NPTEL Course

Course Title: Security Analysis and Portfolio Management

Instructor: Dr. Chandra Sekhar Mishra

Module-6

Session-12

Valuation of Equity Shares – II

Outline • Cash flow based valuation • Dividend Discount Model • FCFF • FCFE • Valuation in special cases

Cash flow based valuation: Cash is King. A company’s value is driven by its ability to generate cash flow over the long term (Copeland et al, 2000). Since the investors invest primarily cash in an enterprise, there are expectations that the enterprise generates cash flow for future growth and returning back to the investors. Since the cash flows occur at different points of time, one need to bring the cash flow to present value. That is why the cash flow based valuation is known as discounted cash flow approach. Different cash flow based valuation methods / models are discussed subsequently.

Dividend Discount Model (DDM): This model is applied to value equity. Dividend is the distribution of profit to the equity holders. Dividends can be distributed in terms of cash or shares i.e. bonus shares. DDM considers cash distributed as dividend. Firms are expected to declare dividend with the help of cash flow generated in normal course of business. Investors like pensioners look at dividend as a regular source of income and may not be bothered about change in market price as long as dividends remain stable. Similarly institutional investors like pension funds favour equity shares such companies that declare good amount of dividend. In DDM, the expected dividends of company are discounted to present to find the value of an equity share. The generic version of the model is as below:

Where, P0 is the price of equity share today and D1, D2… are the expected dividend per share (DPS) for year 1, 2 and like. ke is the expected rate of return of equity investors.

No Growth or zero growth model: If expected DPS remains same for all the years to come [i.e. D1, = D2 = D3, ….] the above model can be approximated as below:

Suppose the dividend and ke are Rs.4 and 12% respectively, then P0 = Rs.4/0.15 = Rs.26.67

∞

∞

++

++

++

+=

)k(1D......

)k(1D

)k(1D

)k(1D P

e3

e

3

2e

2

e

10

e0

kD P =

Constant Growth in Dividend: If the dividend is expected to grow at a constant rate for all the time to come, then the DDM approximates as below:

Example: Present dividend per share (D0) is Rs.4 and is expected to grow at 6% per annum till perpetuity and cost of equity of 12%.

First we need to estimate D1.

D1 = Rs.4*(1+0.06) = Rs.4.24

Then P0 = Rs.4.24/(0.12-0.06)=Rs.70.67

Multi Stage Growth Model (variable growth model): It is unlikely that dividends will grow at a constant rate. Dividends might grow at higher rate in the initial years known as super normal growth period and then grow at constant rate, which is termed as stable stage growth. In such case, one has to estimate the dividends for different years of super normal or high growth period separately and discount them to present value and then bring the value of stable stage dividend to present value separately.

Example: Multi Stage Growth

D0 = Rs.4

Dividend is expected to grow at 12% for next three year and then at 10% for subsequent 2 two years after which the growth will stabilize at 8%. If the cost of equity is 15%, what is the value per share?

Example: Multi Stage Growth, contd..

Step I: One has to estimate the dividends for year 1 through 6:

D1 = Rs.4.00*(1.12)=Rs.4.48

D2 = Rs.4.00*(1.12)2=Rs.5.02

D3 = Rs.4.00*(1.12)3=Rs.5.62

D4= Rs.5.62*(1.10)=Rs.6.18

D5= Rs.6.18*(1.10)=R.6.80

D6= Rs.6.80*(1.08)=Rs.7.34

Step II: Find the terminal value at the end of 5th year after which constant growth starts.

TV5 = D6/(ke-g) = Rs.7.34 / (0.15-0.08)=Rs.104.91

Step III: Discount the individual dividends from year 1 to 5 as well as TV5 to present value and sum all the values to find the value per share:

g - kD Pe

10 =

Rs.70.46)15.1(91.104

)15.1(80.6

)15.1(18.6

)15.1(62.5

)15.1(02.5

1.154.48 P 554320 =+++++=

Free Cash Flow Approaches: Free cash flow is the cash flow available after meeting all the claims. It can be free cash flow to firm, FCFF (i.e. from all stake holders’ point of view) or free cash flow to equity, FCFE (from equity holders’ point of view). By using FCFF, the value of company can be found and from that valuation of equity can be derived. By using FCFE, the value of equity can directly be found out.

Firm Valuation

The value of the firm is obtained by discounting expected cash flows to the firm, i.e., the residual cash flows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions.

∑n=t

1=tt

t

WACC)+(1Firm toCF

=Firm of Value

Where,

CF to Firmt = Expected Cash flow to Firm in period t

WACC = Weighted Average Cost of Capital

Value of Equity

= Value of firm – Value of Preference Share Capital (if any) – Value of Debt

Equity Valuation: The value of equity is obtained by discounting expected cash flows to equity, i.e., the residual cash flows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm.

∑n=t

1=tt

e

t

)k+(1Equity toCF =Equity of Value

Where,

CF to Equityt = Expected Cash flow to Equity in period t

ke = Cost of Equity

Key Ingredients for FCF Approach

• Discount rate Cost of equity Cost of capital (WACC) [it considers the cost of capital for all components of capital

like equity capital, preference share capital, debt etc.] • Estimation of cash flows

Estimation of operating income Estimation of tax rate Estimation of capital expenditure and net working capital

• Estimation of growth rate in cash flows Growth rate = Reinvestment rate x return on capital

• Other considerations like non-operating assets, excess cash

Generic Model for FCFF

In general, FCFF = EBIT (1-t) + Depreciation - Capital Expenditures - Change in Non-cash WC

Example for FCFF valuation model1

The following valuation example relates to a hypothetical firm engaged in manufacturing of drugs and pharmaceuticals. It is expected to grow at a super normal growth rate for the next three years after which it is expected to have normal growth, constant over its life. The reinvestment rate is based on capital expenditure, change in working capital and net of depreciation for a given year.

Rs. Crore Year 0 1 2 3 4 Growth rate 22.50% 22.50% 22.50% 4.80% NOPAT [EBIT (1-t)] 100 122.50 150.06 183.83 192.65 Reinvestment Rate [% of NOPAT] 75% 75% 75% 40% Cost of Equity 16.00% 16.00% 16.00% 12.00% Cost of Debt [pre-tax] 8% 8% 8% 7% Debt Ratio 20% 20% 30% 40% Cost of Capital (WACC) 13.76% 13.76% 12.64% 8.88% Return on Capital 30% 30% 30% 12% Tax rate 40%

FCFF

30.63 37.52 45.96 115.59

Terminal Value [FCFF from 4th year onwards]

2833.09

PV of FCFF and Terminal Value

26.92 28.99 2014.52

Value of operating assets 2070.43 Non-operating assets [given] 120.00 Value of the firm 2190.43 Market value of debt [given] 300.00 Value of equity 1890.43

Other Approaches for Valuation

Private Equity Approach: Private equity players typically invest in high expected return, high growth potential, thus high risk companies. They apply a higher discount rate for valuation.

Valuation for Mergers and Acquisitions: To the value of equity determined by different approaches, a control premium is added to find the value of equity stake in the company.

*******

1 Adapted from Damodaran, A (2006), Damodaran on Valuation – Security Analysis for Investment and Corporate Finance, Wiley and Sons.

References:

Copeland, Tom, Koller, T & Murrin, J (2000), Valuation – Measuring and Managing the Value of Companies, 3e, John Wiley & Sons Damodaran, Aswath (2007), Corporate Finance – Theory and Practice, 2e, Wiley India Damodaran, A (2006), Damodaran on Valuation – Security Analysis for Investment and Corporate Finance, Wiley and Sons. Reilly and Brown (2006), Investment Analysis and Portfolio Management, 8e, Thomson (Cengage) Learning, New Delhi Bodie et al (2009), Investments, 8e, Tata McGraw Hill, New Delhi Prasanna Chandra (2008), Investment Analysis and Portfolio Management, 3e, Tata McGraw Hill, New Delhi

Questions and Answers

Q.1: Ken Limited has just declared Rs.6.00 as dividend per share (DPS). The beta of Ken’s stock is 0.8. The market rate of return and risk free rate of return are 14% and 7% respectively.

a) If the DPS of Ken Limited is expected to remain constant, what is the value of share? b) If the DPS is expected to grow @6% per annum constantly, what is the value per share?

Ans.:

Applying capital asset pricing model,

The expected rate of return = ke = Rf + β*(Rm – Rf) = 0.07 + 0.8 * (0.14 – 0.07) = 0.126 = 12.6%

a) Value per share = DPS / ke = Rs.6.00 / 0.126 = Rs.47.62 b) DPS1 = DPS0 * (1 + g) = Rs.6.00 * 1.08 = Rs.6.48

Value per share = DPS1 / (ke – g) = Rs.6.48 / (0.126 – 0.06) = Rs.98.18

Q.2: Zairo Limited has just declared Rs.5.00 as dividend per share. This is expected to grow at 15% for the next three years, then @ 10% for subsequent 2 years and further @ 6% constantly per annum from 6th year onwards. If one’s expected rate of return is 14%, how much one should pay for buying the share?

Ans.: This is a multi-stage dividend model.

Expected dividend per share by taking the appropriate growth rates:

Year: 0 1 2 3 4 5 6 DPS (in Rs.) 5.0000 5.7500 6.6125 7.6044 8.3648 9.2013 9.7534 Present value of DPS @ 14% (in Rs.)

5.0439 5.0881 5.1327 4.9526 4.7789

Present value of Dividends 1 through 5 = Rs. 24.9962 Terminal value at the end of year 5 = DPS6 / (ke – g) = Rs.9.7534 / (0.14 – 0.06) = Rs.121.9171 Present value of terminal value = Rs.121.9171 / (1 + ke)5 = Rs.63.3199 Value per share = Rs.24.9962 + Rs.63.3199 = Rs.88.62

Q.3: Find the value of XYZ Co’s equity share by using free cash flow to firm (FCFF) approach with the help of following information.

SOURCES OF FUNDS 2009-10 APPLICATION OF FUNDS 2009-10 Shareholders’ funds Gross fixed assets 1,100 Equity share capital (12 crore shares of Rs.10 each)

120 Less: accumulated depreciation 400

Reserves and Surplus 280 Net fixed assets 700 10% Loan 600 Net working capital 300 1,000 1,000

The EBIT of XYZ for 2009-10 is Rs.250 crore. Depreciation for the year is Rs. 70crore The company is subject to 40% tax rate. The growth in sales, depreciation NOPAT (net operating profit after tax), gross fixed assets and net working capital will be 18% for the first three years, 10% for the next two years and 7% thereafter. There will be no change in the tax rate and present debt ratio. The expected rate of return of equity shareholders is 16%.

Ans.: The net operating profit after tax for 2009-10 = EBIT * (1 – tax rate) = Rs.250crore * (1 - 0.40) = Rs.150crore.

Debt ratio = 0.60

Post tax cost of debt: 0.06

Weighted average cost of capital (k) = Wd * Kd + We * Ke = 0.60 * 0.06 + 0.40 * 0.16 = 0.10

Forecasted FCFF:

Year: 2009-10 2010-11 2011-12 2012-13 2013-14 2014-15 2015-16 Growth rate (%)

18% 18% 18% 10% 10% 7%

Assets (end value) 1,000 1180.00 1392.40 1643.03 1807.34 1988.07 2127.23 NOPAT 150.00 177.00 208.86 246.45 271.10 298.21 319.09 Depreciation 70.00 82.60 97.47 115.01 126.51 139.16 148.91 Increase in assets

180.00 212.40 250.63 164.30 180.73 139.16

FCFF

79.60 93.93 110.84 233.31 256.64 328.83 Discounted value of FCFF (@10%)

The terminal value of the firm = FCFF6 / (k – g) = 323.83 / (0.10 – 0.07) = Rs.10,961 crore

Present value of FCFF from 2010-11 till 2014-15 = Rs.551.97 crore

Present value of terminal value = 10,961 / (1+.10)5 = Rs.6805.85 crore

Total value of the firm = Rs.7357.81 crore

Value of equity = Value of firm – value of debt = Rs.7357.81 crore – Rs.600 crore = Rs.6,757.81 crore

Value per share = Rs.6,757.81 crore / 12 crore= Rs.563.15