christopher b. stone ‘01 present value of future cash flow r = discount rate n = number of periods...

Christopher B. Stone ‘01

Present value of future cash flow

nr1

FV PV

r = discount raten = number of periods

Discounting: calculation of present valuesDiscounting: calculation of present valuesCompounding: calculation of future valuesCompounding: calculation of future values


Annuities

CF0CFt

n n nn n

PmT PmTPmTPmTPmT

PmT PmTPmTPmT PmT

In advance

In arrears


Internal rate of return

IRR is that unique discount rate which, when applied to a series of future cash flows, yields a net present value of 0.


Financial management rate of return

Series A Series B Series CCF0 (100.00)$ (100.00)$ (50.00)$ CF1 -$ 7.18$ (42.82)$ CF2 -$ 7.18$ 7.18$ CF3 -$ 7.18$ 7.18$ CF4 -$ 7.18$ 7.18$ CF5 141.42 117.18 107.18$ IRR 7.18% 8.86% 8.12%

Only Series A is a “pure” IRR

Series B and Series C have money extracted from the system

Series C has money invested in the system after t0

The IRR model assumes1) That money invested in the system is held in an account bearing interest at the IRR before being invested;2) That money extracted from the system is re-invested in anaccount yielding the IRR.

IRR FMRR

IRR Safe rate

IRR Re-investment rate

Negative cash f low s after t0, before they are invested, are held in an account that produces interest at

Money extracted from the system is re-invested at

FMRR bifurcates negative and positive cash flowsFMRR bifurcates negative and positive cash flows


Financial management rate of return

PV FV

(50) (50)

(107.18)(7.18) (7.18)(7.18)(7.18)

Future valued at re-investment rate

PV’ed at safe rate

FMRR > re-investment rate for worthwhile investmentsFMRR > re-investment rate for worthwhile investments


Hurdle rates

The earnings you foregoby deploying capital in adifferent way

The rate you must get on an investment for the deal to make sense

If hurdle rate < IRR, NPV is positiveIf hurdle rate < IRR, NPV is positive


Sensitivity analysis

If you discount your cash flows @ the HRand get a + NPV, the NPV represents yourprofit over the life of the deal.

If HR<IRR, + NPV

NPV @ HR is the positivecushion you have

nr1

FV PV

Annuitize this figure(calculate PmT) to get Net Uniform Series (NUS)


Recourse debt

C red ito r can sue deb to r if no t re -pa id

M ight be secured , m ight no t

M os t co rpo ra te deb t is recourseE xcep t ion: rea l es ta te

R ecourse

B orrow er has no pe rsona l liab ility

M us t be secured , o the rw ise , it 's no thing

Y ou can s t ill sue fo r f raudulent conveyances , e tc .

Non-recourse

D eb t


Compounded interest

A t Y R 1 , I ow e $12The $12 does no t accrue inte res t if unpa id

S im p le

A t Y R 1 , I ow e $12The $12 inte res t itse lf acc rues inte res t

C om pound

Inte res tI bo rrow $100 @ 12%


Capital asset pricing model

)( fmfe RRβRk

Cost ofcapital Risk-free

returnUSG securities

Average rate of returnon common stocks

(S&P 500)

Co-varianceof returns against

the portfolio(departure from the average)

B < 1, security is safer than S&P 500 averageB > 1, security is riskier than S&P 500 average

Cost of equity capital = return expected on firm’s common stockCost of equity capital = return expected on firm’s common stock

Cost of capital = Risk-free return + compensation for additional risk beyond a USG bondCost of capital = Risk free return + (β x market risk premium)Cost of capital = Risk free return + (β x margin by which stock market exceeds risk-free return


Lease financing

R un-o f- the -m ill " lease"

Lessee incurs a tax-deduc t ib lepe r iod ic expense

Lesso r enjoys the tax shie ldo f dep rec ia t ion

O pera t ing lease

Long-te rm f inanc ingIs like long -te rm deb t

T it le is usua lly trans fe rredto lessee a t the end o f the lease te rmfo r a nom ina l am ount

A re re f lec ted in com pany 'sf inanc ia l s ta tem ents

C ap ita lized lease

Lease f inanc ing


Income statement

Total revenuesLess Cost of goods soldLess Fixed costs / purchasesLess Change in inventory

Beginning inventoryEnding inventory

EBITDALess depreciation

EBITLess interest

EBTLess taxes

Earnings for common & preferredLess preferred dividends

Earnings for common & preferredLess sinking fund

Unrestricted earnings


Methods of inventory valuation

Lower of cost or m arket Cost

F IF OF irst g ood s in to in ven tory

are first g ood s ou t

Cost O NLY

L IF OLast g ood s in to in ven tory

are first g ood s ou t

En d in g in ven tory valu ation m eth od s


Benefits of FIFO and LIFO

FIFO LIFO

TechniqueValue closing inventory at end-of-year (current) prices

Value closing inventory at beginning of year prices

Inflationary

Increases value of closing inventory

LESS change in inventoryHigher EBITDA

Decreases value of closing inventory

MORE change in inventoryLow er EBITDA

Deflationary

Decreases value of closing inventory

MORE change in inventoryLow er EBITDA

Increases value of closing inventory

LESS change in inventoryHigher EBITDA

Method

Eco

no

my

Must use the same method for financial & tax accountingMust use the same method for financial & tax accounting


FIFO and LIFO calculations

LIFO LIFO LIFOCost LCM Cost Cost LCM Cost Cost LCM Cost

Gross revenues 200$ 200$ 200$ 80$ 80$ 80$ 200$ 200$ 200$ Less COGS 100$ 150$ 100$ 100$ 50$ 50$ 50$ 50$ 50$

Purchases 100$ 100$ 100$ 50$ 50$ 50$ 50$ 50$ 50$ Change in inventory -$ 50$ -$ 50$ -$ -$ -$ -$ -$

Opening inventory 100$ 100$ 100$ 100$ 50$ 100$ 50$ 50$ 100$ Closing inventory 100$ 50$ 100$ 50$ 50$ 100$ 50$ 50$ 100$

Gross income 100$ 50$ 100$ (20)$ 30$ 30$ 150$ 150$ 150$

Qty 10 10 10 10 10 10 10 10 10Price 20$ 20$ 20$ 8$ 8$ 8$ 20$ 20$ 20$

Qty 10 10 10 10 10 10 10 10 10Price 10$ 10$ 10$ 5$ 5$ 5$ 5$ 5$ 5$

Qty 10 10 10 10 10 10 10 10 10Price 10$ 10$ 10$ 10$ 5$ 10$ 5$ 5$ 10$

Qty 10 10 10 10 10 10 10 10 10Price 10$ 5$ 10$ 5$ 5$ 10$ 5$ 5$ 10$

Market price @ end of year 5$ 5$ 10$

Under FIFO-LCM, opening inventories in the next year should be valued at COST

Year 3FIFO FIFO FIFOITEM

Closing inventory

FactsSales

Purchases

Opening inventory

Year 1 Year 2


Depreciation methods

Straig h t l in e

Su m of th e years

150% m eth od Dou b le d eclin in g b alan ce

Declin in g b alan ce

Accelerated

Dep reciation m eth od s

= Cost-salvage value Useful life

= Cost-salvage value * remaining years of useful lifen(n+1) 2

Keyed off the remaining balance in each year AFTER depreciationDoes NOT use salvage value


Straight line & sum of the years depreciation

Remaining years Denominator Coefficient Base1 4 10 0.4 10,000$ 4,000$ 2 3 10 0.3 10,000$ 3,000$ 3 2 10 0.2 10,000$ 2,000$ 4 1 10 0.1 10,000$ 1,000$

FactsCost 12,000$ Salvage Value 2,000$ Useful Life 4

Calculation (sum of the years) DepreciationExpense

Year

Year Depreciation Expense01 2,500$ 2 2,500$ 3 2,500$ 4 2,500$

Cost 12,000$ Salvage Value 2,000$ Useful Life 4

Facts

Straight-line

Sum of the years


Declining balance depreciation

%Useful

life (yrs)Coefficient

Depreciation expense

Remainingbalance

%Useful

life (yrs)Coefficient

Depreciation expense

Remaining balance

0 12,000.00$ 12,000$ 1 150% 4 0.375 4,500.00$ 7,500.00$ 200% 4 0.5 6,000$ 6,000$ 2 150% 4 0.375 2,812.50$ 4,687.50$ 200% 4 0.5 3,000$ 3,000$ 3 150% 4 0.375 1,757.81$ 2,929.69$ 200% 4 0.5 1,000$ 2,000$ 4 150% 4 0.375 929.69$ 2,000.00$ 200% 4 0.5 -$ 2,000$

Useful life (yrs) 4Cost 12,000$ Salvage value 2,000$

Year

150% method Double declining balance method

Facts

Coefficient CoefficientCalculations Calculations

$12,000 x .375 = $4,500


Depreciation graphs

Methods of depreciation

$-

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

0 1 2 3 4

Year

Val

ue

of

ass

et

Straight line

Sum of the years

Declining balance @ 150%

Double declining balance


Capitalization vs. expenses

R epa irs

R ecurr ing eventstha t p roducelong - lived asse ts

E xpenses

E xcep tion: recurr ing eventscan be expensed

C rea te an asse t tha tp roduces revenue

beyond 1 yea r

R epa ir + upg radeUpgrade is cap ita lized

C ap ita liza t ion

E xpend itures


Merger accounting

Based on BO O K (h istorical) valu es

Resu lts in h ig h er n et in com eon fu tu re b alan ce sh eets1) B ook va lue < F M V2) G oodw ill m us t be am ort ized

MUST b e u sed if an d on ly ifall 12 con d ition s are m et

Poolin g

Based on fair m arket valu e (F MV)

Pu rch ase

Meth od s of accou n tin g for b u sin ess com b in ation s

Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling


Pooling method

Cash 300,000$ Debt 250,000$ Inventory 50,000$ Debt -$ Plant 400,000$ Plant 150,000$

Common 300,000$ Common 100,000$ R/E 150,000$ R/E 100,000$

Total 700,000$ Total 700,000$ Total 200,000$ Total 200,000$

FMV of Y'sInventory 60,000$ (Notice that FMV's are irrelevant to the pooling method)Plant 180,000$

EarningsX 15,000$ Y 20,000$

Consideration for X's acquisition of YX common 250,000$

or

Cash 300,000$ Debt 250,000$ Cash 300,000$ Debt 250,000$ Cash 300,000$ Debt 250,000$ Investment 200,000$ Inventory 50,000$ Inventory 50,000$ Plant 400,000$ Plant (Y) 150,000$ Plant 550,000$

Common 400,000$ Plant 400,000$ Common 400,000$ Common 400,000$ R/E 250,000$ R/E 250,000$ R/E 250,000$

Total 900,000$ Total 900,000$ Total 900,000$ Total 900,000$ Total 900,000$ Total 900,000$

Assets Liabiliites

Equity

X Corp Y CorpAssets Liabiliites

Equity

Facts

X Corp (after acquisition)Assets Liabiliites

Equity

X Corp (after acquisition)Assets Liabiliites

Equity

X Corp (consolidated)Assets Liabiliites

Equity

Pooling: Uses book value, A inherits T’s retained earningsPooling: Uses book value, A inherits T’s retained earnings


Purchase method

Cash 300,000$ Debt 250,000$ Inventory 50,000$ Debt -$ Plant 400,000$ Plant 150,000$

Common 300,000$ Common 100,000$ R/E 150,000$ R/E 100,000$


FMV of Y'sInventory 60,000$ (Purchase method uses FMV)Plant 180,000$

EarningsX 15,000$ Y 20,000$

Consideration for X's acquisition of YX common 250,000$

or

Cash 300,000$ Debt 250,000$ Cash 300,000$ Debt 250,000$ Cash 300,000$ Debt 250,000$ Investment 250,000$ Inventory 60,000$ Inventory 60,000$ Plant 400,000$ Plant (Y) 180,000$ Plant 580,000$

Common 550,000$ Plant 400,000$ Common 550,000$ Goodw ill 10,000$ Common 550,000$ R/E 150,000$ Goodw ill 10,000$ R/E 150,000$ R/E 150,000$

Total 950,000$ Total 950,000$ Total 950,000$ Total 950,000$ Total 950,000$ Total 950,000$

X Corp Y CorpAssets Liabiliites Assets Liabiliites

Equity Equity

Facts

X Corp (after acquisition) X Corp (after acquisition)Assets Liabiliites Assets Liabiliites

Equity Equity Equity

X Corp (consolidated)Assets Liabiliites

Purchase: Uses FMV, A doesn’t inherit T’s retained earningsPurchase: Uses FMV, A doesn’t inherit T’s retained earnings


Goodwill

R ep u ta tion , ta len ted m g m t., g ood re la tion sh ip s w ith su p p lie rs , e tc .C an n o t b e so ld ap art from id en tifiab le asse ts

E n te rp rise can record g ood w ill O N L Y w h en it p u rch ases an en tire b u s in ess

A m ortizab le u n d er a 4 0 -yr p eriod (u su a lly - sh orte r in h ig h -tech )

P u rch ase p riceL ess F M V o f asse ts

R es id u a l m eth od E xcess earn in g s m eth od

V a lu in g g ood w ill

G ood w ill

AmountAverage earnings over X years 150,000$

Less expected return on identif iable assets 100,000$ Excess earnings 50,000$

Amount @ 10% interest that w ill produce $50,000 in excess earnings each year(I.e., goodw ill)

500,000$

Identifiable assets (book value? FMV?) 1,000,000$ Return on assets 10%

Item

Facts


Stock and dividend issuanceCash 10,000$ Cash 10,000$

c/s 100$ c/s 10,000$ Paid-in capital 9,900$


1) Board authorizes and issues 100 shares at @1 par value, selling for $100 per share 5) As in #4; Board buys a Van Gogh for $2,0002) Board authorizes and issues 100 shares of "no-par stock" for $100/share 6) Painting is distributed as dividend ("deemed sale")3) As in #1; earnings for the year are $5,0004) As in #3; Board declares dividend of $1,000 7) Covertible debt to stock

Cash 10,000$ Cash 10,000$ Cash 5,000$ Cash 4,000$

c/s 100$ c/s 100$ Paid-in capital 9,900$ Paid-in capital 9,900$ Retained earnings 5,000$ Retained earnings 4,000$


Cash 10,000$ Cash 10,000$ Cash 2,000$ Cash 2,000$ Painting 2,000$ Deemed cash 4,000$

c/s 100$ c/s 100$ Paid-in capital 9,900$ Paid-in capital 9,900$ Retained earnings 4,000$ Retained earnings 6,000$


Cash 10,000$ Cash 2,000$

c/s 100$ Paid-in capital 9,900$ Retained earnings 2,000$

Total 12,000$ Total 12,000$

Cash 100,000$ Debt 50,000$ Cash 100,000$ Debt -$ Cash Cash

c/s 50,000$ c/s 100,000$


Cash 900$ Debt 300$ Cash 750$ Debt 300$

c/s 100$ c/s 100$ Paid-in capital 200$ Paid-in capital 200$ Retained earnings 300$ Retained earnings 300$

Treasury shares (150)$

Total 900$ Total 600$ Total 750$ Total 750$

Cash 1,200$ Debt -$ Cash 1,200$ Debt -$

Scenario 1 (par stock issued) Scenario 2 (no-par stock issued)Assets Liabiliites Assets Liabiliites

Equity Equity

Scenario 3 (earnings of $5,000 reported)

Facts

Assets Liabiliites

Equity

Scenario 4 (div of $1,000)Assets Liabiliites

Equity

Scenario 5 (Board buys a Van Gogh)Assets Liabiliites

Equity

Scenario 6a (Van Gogh distributed as div - "deemed sale")Assets Liabiliites

Equity

Scenario 6b (Van Gogh distributed as div - "deemed sale")Assets Liabiliites

Equity

Scenario 8: convertible debt (before)Assets Liabiliites

Equity

Scenario 8: convertible debt (after)Assets Liabiliites

Equity

Company has 100 outstanding shares of $5 par value common Assets Liabiliites

Equity

Buys back treasury shares for $150Assets Liabiliites

Equity

Initial conditionAssets Liabiliites

Company declares a stock dividend of 10 shares @ $6/shareAssets Liabiliites


Liquidity ratios

Currentratio

=Current assets

Current liabilities

Quickratio

= Current assets - inventoryCurrent liabilities

Cash flowliquidity

ratio=

Cash flow from operations*Current liabilities

*From the cash flow statement


Leverage ratios

Debtratio

=Liabilities

Assets

Debt/equityratio

=LiabilitiesNet worth


Financial leverage index

Financialleverage

index=

Return on equityAdjusted return on assets

= Net earnings* / equity**[Earnings + interest (1-tax rate)] / assets

* Note this does not include pfd div**Or market cap

Is a company trading positively on its leverage? I.e., is it bringing in capital at less than the return?


Activity ratios

Accounts receivable turnover

=Net sales*

Accounts receivable

*From the income statement

Inventoryturnover

=COGS*

Inventory

Accounts payable turnover

=Total expenses*

Accounts payable


Operating cycle

Capitalinfusion

$

Sale

InventoryAccountsreceivable

Avg. amount of time inventory is outstanding +

Avg. amount of time receivables are outstanding

Operatingcycle

=


Capitalinfusion

$

Sale

Cash conversion cycle

Avg. amount of time inventory is outstanding +

Avg. amount of time receivables are outstanding-

(Avg. amount of time payables are outstanding)

Cashconversion

cycle=

Accountspayable

(Payment)Accountsreceivable

Inventory


Profitability ratios

Gross profitmargin

=Gross profitGross sales

This is very much driven by variable costs / cost of goods sold. Overhead is NOT included.

Measures profitability

A business can be profitable and still trade negatively on its leverageA business can be profitable and still trade negatively on its leverage


P/E ratio

P/E ratio =Stock price per share

Earnings per share

G row th stockH ig h P /E ra tio

Value stockL ow P /E ra tio

Return ontotal assets

=Earnings + interest

Assets

christopher b. stone ‘01 present value of future cash flow r = discount rate n = number of periods...

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