christopher b. stone ‘01 present value of future cash flow r = discount rate n = number of periods...
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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
Christopher B. Stone ‘01
Annuities
CF0CFt
n n nn n
PmT PmTPmTPmTPmT
PmT PmTPmTPmT PmT
In advance
In arrears
Christopher B. Stone ‘01
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.
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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)
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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%
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
Depreciation graphs
Methods of depreciation
$-
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
0 1 2 3 4
Year
Val
ue
of
ass
et
Straight line
Sum of the years
Declining balance @ 150%
Double declining balance
Christopher B. Stone ‘01
Capitalization vs. expenses
R epa irs
R ecurr ing eventstha t p roducelong - lived asse ts
E xpenses
E xcep tion: recurr ing eventscan be expensed
C rea te an asse t tha tp roduces revenue
beyond 1 yea r
R epa ir + upg radeUpgrade is cap ita lized
C ap ita liza t ion
E xpend itures
Christopher B. Stone ‘01
Merger accounting
Based on BO O K (h istorical) valu es
Resu lts in h ig h er n et in com eon fu tu re b alan ce sh eets1) B ook va lue < F M V2) G oodw ill m us t be am ort ized
MUST b e u sed if an d on ly ifall 12 con d ition s are m et
Poolin g
Based on fair m arket valu e (F MV)
Pu rch ase
Meth od s of accou n tin g for b u sin ess com b in ation s
Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling
Christopher B. Stone ‘01
Pooling method
Cash 300,000$ 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
Christopher B. Stone ‘01
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$
Total 700,000$ Total 700,000$ Total 200,000$ Total 200,000$
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
Stock and dividend issuanceCash 10,000$ Cash 10,000$
c/s 100$ c/s 10,000$ Paid-in capital 9,900$
Total 10,000$ Total 10,000$ Total 10,000$ Total 10,000$
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$
Total 15,000$ Total 15,000$ Total 14,000$ Total 14,000$
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$
Total 14,000$ Total 14,000$ Total 16,000$ Total 16,000$
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$
Total 100,000$ Total 100,000$ Total 100,000$ Total 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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
Leverage ratios
Debtratio
=Liabilities
Assets
Debt/equityratio
=LiabilitiesNet worth
Christopher B. Stone ‘01
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?
Christopher B. Stone ‘01
Activity ratios
Accounts receivable turnover
=Net sales*
Accounts receivable
*From the income statement
Inventoryturnover
=COGS*
Inventory
Accounts payable turnover
=Total expenses*
Accounts payable
Christopher B. Stone ‘01
Operating cycle
Capitalinfusion
$
Sale
InventoryAccountsreceivable
Avg. amount of time inventory is outstanding +
Avg. amount of time receivables are outstanding
Operatingcycle
=
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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
Christopher B. Stone ‘01
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