEROEBVEROEg

gt = t

t

t ROENI

RE*

1

1

gt =Retention ratio*Return on Equity

gt =b*ROEt

T.J MABVURE (Mr.)

g is the growth rate in Earnings per share

This relationship assumes that the ROE doesn’t change over time. If it

changes, that is ROEt≠ROEt-1 the growth rate in period t(now) will be given

by the following relationship.

gt=

t

t

ttt ROEbNI

ROEROEBVE*

1

11

the first term,

1

11

t

ttt

NI

ROEROEBVEmeasures the effect of changing the

ROE on the existing equity base. Increases in the ROE make it more

profitable to create a higher growth rate.

The following information was reported in 2010

BVE = $19000

NI = $5000

b = 70%

ROE = %32.26100*19000

5000

g = 70*0.2632

= 18.42%

Suppose that in 2011 we had projected that the ROE will increase to 35%

from the current 26.32%. The retention ratio will however remain at 70%.

T.J MABVURE (Mr.)

Therefore we now use the other method.

g =

%48.5735.0*7.05000

2632.035.019000

An increase in the ROE of 35% translates to an increase of:

%05.212100*42.18

42.1848.57

In the growth rate of earnings, i.e. the

higher the ROE, the higher the growth in the earnings.

The relationship between the growth rate and leverage

In this case leverage is being measured using the D/E (gearing).

The ROE and by implication the growth rate in earnings is affected by the leverage

decisions of the firm. Increasing leverage will lead to a higher return on equity if the pre-

interest after tax return on assets exceeds the after tax interest rates paid on debt. This

is captured in the following formulation of the ROE, i.e. expansion of ROE.

Pre-interest after tax earnings= EBIT (1-T)

The expanded version of the ROE:

ROE = ROA+ D/E(ROA-i)(1-T)

= ROA+ D/E(ROA-I)(1-T)

Where ROA=BVA

TEBIT )1(

D/E=BVE

BVD BVD=Book value of Debt

BVE=Book value of equity

T.J MABVURE (Mr.)

i=BVD

pensesInterestEx

T=Tax rate

BVA=BVD+BE

Interest expenses are those found in the income statement.

Using this expanded version of the ROE the growth rate in earnings:

g=b*[ROA+D/E (ROA-i)(1-T)]

The effect of the product line analysis with respect to growth rate

A firm with an ageing product line mix may look healthy in terms of historical growth

and current profitability, but it is not likely to sustain this growth into the future. The

analysis of growth for a firm can be made more complete by looking at its individual

products line and examining where they stand in terms of the PLC.

The growth rate across product lines can then be estimated using the following

relationship:

gjt=b*[Mjt*Tjt-D/E(Mjt-i(1-T)]

Where gjt =growth rate in year t for product line j

Mjt =Pre-interest after tax profit margin in year t for product

line j

=Sales

TEBIT )1(

Tjt =Asset turnover in year t for product line j

=sTotalAsset

Sales

D/E=gearing ratio of the firm as a whole

i =interest expenses

=BVD

pensesInterestEx

T =Tax rate

T.J MABVURE (Mr.)

Now to ke

Ke=Rf+β(Rm-Rf) CAPM

Rf=Risk free rate which can be the Treasury bill rate as a proxy for the risk free rate,

normally it’s the money market rate.

Rm =Average return on the market index, ie Holdings Period Return (HPR) on the

index.

Rm=HPR=1

12

M

MM

M2=Index at the end of the year

M1=Index at the beginning of the year

Beta coefficient(β)

The beta coefficient measures the risk of the asset in relation to the market. The

volatility of the return on the assets in relation to return on the security is measured by

this beta.

if an asset has a β=1.2,it means that if the return on the market increases by 10% then

the expected return on the security will increase by 10*1.2=12. if the market is bullish

you hold an offensive security. If the market sentiments are bearish you hold a defensive

security.

To estimate the β we regress the excess returns on the security (Ri-Rf) against the excess

returns on the market (Rm-Rf).

T.J MABVURE (Mr.)

Diagram

SCL Ri=α+βRm+ei

Ri-Rf

Rm-Rf

The beta coefficient for a private company

Get the average gearing ratios for similar companies that are listed as well the average

β.

Suppose our market consist of 3 listed banks and we have gathered the following

information about the banks.

Firm Beta D/E

Barclays 1.30 0.45

CBZ 1.00 0.30

NMB 1.50 0.50

Average 1.27 0.42

What is the beta for Stanbic whose debt ratio is 35% and is not listed?

T.J MABVURE (Mr.)

The beta of a levered firm βL:

βL =βU[1+(1-t)(D/E)]

βU=β for an unlevered firm

βU = EDT

L

/11

Then calculate the unlevered betas of the firm’s; we want to remove the leverage effect

from the company’s. Assuming that tax rate is 45%.

βU =

03.142.045.011

27.1

βL =1.03[1+(0.55)(0.35)]

=1.23

Therefore the β for Stanbic is 1.23

The formula has now taken into effect the 35% leverage of Stanbic.

T.J MABVURE (Mr.)

Valuation of companies-Discounted Cash Flow Valuation (DCF)

Valuation of Equity

i.Valuation using the stable growth model

ii.Two stage model

iii.Three stage model

We are canceling out the decline stage

High Growth Period Transition Growth Period Stable Growth Period

Growth

Rate

0 2 3 4 5 6 7 8 9 10 11 12 Time(Years)

In the stable phase the company is growing but the growth is stable

Opportunities for expansion are no longer there

The growth rate is now equivalent to that of the economy, that is, it is identical to

normal growth rate

T.J MABVURE (Mr.)

Stable growth Model

P0=nn gKe

FCFE

1

Where gn=stable growth rate which is expected to be maintained in perpetuity

This assumption is suitable for a firm that is large In size (because it has

gained relative market share in that industry) but is not likely to grow

much faster than the economy in the long term because

there are no more growth opportunities in that industry.

It generates large cash flows, which means that it will pay out much less dividends than

it’s generating in FCFE, because of this the financial leverage will be higher but stable.

Free cash flows large that’s why it’s called a cash cow.

Free cash flows also used to pay dividends as well as support other SBUs.

e.g. The following information was reported by ABC Limited

$

EPS 6.30

CAPEX per share 6.30

Depreciation per share 5.56

ΔWC 1.50

Debt ratio 30%

1. Earnings, Capex, Depreciation and other WC are all expected to grow at 7% p.a,

the β coefficient is 0.91. the TB is 8.5%, and the average return on the

market(Rm) is 14%

Question

Estimate the value per share.

T.J MABVURE (Mr.)

Once a company enters into a stage (introduction, Growth, Maturity) the debt ratio in

that category is considered optimal and can only change when it comes out of the

stage.

Can use EPS instead of Net income but have to reduce everything to per share.

Ke= Rf+β(Rm-Rf)

= 8.5+0.91(14-8.5)

= 13.51

β very low because the company is now in the growth stage

EPS-(CAPEX-Depreciation)(1-d)-( ΔWC)(1-d)

FCFE =6.30-(6.30-5.56)(1-0.30)-1.50(1-0.30)

=4.732

P0=gKe

FCFE

1

=gKe

gFCFE

)1(

=

07.01351.0

07.1732.4

=$77.78

T.J MABVURE (Mr.)

Two stage model

Earlier we assumed that the firm was in stage 1 and now the firm is in stage 2. We will

Have FCFE1, FCFE2, FCFE3, and then discount them to year 0 to get P0.

This is designed to value a firm that is expected to grow much than a stable firm in the

initial period and at a stable rate after that. The PV of the share is the value of the FCFE

per year (p.a) for the extra ordinary growth period (growth above the normal growth)

plus the present value of the terminal price at the end of the period.

P0 =PV of FCFE+PV of Terminal price

= n

nnt

tt

t

Ke

P

Ke

FCFE

111

n = end of the high growth period

Pn =Price at the end of high growth period

=nn

n

gKe

FCFE

1

Ken = Ke for the stable growth period

gn = g for the stable growth period

Ke = Ke for the high growth period

g = growth rate for the high growth period

ABC Ltd has a history of extra ordinary growth but its growth rate is now stabilizing

because it’s becoming a much larger company and its products are maturing and facing

competition.

The company pays very low dividends but has some FCFE. This FCFE is likely to increase

as the company gets larger and the growth rate stabilizes.

T.J MABVURE (Mr.)

The financial leverage is currently considered stable. The financial report for this year

has the following data.

EPS 35

Revenue per share 65

Capex per share 12

Depreciation per share 5

The following estimates have been made for the high growth period:

Length of period 4 years

Return on Equity 25%

Retention ratio 90%

The company pays very low dividends because its shareholders are more interested in

capital gains.

g=b*ROE=0.90*25=22.5%

The following market parameters will apply during this period:

TB rate 16.5%

Average return on the market 30%

β coefficient 1.9

Ke = Rf+β(Rm-Rf)

= 16.5+1.9(30-16.5)

= 42.15%

CAPEX, Depreciation and revenues are expected to grow at the same rate as

earnings

The WC is expected to be 15% of revenues. The debt ratio which is considered to

be optimum at this stage will be 10%.

T.J MABVURE (Mr.)

Inputs for the stable growth stage period:

The ROE will increase to 35%

The retention ratio will decrease to 60% as the company pays higher dividends

The β during the stable growth stage period will decrease to 1.0 because of

reduced operating risk.

The debt ratio will increase to 25% which will be considered optimal at this stage

Risk free rate will be 16.5%

Rm will be 30%

CAPEX will cancel out with depreciation

WC is 15% of Revenues

Question

Estimate the value per share. The assumption is that the debt ratio is at its optimal level

High growth phase

Year 0 1 2 3 4

EPS(g=22.5%) 35 42.875 52.522 64.339 78.816

Revenue(g=22.5%) 65 79.625 97.54 119.487 146.37

WC(15% of

Revenues)

9.75 11.944 14.63 17.923 21.956

ΔWC - 2.194 2.686 3.293 4.033

CAPEX(g=22.5%) 12 14.7 18.008 22.059 27.023

Dep(g=22.5%) 5 6.125 7.50 9.19 11.259

T.J MABVURE (Mr.)

Year 0 1 2 3 4

EPS 35 42.875 52.522 64.339 78.816

-(CAPEX-

Dep)(1-d)

6.3 7.7175 9.4572 11.582 14.1876

-( ΔWC)(1-d) 1.9746 2.4174 2.9637 3.6297

FCFE 33.1829 40.6474 49.7933 60.9987

We then discount the cash flows to find their present value:

PV = 4

1 1

4

1 Ke

P

Ke

FCFEn

tt

t

=

735.754215.1

9987.60

4215.1

7933.49

4215.1

6474.40

4215.1

1829.33432

Next step is to calculate P4. P4 is the value of all cash flows in year 4 from year 5 onwards.

In these calculations we use the new g.

g= b*ROE=0.6*35=21%

4 5

Revenue(g=21%) 146.37 177.047

WCvcfdsfedqw 21.9555 26.557

∆WC 4.6015

EPS(g=21%) 78.816 95.367

-∆WC(1-d) 3.4511

FCFE 91.916

T.J MABVURE (Mr.)

𝑇𝑉 =91.916

0.30 − 0.21= 1021.289

𝑃𝑉 =1021.289

(1.4215)4= 250.129

𝑃0 = 75.735 + 250.129 = $325.864

Three stage model

The company is still at the introduction stage and wants to move through other stage, which

is to grow and then mature.

High Growth Phase

Growth Rate

Transition Growth Phase

Stable Growth Phase

Time (Years)

T.J MABVURE (Mr.)

P0= 1

2

12

2

2

2

1

21

2

1

1111111 1

n

n

nn

n

nn

ntnn

n

n

n

tn

tt

t

KeKe

P

KeKe

FCFE

Ken

FCFE

CAPEX VS Depreciation

It’s reasonable to assume that as a firm goes from high growth to stable growth the

relationship between CAPEX and depreciation will change. In the high growth stage CAPEX

is likely to be much higher than depreciation.

In the high growth stage CAPEX is likely to be much higher than depreciation, because we

are buying new assets and depreciation, that is wearing and tear is minimal.

In the transition stage the difference is likely to narrow down and in the stable phase they

are likely to be equal.

Growth Rate

CAPEX

Depreciation

Time (Years)

T.J MABVURE (Mr.)

e.g.

A company is expecting a growing rate in earnings in excess of 30% per year due to the high

growth rate of its markets and its market share. The firm currently pays no dividends but has

a negative free cash flow to equity due to its large CAPEX and working capital requirements.

The firm is using very little debt in relation to equity and does not plan to change this in the

near future.

Current financial information is as follows:

$

Earnings per Share 4000

CAPEX per share 5000

Depreciation per share 2000

Revenues per share 15000

WC as a % of revenues 30%

Inputs (Projections) for the high growth period

The high growth period will last for four years and during this period the ROE is expected

to be 60%.

The retention ratio will be 100%, therefore g will be 60 %(g=b*ROE=0.60*100).

CAPEX, depreciation and revenues will grow at the same rate as earnings which is 60%,ie

CAPEX, Depreciation will increase at 60%.

WC will be maintained at 30% of revenues.

The debt ratio(D/E) will be 5% and the following market parameters will apply:

β coefficient 1.9

Rf 15%

Rm 22%

Ke=28.3%

T.J MABVURE (Mr.)

Inputs for the transition period

Length of period 4years

The growth rate in earnings will decline from 60% in yr 4 to 15% in yr 8

linearly.

Capex will grow at 40% p.a and depreciation will continue to grow at the original growth

rate.

Working capital will now be 20% of revenues which will now be growing at

40%.

The debt ratio will increase to 10%.

The other market parameters will remain the same but the β will decline to 1.0 in year 8

linearly.

Inputs for the stable period

Earnings will grow at 10% in perpetuity

Capex will be exactly offset by depreciation (we are now replacing what we bought and

not buying.

Revenue will grow at10%

WC will remain at 20% of revenues

The debt ratio will increase to 20%

The β will decrease to 0.9

The other parameters will remain the same.

Question

Calculate the value per share and comment on how the value may be used by an analyst

T.J MABVURE (Mr.)

Exercise

1. A company has the following information:

Current Information

$

Earnings per share 5 000

Capital expenditure per share 6 000

Depreciation per share 2 500

Revenue per share 16 000

Working Capital as a percentage of Revenues 20%

Inputs projections for the high growth period

1. The high growth period will last for four years and during this period the Return and

Equity is expected to be 65%.

2. The retention ratio will be 95%.

3. Capex, Depreciation and Revenues will grow at the same ratio as earnings.

4. Working capital will be maintained at 20% of revenues.

5. The debt ratio will be 5.5% and the following market parameters will apply.

Β 1.9

Rf 16%

Rm 20%

Inputs for the transition period

1. Length of period will be four (4) years

2. The growth rate will decline to 20% in year eight (8) linearly.

3. Capex will grow at 45% and Depreciation will continue to grow of the original growth

rate.

4. Revenues will now be growing at 40% and WC will be 20% of revenue.

5. The debt ratio will increase to 10%

6. The other market parameters will remain the same but the beta coefficient will

decline to 1.0 in year eight linearly.

T.J MABVURE (Mr.)

Inputs for the Stable period

1. Earnings will grow at 15% in perpertuity.

2. Capital expenditures will be exactly offset by depreciation.

3. Revenues will grow at 15%.

4. Working capital will remain at 20% of revenues

5. The debt ratio will increase to 20%.

6. The beta will decrease to 0.8.

7. The other parameters will remain the same.

Required

Calculate the value per share and commend. [30]

VALUE OF A FIRM

Free cash flow to the firm (FCFF) is the sum of the cash flows to all the claimholders in the

firm including debt holders, preference shareholders and equity holders. To value the firm

we discount the FCFF at the required rate which is the weighted average cost of capital

(WACC).

FCFF=EBIT (1-T)-(Capex-Depreciation) - ΔWC. The debt ratio does not apply in the

determination of the FCFF. For a firm in the stable growth period the value of the firm is

determined as follows.

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐹𝑖𝑟𝑚 = ∑𝐹𝐶𝐹𝐹𝑡

(1 + 𝑊𝐴𝐶𝐶)𝑡

𝑛

𝑡=1

+

𝐹𝐶𝐹𝐹𝑛+1

𝑊𝐴𝐶𝐶𝑛−𝑔𝑛

(1 + 𝑊𝐴𝐶𝐶)𝑛

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐹𝑖𝑟𝑚 = ∑𝐹𝐶𝐹𝐹𝑡

(1 + 𝑊𝐴𝐶𝐶)𝑡+

𝑛

𝑡=1

𝑃𝑛

(1 + 𝑊𝐴𝐶𝐶)𝑛

gn=Expected growth rate in perpetuity

This model requires that the growth rate of the firm should be reasonable, relative to

the normal growth rate of the economy.

T.J MABVURE (Mr.)

The relationship between Capex and depreciation must also be consistent with the

assumptions of stable growth, ie a stable firm generally should not have Capex that are

significantly greater than depreciation, since there are no growth opportunities there

would be no need for additional capital investment.

e.g. Two stage model

The valuation of a firm which is highly leveraged.

The base year information

$

EBIT 5000

Cape x 1000

Depreciation 700

Revenues 15000

WC as a % of Revenues was 25%

Tax rate 35%

TB rate 15%

Rm 22%

The firm is approaching a high growth phase which will last for 4 years

after which earnings will stabilize.

Expected growth rate for operating earnings (EBIT) during the high growth

phase will be 25% p.a

β will be 1.7

The other market parameters will remain the same.

The WC as a % of revenue 25%

The pre-tax cost of debt 25%

The debt ratio(D/E) 45%

This high level of leverage is the result of a leveraged buyout

in the last 2 years.

It’s anticipated that this high debt ratio will be reduced gradually over the next 4 years

to acceptable levels.

Capex, revenues and depreciation will grow at 25%

T.J MABVURE (Mr.)

Inputs for the stable growth phase

Expected growth rate in earnings 10%

Β throughout the period 0.96

Pre-tax cost of debt 9%

Debt ratio(D/E) 30%

CAPEX will be offset by depreciation

WC as a % of revenue 25%

Revenues will grow at 10%

Q. Calculate the Value of the Firm

WACC=Wdkd (1-T)+Weke

High growth stage

Year 0 1 2 3 4

Capex(g=25%) 1000 1250 1562.5 1953.125 2441.406

Depreciation(25%) 700 875 1093.75 1367.188 1708.98

Revenues(g=25%) 15000 18750 23437.5 29296.875 36621.094

WC(25% of

Revenues)

3750 4687.5 5859.375 7324.219 9155.274

ΔWC 937.5 1171.875 1464.844 1831.055

EBIT(g=25%) 5000 6250 7812.5 9765.625 12207.031

-T(EBIT) 1750 2187.5 2734.375 3417.969 4272.461

-(CAPEX-

depn)

300 375 468.75 585.937 732.426

-( ΔWC) 937.5 1171.875 1464.844 1831.055

FCFF 2750 3437.5 4296.875 5371.089

T.J MABVURE (Mr.)

Ke=Rf+β(Rm-R)

=15+1.7(22-15)

=26.9%

WACC =WeKe+WdKd(1-T)

=0.55(26.9)+0.45*25(1-0.35)

=22.1075

=22.11%

145.9333

2211.1

089.5371

2211.1

875.4299

2211.1

5.3437

2211.1

2750

)1 432

t

t

WACC

FCFFPV

Stable phase

Revenue Yr 5 36621.094(1.10) =40283.20

FCFF EBIT (1-T)- ΔWC

WC5 40283.20*0.25 =10070.80

WC4 =9155.274

ΔWC 915.53

EBIT(1-T) =12207.031(1.10)(1-0.35) =8728.027

FCFF =8728.027-915.53 =7812.497

Ke=15+0.96(22-15) =21.72

Kd=9(1-0.35) =5.85

WACC=0.70(21.72) +0.30*5.85 =16.96%

5201.11224810.01696.0

497.78124

V

T.J MABVURE (Mr.)

PV of V4=

55055.504862211.1

5201.1122484

Total Value=9333.95+50486.55055=59 820.50055

Or

Year 4 5

Revenue(g=10%) 36621.094 40283.20

WC(25% of Revenue) 9155.274 10070.80

ΔWC 1831.055 915.53

EBIT(g=10%) 12207.031 13427.73

-T(EBIT) 4699.706935

-ΔWC 915.53

FCFF 7812.49

679.11226410.01696.0

493.78124

V

PV of V4=

819.504932211.1

679.1122644

Total Value=9333.95+50493.819=59 827.769

Three stage Firm valuation model

The following information was reported for Yoruba Investments

$m

EBIT 10000

Capex 6700

Depreciation 6500

Revenues 20000

WC 25% of Revenues

Tax rate 40% for all periods

TB rate 15%

Return on the market 22%

T.J MABVURE (Mr.)

High Growth Period


Growth rate in revenues and EBIT 40%

β=1.8, Rm=22%, Rf=15%

Debt ratio 10%

After tax cost of debt 10%

Capex and Depreciation will grow at 30%

WC 10% of Revenues

Transition Period

Length of Period 6 years

Growth rate of EBIT and Revenue will decline linearly from 40% in year 6 to 25% in year 12

Capex will grow at 20%

Depreciation will grow at 30%

β will drop from 1.8 in Y6 to 1.10 in Yr 12 linearly

WC=10% of revenues

Debt ratio 20%


Stable Period

Growth rate in EBIT and Revenues 5%


Capex and Depreciation will cancel each other

Β=0.90, Debt ratio=30%

WC=10% of Revenues

Q. Calculate the value of the firm and comment on your findings

T.J MABVURE (Mr.)

Exercise

1. The following information was reported for Yoruba investments

Base your information

EBIT 10 000

Capex 6 700

Depreciation 6 500

Revenues 20 000

WC as a % of revenues 25%

Tax rate 40%

TB rate 15%

Return on the market 22%

The firm will go through a high growth period lasting 6 years. This will be followed by another 6

year transition period of lower growth rates after which the growth rate will stabilize.

The following estimates have been made in respect of each growth phase

High growth period

Growth rate in revenues and EBIT 40%

P = 1.80, Rm = 22%, Rf = 15%

Debt ratio 10%

Capex and depreciation will grow at 30%


WC will be 10% of revenues

T.J MABVURE (Mr.)

Transitional period

Growth rate of EBIT and revenues will decline linearly from 40% in year 6 to 8% in year twelve

(12).

Capex will grow at 20%


β will drop from 1.80 in year 6 to 1.1 in year 12 linearly.

WC = 10% of revenues

Debt ratio = 20%


Stable period

Growth rate in EBIT and revenues 5%


Capex and depreciation will grow @ 5%

β =0.90

debt ratio 30%

WC = 10% of revenues

Required

Calculate the value of the firm [30]

2. What are the challenges faced by a firm that desires to value its share and the firm

itself using the discounted cash flow approach? [6]

3. The following Information was Reported for CBZ Plc

$m

EBIT 700

CAPEX 500

Depreciation 400

Working capital 10% of Revenues

Revenues 1 000

Tax rate 35%

T.J MABVURE (Mr.)

High Growth Rate

Length of Period 4 years

Growth rate in Revenues & EBIT 40%

Growth rate in CAPEX & depreciation 40%

Β = 1.80 Rm = 20 Rf 15%

Debt ratio 10%


Working capital is 10% of Revenues

Transition Period


Growth rate in EBIT & Revenues will decline from 40% to 10% in year 8 linearly

CAPEX will grow at 10%


Β will drop from 1.80 to 0.8 in year 8 linearly

Working capital is 10% of Revenues

Debt ratio is 15%


Stable Period

Growth rate in EBIT and revenue will be 5% in perpertuity


CAPEX and Depreciation will cancel each other

Β = 0.7, debt ratio 25%

Working capital is 10% of Revenues.

Required

Calculate the value of the firm and comment. [36]

T.J MABVURE (Mr.)

RELATIVE VALUATION

Another method for valuation is the relative valuation method. In this valuation model we

use the following:

i) P/E multiple= EPS

P0 0P Price per share

ii) PBV =BVE

P0

iii) Price to Sales=Sales

P0

Estimate the P/E ratio of the fundamentals

The P/E ratio can be related to the same fundamentals that determine the value using

discounted CF models. The fundamentals are:

a. The expected growth rate in earnings and dividends per share.

b. Dividends payout ratios

c. Risk as reflected in the cost of equity

The P/E ratio for a stable firm

A stable firm is a firm that is growing at a rate that is comparable to the normal growth

rate in the economy in which it’s operating.

For a stable firm the value of equity is given by the following:

nn gKe

DP

1

0 If we use the dividend growth model

T.J MABVURE (Mr.)

Since DPS1=EPS0 (Payout ratio) (1+g) =Dividends next year, i.e. dividends at the end of

this year.

This means that the value of equity (P0)

nn gKe

goPayoutRatiEPSP

100

We know that 0

0

EPS

PEP

Therefore

nn gKe

goPayoutRati

EPS

PEP

1

0

0

If the EP ratio is stated in terms of expected earnings in the next period, ie we are

saying:

1

0

0

0

1 EPS

P

gEPS

P

EPS1=EPS next year

EPS0=EPS this year

nn gKe

oPayoutRati

EPS

P

1

0

This means that the P/E ratios is an increasing function of the payout ratio and the

growth rate in earnings and a decreasing function of the riskiness of the firm as reflected

in the β coefficient of the firm in Ke(Required rate of return).

Therefore in calculating P/E we are calculating.

nn gKe

goPayoutRati

EPS

PEP

1

0

0 OR

nn gKe

oPayoutRati

EPS

P

1

0

T.J MABVURE (Mr.)

This is the P/E ratio taking into account the fundamental characteristics of the firm. These

fundamentals are:

a) The expected growth rate in earnings and dividends

b) Risk ness of the firm’s cash flows as reflected by the beta of the company in the

cost of equity(Ke)

c) Dividend payout ratio.

e.g. A firm had EPS of $600 in 2009 and paid out a dividend of $230. The growth rate in

earnings and dividends in the long term (stable state) is expected to be 15%. The market

parameters are as follows: Rf=20%, Rm=25%, β=1.2

Calculate the P/E today based on these fundamentals.

Ke=26%

Payout ratio= 3833.0600

230

Times

gKe

goPayoutRati

EPS

PEP

nn

007.415.026.0

15.13833.01/

0

0

If the Market P/E at the time of the analysis was say 10.5. The low P/E of 4.007 is an

indication that the firm was maybe not paying out what it could afford as dividends.

If the firm is paying out significantly less dividends than it can afford we can use FCFE

instead of DPS to calculate P/E.

E.g. A firm had EPS of $600 in 2009 and paid out a dividend of $230. The growth rate in

earnings and dividends in the long term (stable state) is expected to be 15%. The market

parameters are as follows: Rf=20%, Rm=25%, β=1.2. The FCFE per share was $500

The P/E ratio based on these fundamentals will be:

Ke=26%

T.J MABVURE (Mr.)

8333.0600

500

EPS

FCFEPayout

EPS

FCFE is the free cash flow payout ratio, as an equivalent of the dividend payout ratio.

711.811.0

9583.0

15.026.0

)15.1(8333.0

EP

The firm didn’t payout dividends, i.e. we are saying what will be the P/E if we use FCFlows

rather than the dividends that are giving a 4.007 value.

If the company was selling at a P/E of $10.5, then dividends alone can’t be blamed for the

low valuation.

The low value of the firm is not solely to do with dividends. The firm is overvalued by the

market yet the fundamentals are lowly valuing the firm.

E.g.A Company has EPS of $100 and paid out a dividend of $18.50/share. The growth rate in

earnings and dividends is expected to be 15%. The β=0.9, TB=15%, Rm=22%. Calculate the

P/E ratio based on these fundamentals.

Ke=21.3%

Dividend payout ratio= 185.0100

5.18

g=15%

TimesEP 38.315.0213.0

)15.1(185.0

T.J MABVURE (Mr.)

e.g.

A Company is currently selling at a P/E ratio of 6.00. The company had EPS of $120 and paid

out dividends of $30/share. Expected growth rate in earnings is 15%. RF=15%, Rm=22%,

β=0.9. Comment on the value of the company. Free cash flow to Equity per share=$45

Ke=21.3%

Dividend payout= 25.0120

30

g=15%

TimesEP 56.4

15.0213.0

15.125.0

FCF payout= 375.0120

45

g=15%

TimesEP 845.6

15.0213.0

15.1375.0

The Firm is undervalued by the market according to the FCFE.

Dividends are to blame for the low value of the firm.

The firm is conservative when it comes to dividends payout

The market is paying more than what the company is worth given the fundamentals of the

company according to the dividends of the company.

The company is paying out less dividends than what the market is expecting.

T.J MABVURE (Mr.)

Comment

The market is overvaluing the company because the company is paying less dividends than

what the market is expecting and the market is anticipating higher cash flows than what is

being generated and at the same time the market is understating the riskiness of the cash

flows or the riskiness of the firm.

Comparing the P/E ratio with other P/E’s

P/E’s across countries(markets)

P/E’s across time

P/E’s across firms

SEE ASWATH DAMODARAN

P/E Ratio for a High Growth Firm

Valuation for high growth; two stage model

alValuePVofTer

Ke

FCFEP

n

t

min11

0

alValueTergnKen

FCFEPn n min1

The P/E ratio for a high growth firm can also be related to the fundamentals in the case of

the two stage model.

T.J MABVURE (Mr.)

nnn

n

n

n

n

n

KegKe

ggoPayoutRati

gKe

Ke

ggoPayoutRati

EPS

PEP

1

111

111

0

0

EPS0 =EPS in the current year

g =Growth rate in the current phase

Ke =Cost of equity in the current year (phase)

gn =Growth rate after the first phase(growth rate in the stable period)

Payout ratio =Payout in the current phase (first)

Payout ration =Payout in the second phase

Ken =Cost of equity in the second phase

n =Length of the current phase

The P/E ratio is determined by:

1) The payout ratio during the high growth phase and the stable period, the P/E ratio

increases as the payout ratio increases.

2) The riskiness of the firm through the discount rate Ke. The higher the risk the lower the

P/E.

3) The expected growth rate in earnings in both the high growth and stable periods. The

higher the growth rate, the higher the P/E. If the firm is not paying dividends we use the

ratio of the free cash flow to equity to EPS instead of the dividend payout ratio.

T.J MABVURE (Mr.)

e.g.

A firm is expecting a six year period of high growth after which the growth rate will

normalize in line with the growth rate of the economy.

The following data pertains to the high growth period:

Expected ROE 25%

Expected payout ratio 30%

Therefore growth rate in the high growth period will be:

g=b*ROE=(1-0.30)*25 =17.5%

β 1.6

Rm 20%

Rf 15%

Ke=Rf+β(Rm-Rf)

=15+1.6(20-15)

=23

Stable growth period

Expected growth rate 10%

Expected ROE 25%

β 0.9

Rf 15%

Rm 20%

Ken=Rf+β(Rm-Rf)

=15+0.9(20-15)

=19.5

Calculate the P/E ratio and commend

T.J MABVURE (Mr.)

g=b*ROE

b=1-payout

g=ROE(1-Payout)

g=ROE-ROE*Payout

ROE*Payout=ROE-g

Payoutn=𝑅𝑂𝐸−𝑔

𝑅𝑂𝐸

Therefore Payoutn= 60.025.0

10.011

ROE

g

OR

g=b*ROE

𝑏 =𝑔

𝑅𝑂𝐸=

0.10

0.25= 0.4

1-b= Payout Ratio

1-0.4=0.6

Therefore Payoutn=0.6

82.6818165747.6279792579.5538373168.1

23.110.0195.0

10.1175.16.0

175.023.0

23.1

175.11175.130.0

1

111

111

6

66

6

n

n

n

n

n

n

KegnKen

ggPayout

gKe

Ke

ggPayout

EP

Question.

T.J MABVURE (Mr.)

A firm is expected to have five years of high growth after which it will be in a steady state.

Inputs for the high growth period

Expected ROE 22%


β 1.8

Rm 22%

Rf 15%

Stable period


β 0.75

Rf 15%

Rm 22%

Expected ROE 15%

Calculate the fundamental P/E and commend

Exercise

T.J MABVURE (Mr.)

1. A company is expecting an eight year period of high growth after which the growth rate

will normalize in line with the growth rate of the economy.

Data for the high growth period

Expected Return an Equity 30%


Rm 22%

Rf 17%

Β 1.8

Stable growth period


Expected Return on Equity 30%

Β 1.0

Rf 17%

Rm 22%

Required

Calculated the P/E ratio and commend. [15]

PRICE TO BOOK VALUE(PBV)

The book value of equity is the difference between the book value of assets and the

book value of liabilities.

The measurement of the BVA is largely determined by accounting conventions.

Book value VS market value

The Market value of an asset reflects its earning power and expected cash flows since

the book value of an asset reflects its original cost. It might deviate significantly from

the market value if the earning power of the asset has increased or decreased

significantly since its acquisition.

Reasons for using book values ratios

T.J MABVURE (Mr.)

The following are the reasons why investors use price to book value ratios.

1. Book value provides a relatively stable intuitive (easily understood) measure of

value.

2. Price to book value ratios can be compared across similar firms for signs of under or

overvaluation, even firms with negative earnings which can’t be valued using the PE

ratios.

Disadvantages of using PBV ratios

Book values like earnings are affected by accountants’ decisions on depreciation and

other variables (accountants can manipulate the book values by either increasing or

decreasing depreciation).

When accounting standards vary widely across firms(some companies may not be

consolidating the earnings of their subsidiaries; stock valuation methods such as

FIFO,LIFO,AVCO, straight line, and reduced balance method may be in use in

different companies).

Book values may not carry much meaning for service firms that don’t have

significant fixed assets (e.g. insurance companies; most of the assets are in

investments a.w.a real estate).

PBV for a stable firm

nn gKe

DPSP

1

0

Substituting EPS0 (Payout) (1+g) for DPS1

gnKen

gPayoutEPSP

100

BVE

EPSROE 0

BVEROEEPS *0

T.J MABVURE (Mr.)

This means that

nn gKe

gPayoutBVEROEP

1**0

BVE

PPBV 0

Dividing both sides by BVE

nn gKe

gPayoutROE

BVE

P

1*0

If we express the book value of equity in terms of expected BVE for next year.

nn gKe

PayoutROE

gBVE

P

*

1

0

nn gKe

PayoutROE

BVE

P

*

1

0

This indicates that the PBV ratio is an increasing function of the ROE, the payout ratio and

the growth rate of earnings. It is a decreasing function of the risk ness of the firm as

indicated by β in Ke.

nn gKe

PayoutROEPBV

BVE

P

*1

1

0

g=b*ROE

=ROE (1-Payout)

Relating g to the ROE.

g = ROE*b

=ROE (1-Payout)

T.J MABVURE (Mr.)

=ROE-ROE (Payout)

g+ROE*Pay=ROE

ROE*Payout=ROE-g

ROE*Pay is identical to ROE-g

nn

n

gKe

gROE

BVE

P

0

This relationship is telling us that the PBV of a stable firm is determined by the

differential between the ROE and the required Rate of return on its profits.

If the ROE exceeds the RRR (Ke) the price will exceed the BVE (because g is constant).

This formulation can therefore be used to estimate the PBV ratios for firms that don’t

pay dividend.

A firm had EPS of $900 in 2009 and paid 50% of its earnings as dividends that year, the

growing rate of earnings and dividends in the long term is expected to be 15%. The ROE for

the firm is 25%. The following parameters apply:

β =0.9, Rm=20%, Rf=15%

Therefore Ke=19.5%

Qn. what is the PBV a) Today b) next year and (c) when the company is not paying

dividends

gKe

gROE

BVE

PPBV

1

01

PBVToday

gKe

gPayoutROEPBV

BVE

P

1*0

0

0

gKe

PayoutROEPBV

BVE

P

*1

1

0 PBV based on expected earnings next year

T.J MABVURE (Mr.)

gKe

gROE

BVE

P

1

0 PBV based on return differential (used when we are dealing with a firm that

does no payout dividends).

Therefore PBV today

Times

gKe

gPayoutROE

BVE

P19.3

15.0195.0

15.15.025.0)1(*

0

0

Times

gKe

PayoutROEPBV 78.2

15.0195.0

5.025.0*1

TimesgKe

gROE

BVE

P22.2

15.0195.0

15.025.0

1

0

The purpose of these values is to compare the fundamental based PBV and the market

PBV.

Let’s suppose the market PBV is 2.00 then the price per share is twice the Book Value

of the share.

The market is saying the market price of the share is twice the book value.

NB. What is the relationship between the PBV and the ROE?

If the ROE decreases the PBV will also decrease because g will also decrease, therefore

a firm with a high ROE will sell above its book value. A firm with a mismatch between

the PBV and the ROE will attract the attention of investors.

A mismatch is a low priced book value associated with a high ROE or a high PBV

associated with a low ROE.

High Price to book value is always associated with high ROE.

T.J MABVURE (Mr.)

The ratio between PBV and ROE indicates whether a firm is overvalued or undervalued.

A ratio of less than one indicates an undervalued firm.

Low ROE High

High

Overvalued

Correctly valued

Correctly valued

undervalued

Low

PBV

Let’s suppose we have the following information about several companies

Exercise

1. A firm had EPS of $1 800 in 2009 and paid 60% of its earnings as dividends that year. The growth

rate of earnings and dividends in the long term is expected to be 15%. The ROE for the firm is 25%.

The following parameters apply

β =1.1, Rm =25% Rf = 10%

a) What is the PBV today [7]

b) What is the PBV next year [7]

c) What is the PBV assuming the company was not paying out dividends [6]

2. The relationship between ROE and PBV shows whether a firm is undervalued, overvalued,

correctly valued. Explain this statement with the assistance of a diagram. [5]

T.J MABVURE (Mr.)

Price/Sales per Share(PS)

This is again related to the dividend model

Unlike the price to earnings or the PBV which can become negative and therefore

meaningless. The price to sales multiple is always positive even for firms in trouble (can be

applied in all situations). Earnings and book values are heavily influenced by accounting

decisions such as decisions on:

a) Depreciation and inventory valuation, revenues are however not easy to

Manipulate.

The price to sales ratio can also be related to fundamentals such as:

a) Growth rates in earnings and dividends

b) Payout ratios

c) Risk through Ke

Value of equity for a stable firm

nn gKe

DP

1

0

But D1=EPS0 (Payout)(1+g)

Therefore nn gKe

gPayoutEPSP

)1)((00

In this case we are interested in the profit margin (PM)

Sales

NetIncomePM

areSalesPerSh

EPSPM 0

T.J MABVURE (Mr.)

Therefore EPS0=PM (Sales per share)

Substituting:

nn gKe

gPayoutareSalesPerShPMP

10

But Price to Sales (PS) =Sales

P0

Therefore

nn gKe

gPayoutPM

Sales

P

10

This is the fundamental relationship we want

If the profit margin is based on expected earnings next year we can re-write this as

follows:

nn gKe

PayoutPM

gSales

P

1

0

nn gKe

PayoutPM

Sales

P

1

0

The price to sales ratio is an increasing function of the profit margin, the payout ratio and

the growth rate in earnings and dividends. It is a decreasing function of the riskiness of the

firm as reflected in the Ke(Required rate of return).

After calculation you have to relate your answer to these fundamentals as said above.

T.J MABVURE (Mr.)

e.g.

A Company had revenues/share of $200 in 2010 and EPS of $10. It paid out 65% of its

earnings as dividends. The growth rate in earnings and dividends in the long-term is

expected to be 10%, β=0.9, Rf=15%, Rm=20%. Calculate the current price to sales ratio based

on these fundamentals and also the Price to sales ratio based on expected earnings next

year.

Ke=19.5% PM= 05.0200

10

Re

arevenuePerSh

EPS

3763.0

10.0195.0

10.165.005.010

gKe

gPayoutPM

Sales

P

3421.010.0195.0

65.005.0

1

0

gKe

PayoutPM

gSales

P

These must be compared to the market price to sales multiples.

Suppose the company was trading on a price to sales of 0.5 then we would conclude that

it’s overvalued according to the fundamentals.

Relationship between the price to sales (PS) and the PM

The key determinant of the PS ratio is the PM.

Firms involved in businesses that have high margins can expect to sale for much higher PS

multiples (they will be trading on higher PS than the market). A decline in PM has two

effects.

1. reduction in PS Multiple

2. reduction in the growth rate of earnings

We can use the ratio between the sales per share to book value of equity to link the profit

margin to the expected growth rate.

g=b*ROE

T.J MABVURE (Mr.)

Since ROE=BVE

Sales

Sales

NI*

ROE= overEquityTurninofitMOperating *argPr

This is the pyramid that builds up the ROE. A DuPont type of ROE.

Therefore BVE

Sales

Sales

NIbg **

BVE

SalesPMbg **

g=retention ratio*profit margin*equity turnover

The higher the PM the higher the expected growth rate provided that sales will not

decrease proportionately to the increase in profit margin.

This whole discussion related to a firm which is in a stable growth period.

PS for a high growth model (Two stage model)

In the two stage model:

P0=PV of expected dividends in the high growth period+PV of the terminal Price

= n

n

tt

Ke

Pn

Ke

Dt

111

Where nn

n

gKe

DPn

1 this is the same concept with the free cash flows

The H-model is a short cut for the above

D0=EPS0 (Payout)

When the growth at the end of a high growth period is assumed to be constant forever,

then the value of the firm(P0):

nnn

n

n

n

n

n

KegKe

ggPayoutEPS

gKe

Ke

ggPayoutEPS

P

1

11*1

111*

0

0

0

But EPS0=Sales*PM

Therefore Sales

EPSPM 0

T.J MABVURE (Mr.)

PS=

n

n

n

n

n

n

KegnKen

ggPayout

gKe

Ke

ggPayout

PMSales

P

1

111

111

0

This is telling us that the PS multiple is determined by the following factors

a) The net profit margin, ie the PS multiple is an increasing function of the Net profit

margin.

b) The payout ratio i.e. to say the higher the payout ratio, the higher the PS multiple.

c) Risk as reflected in Ke, ie to say the higher the risk the lower the PS multiple.

d) The growth rate in earnings, the higher the expected growth rate the higher the PS

multiple.

Question

A firm is expected to go through two growth periods, that is the high growth period and a

stable period.


Expected length of period 7 years


The Average profit margin 15%

Payout ratio 6%

β 1.4

Rm 30%

Rf 25%

Stable period

During the stable period the profit margins will be maintained at 15%

Expected growth rate in earnings 7%

Payout ratio 65%

β 1.2

Rm 30%

Rf 25%

Qn. estimate the PS multiple

T.J MABVURE (Mr.)

Growth stage

n =7

g =30%

PM =15%

Payout =6%

Ke = 32%

gn =7%

Payoutn =65%

Ken =31%

n

nn

n

n

n

n

n

KegKe

ggPayout

gKe

Ke

ggPayout

PMPS1

111

111

45.0449923112.0

604185044.2395302371.015.032.107.031.0

07.130.165.0

30.032.0

32.1

30.1130.106.0

15.07

77

7

T.J MABVURE (Mr.)

Growth rate

We can use the following relationship to compare different competitive strategies which

are: High margin, low volume (product differentiation), low margin high volume (cost

leadership).

g=b*PM*BVE

Sales

A firm is considering these two strategies:

High Margin- low Volume Low Margin-High Volume

PM 30% 10%

Sales/BVE 4 8

The firm is expected to payout 20% of its earnings as dividends.

The growth rate in earnings after two years is expected to be 7% p.a in perpetuity.

The book value of equity per share is currently $15,β=1.6, Rm=25%,Rf=20%. Ke=28%.

The payout in the stable period is 60%

In the stable period the β will decrease to 1.0, and other parameters will remain the same.

Ken=25%.

To compare these strategies we have to look at PS multiple in each case.

T.J MABVURE (Mr.)

High Margin- Low Volume Strategy

g=b*PM*BVE

Sales

g=0.8*0.3*4=96%

Ke =20+1.6(25-20)

=28%

Ken =20+1.0(25-20)

=25

n

nn

n

n

n

n

n

KegKe

ggPayout

gKe

Ke

ggPayout

PMPS1

111

111

741416015.2

362858073.8775195312.0.30.0

28.107.025.0

07.1*96.1*6.0

96.028.0

28.1

96.11*96.1*20.0

3.02

22

2

PS

P0=PS* BVEBVE

Sales*

𝑃0 = 2.741392015 ∗ 4 ∗ 15

=$164

T.J MABVURE (Mr.)

Low Margin-High Volume strategy

g=0.8*0.10*8=0.64

643961588.0855045573.5584570312.01.0

28.107.025.0

07.1*64.1*6.0

64.028.0

28.1

64.11*64.1*20.0

1.02

22

2

PS

Price(P0) =$15*0.64396158*8,𝑃0 = 𝐵𝑉𝐸 ∗ 𝑃𝑆 ∗𝑆𝑎𝑙𝑒𝑠

𝐵𝑉𝐸

=$77.27539056

The high margin results in a price per share of $164 and low price margin results in the price

of $77.28, so the high margin strategy is a better strategy.

Typical Examination

A company has sales per share of $650 with earnings of $125 per share. The book value of

equity was $420 per share. The company paid 20% of its earnings as dividends. Based on these

results calculate the profit margin, the sales to book value, the retention ratio and the growth

rate in earnings. It’s envisaged that the current period is a high growth period which will last

for 2 years. During this period β=1.2, Rf=25%, Rm=30%.

After the high growth period the growth rate will stabilize to 10% p.a and the dividend

payout ratio will be increased to 60%. The β will drop to 1.0 and the other parameters will

remain in the same.

Calculate the price to sales multiple.

192.0650

1250 ShareSales

EPSPM

Payout=20%

55.1420

650

BVE

Sales

T.J MABVURE (Mr.)

g=b*ROE

b=1-Payout

g=b*PM* %8.23420

650*192.0*8.0

BVE

Sales

Ke=31%

Ken=30%

n=2

g=23.80

gn=10%

Ke=31%

Ken=30

Payout=20%

Payoutn=60%

636540742.0

)947220558.236727061.0(192.031.11.030.0

10.12380.160.0

2380.031.0

31.1

2380.112380.1*20.0

192.02

22

2

PS

Second scenario

Suppose that the company cuts the profit margin to 10% all other things being equal. Calculate

the PS multiple. Will this be a wise move?

g is changing because profit margin has changed.

T.J MABVURE (Mr.)

g= 0.8*.10*1.55=0.124

28.0

34.0

83.032.010.0

31.11.030.0

10.112.160.0

12.031.0

31.1

12.1112.1*20.0

10.02

22

2

PS

The PS has declined by:0.28−0.63

0.63= −56%, that is the PS has declined by 56%. Unless the sales

to book value of equity also increase by 56%, the value of the share will decrease.

Exercise

1. A firm is expected to go through two growth periods that is the high growth period and a stable

period




Average profit margin 15%

Payout ratio 5%

β 1.1

Rm 25%

Rf 20%

Stable period

Profit margin maintained @ 15%

Expected growth rate in savings 5%

Payout ratio 70%

β 0.8

Rm 25%

Rf 20%

Required

Estimate the PS multiple [10]

T.J MABVURE (Mr.)

2. Mckintosh Plc is expected to go through two growth periods that is the high growth

period and a stable growth period.



Expected ROE 30%

Expected Payout Ratio 35%

Run 25%

Βf 16%

Β 1.5

Average Profit Margin 20%

Stable Period

Profit Margin 15%

Expected ROE 30%

Payout Ratio 70%

Rm 25%

Rf 16%

Β 1

Required

Estimate the Ps multiple and comment. [15]

3. Kingrose Plc is expected to go through two growth periods that is the high growth

period and a stable growth period.

T.J MABVURE (Mr.)



Expected ROE 25%

Expected Payout Ratio 30%

Rm 25%

Rf 16%

β 1.5

Average Profit Margin 20%

Stable Period

Profit Margin 20%

Expected ROE 30%

Payout Ratio 70%

Rm 25%

Rf 16%

Β 1

Required

Estimate the Ps multiple and comment on your results if the market payout ratio is

eleven (11) times. [15]

T.J MABVURE (Mr.)

SHORT TERM FINANCIAL STRATEGY

This is all about planning. Planning looks at forecast (prediction of what’s going to

happen).

Forecast about sales levels in the future, WC requirements, profit, financing mix (debt to

equity); short term to long term.

Forecasting

Income statement-projected income statement and balance sheet. We would be basing on

the income statement this year and then predict for the next 5 years.

The starting point for an income statement is the sales projections e.g. by 10%.

The projected increase in sales has to be financed. The firm needs extra WC and Fixed

assets.

The increase in WC and fixed assets must be financed

Projected assets to support the increase in sales.

The Fixed assets and WC also depends on whether we are operating at full capacity or

below capacity. The former means there is need for increase in financing and the latter

means there is no need.

Sources of funds to cover the required increase

a) Spontaneous sources, certain current assets will be spontaneously financed by increase in

current liabilities. Increase in sales means more debtors and stocks and it also means

increase in creditors, so there is self financing.

b) Internal sources. Retained earnings; as sales increase the operating earnings also increase.

Retained earnings available are influenced by the dividend policy. Retained earnings are

internal equity, i.e. this is equity financing.

c) External sources:

Financing gap=Financing needs-(spontaneous sources+ internal sources).

The external sources are debt (long term, short term) and equity (new share issues)

Financing feedbacks

Extra dividends payments resulting from new share issues.

Extra interest payments resulting from new debt.

T.J MABVURE (Mr.)

So you will have some ‘what if’ scenarios

Approaches to identifying the financing Gap

a) Constant ratio method

b) Formula method

Constant ratio method

Let’s suppose we have got our income statement for year. We have projected that sales

will increase by 10%.

The DPS this year was $1.16 and this dividend is expected to be increased by about 8%

to$1.2528. There are 50 million outstanding shares which means that the projected

dividend will be 1.2528(50 million)=$62.64=$63

Actual Projected

$

Sales 3000 3300

Operating expenses (2716) (2988)

Operating earnings (EBIT) 284 312

Interest (88) (88)

EBT 196 224

Tax (40%) (78) (90)

Net income 118 134

Preferred dividends (4) (4)

Net income to ordinary 114 130

Dividend to ordinary (58) (63)

Retained earnings 56 67

The constant ratio method assumes that all expenses will increase at the same rate as

sales.

The primary purpose of this part of the forecast is determined by how much income the

company will generate internally through retained earnings.

The forecast now shifts to the statement of financial position.

T.J MABVURE (Mr.)

If the company was operating at full capacity this means that any increase in sales will

also lead to an increase in assets. For e.g. more cash will be required, receivables and

inventory will also increase. New plant and equipment will also be required. These

additional assets will lead to additional liabilities.

Statement of Financial Position

Actual Projected

$ $

Cash 10 11

Accounts receivables 374.5 412

Inventory 615 677

Current assets 1000 1100

Plant and equipment 1000 1100

2000 2200

Accounts payables 60 66

Notes payable 110 110

Accruals 140 154

Long term loan 754 754

1064 1084

Preferred equity 40 40

Ordinary share capital 130 130

Retained earnings 766 833(766+67)

Equity and liabilities 2000 2088

Debt obligations that have nothing to do with sales will not increase when sales increase.

We have spontaneous increase in terms of accounts payable and accruals.

Additional funds needed (AFN)=2200-2088=112.

T.J MABVURE (Mr.)

This is the financing gap which needs to be covered by external sources.

The company requires 200m of new assets to support the projected sales level which is

3300. if the existing capital structure is regarded to be optimal then the additional funds

of $112 must be raised by borrowing from the bank as notes payable, issuing long term

loans(bonds) and selling new ordinary shares.

Raising additional funds needed.

The financing mix will be determined by the target capital structure, conditions in the

debt and equity markets as well as restrictions imposed by existing debt agreements (the

company may have borrowed too much already).

Assuming that the following financial mix is adopted.

Type of financing % Amount Cost(%)

Notes payable 25 28 8 interest

Long term loans 25 28 10 interest

Ordinary share 50 56

On the notes payable we are paying 8% and on the long term 10% interest.

What this means is that there is going to be financing feedbacks which require that we

draw a new forecast, i.e. draft a new one.

The external funds raised to pay for the new assets create additional expenses which

must be reflected in the income statements.

This reduces the initially forecasted additions to retained earnings.

Financing feedbacks

a) Additional interest.

i) Short term debts(notes),i.e. 0.08*$28=$2.24

ii) Long-term debt 0.10*$28=2.80

$5.04m

b) Additional dividend.

Assuming that current share price is $23 and new share can be issued at this price,

therefore: resmillionSham

4.223$

56$

T.J MABVURE (Mr.)

The dividend payout is projected to be $1.25 per share, therefore the additional

dividend payments will be: 2.4*1.25=$3m.

This means that the dividends to ordinary shareholders will now increase to

$66m(63+3).

The net effect of these financing feedbacks is that income reduces by $6 million from

$67m to $61 million.

This reduces the projected retained income to $827m (766+61). This results in a

reduced financed gap of $7m that should be financed using the mix of 25%,short term

debt,25% long term debt,50% equity. It becomes a vicious cycle.

After doing the feedbacks we have to now consider the restated income statement and

balance sheet.

Re-stated income statement

Sales 3300

Costs 2988

EBIT 312

Less interest(88+5) (93)

EBT 219

Tax(40%) (88)

Earnings to shareholders 131

Preferred dividends (4)

Net income 127

Dividends(63+3) (66)

Retained income 61

T.J MABVURE (Mr.)

Restated Statement of Financial Position

Cash 11

Accounts receivables 412

Inventories 677

Total current assets 1100

Plant and equipment 1100

Total assets 2200

Accounts payable 66

Notes payable (110+28) 138

Accruals 154

Long term loans (754+28) 782

Total debt 1140

Preferred equity 40

Common stock (130+56) 186

Retained earnings (766+61) 827

Total equity and liabilities 2193

Additional funds needed are now (2200-2193) =7

We continue doing this until the needed funds becomes insignificant.

After this we analyze the forecast.

Analysis of the forecast

We must analyze the projected financial statements and compare them with our target

ratios as laid down in our long-term plans.

Formula method

The following formula can be used to obtain an estimate of the financial requirements

needed to support any increase in sales:

(Additional funds needed)=required increase in assets-spontaneous increases in liabilities-

increases in retained income.

T.J MABVURE (Mr.)

𝐴𝐹𝑁 = (𝐴∗ 𝑆⁄ )∆𝑆 − (𝐿∗ 𝑆⁄ )∆𝑆 − 𝑀𝑆1 (1 − 𝑑𝑖𝑣)

ΔS=Actual changes in sales

SA* These are assets that must increase if sales are to increase expressed as a % of

sales, i.e. the required dollar increase in assets per dollar increase in sales.

= 667.030002000

This means that for every $1 increase in sales, assets must increase by 67 cents.

Where A=Total assets

A*=assets that must increase

=A if the company is operating at full capacity.

SL* Liabilities that increase spontaneously with sales as a % of sales, i.e. the

Spontaneously generated financing per $1 Increase in sales.

= (60+140)/3000=0.0667

This means that every $1 increase in sales generated $7 cents in spontaneous financing.

L*=the liabilities that increase spontaneously

L=Total liabilities

L will always be greater than L* because other liabilities like long term liabilities does not

increase spontaneously.

S1= Sales (Total) projected for next year

=3300

Where S0=current sales=Current sales=3000

M=Profit margin (net profit margin)-Use Net Income before payment of all dividends

for the calculation of Net Profit Margin

= 039333333.03000

118

Sales

NI

d= 5088.0114

58youtRatiodividendPa

Million

dMSSSLSSAAFN

116

6420200

5088.013300039333333.03000667.0300667.0

1** 1

T.J MABVURE (Mr.)

Additional funds needed (AFN) = 112

AFN = 7

119

If we increase sales by $300 we must increase assets by $200m to support this increase in

sales level.

The $200m of assets (new) will be financed by 20million from spontaneous increases in

liabilities, 64 million from retained earnings. The remaining 118m must come from

external earnings sources.

Assuming that the firm is operating at full capacity.

This formula is only a rough estimate because of the assumptions that we made, which are:

i) Each asset item must grow at the same rate as the sales.

ii) Certain liability accounts e.g. Trade creditors (a/c payable and accruals) also increase

at the same rate as our sales.

iii) Profit margins and dividends payout ratios are constant; which may not be necessarily

true.

What is the relationship between growth and financial requirements?

The faster the growths rate in sales the greater the need for additional financing.

If we apply the formula to differential growth rates.

T.J MABVURE (Mr.)

Growth rate in

sales

∆ in Sales Forecasted Sales AFN

(10%) (300) 2700 (230)

O 0 3000 (56)

3.21 96 3096 0

10 300 3300 118

20 600 3600 293

Spontaneous plus retained earnings will be sufficient to meet the financial needs. It’s like

a break-even point.

The table can be converted into a financial feasibility chart.

Break even growth rate in sales

Solving for g in the equation

028502075.0

49.079999.10179999.1012002000

49.03000300003393333.030000667.03000667.0

509.01000339333333.006667.006667.0

)1(0)*(0)*(0 1

g

ggg

ggg

gSSgSgS

dMSgSSLgSSA

The breakeven point is the growth rate that will be covered by funds generated by

spontaneous increase in liabilities and retained earnings (internally generated equity).

T.J MABVURE (Mr.)

Question.

Tabastan Plc has the following ratio

𝐴∗ 𝑆⁄ = 3.4

𝐿∗ 𝑆⁄ = 2.2

Profit Margin=0.3

Dividend payout ratio=0.70

Sales last year were $300 million

Assuming that these ratios will remain constant, use the additional funds needed (AFN)

formula to determine the maximum growth rate the company can achieve without having to

employ external funds.

Exercise

1. Kusoyomu Plc has the following ratios.

A*/S 4.5

L*/S 2.6

Profit Margin 0.4

Dividend Payout Ratio 0.80

Sales last year were $400 million

Assuming that these ratios will remain constant use the additional funds needed (AFN)

formula to determine the maximum growth rate the company can achieve without having to

employ external funds. [15]

T.J MABVURE (Mr.)

Mergers and acquisitions

Two ways in which a company can expand operations

1. Internal expansion: The acquisition of long term assets over the years gradually.

2. External expansion: Can be achieved through a takeover, which is acquiring control of

the shares and assets in another company. This is more complex because it involves legal,

tax, accounting and management issues.

Types of mergers

a. Horizontal, conglomerate, vertical:

When two firms in the same industry merge, it’s called a horizontal merger, like two

banks, WMMI, and Nissan and Clover Leaf motors.

A vertical merger is where either a firm expands towards a customer or backwards

towards the supplier. The former is the supply chain and the latter is the distribution

chain.

Conglomerate is where you expand along unrelated lines of business. The purpose of this

is to diversify away operating risk, like ZSR who now concentrates away from sugar to

Trador, Advance, Redstar.

Reasons sighted for merger

The most sighted reasons are the possibilities of synergistic benefits arising from the merger.

Always expressed as 1+1=3 effect. That is Vxy>Vx+Vy,ie the value of xy is greater than

the value of x and y stand alone.

Reasons or other benefits are:

Economies of scale; as we increase the production the cost per unit decreases.

Operating economies; as we increase the size of operations the benefits are bound to

increase.

T.J MABVURE (Mr.)

Managerial skills which are endowed with a certain company especially in the highly

technological engineering firms.

Tax considerations; where a company has some tax assessed losses carried over the

years. The idea is to reduce the tax burden. In most of the cases the company has to

convince ZIMRA that the transaction was not for that purpose.

Excess liquidity; the targeted company may have a strong liquidity position e.g. retail

organizations.

Diversification; new products and new markets

Reduced financial costs. The merger may result in reduced cost if the company which is

being targeted has a financial slack (excess borrowing capacity).

Technology, acquisition that takes place in order to take/acquire the technological

expertise of the targeted company.

Terms of the merger

An acquirer can either pay cash for the acquisition or issue its own shares in exchange for the

shares of the target firm.

For an acquisition financed by cash the target company and the acquirer must agree on the

price to be paid per share.

Nominal value

Book value

Market value

Intrinsic value (Real value given the fundamentals of the business).

See Damodaran Aswath

advanced corporate finance-2017 · advanced corporate finance-2017 chinhoyi university of finance...

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