Christopher B. Stone ‘01 Present value of future cash flow n r 1 FV PV r = discount rate n = number of periods Discounting: calculation of present values Discounting: calculation of present values Compounding: calculation of future values Compounding: calculation of future values
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Christopher B. Stone ‘01 Present value of future cash flow r = discount rate n = number of periods Discounting: calculation of present values Compounding:
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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
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
$14,000
0 1 2 3 4
Year
Val
ue
of
ass
et
Straight line
Sum of the years
Declining balance @ 150%
Double declining balance
Christopher B. Stone ‘01
Capitalization vs. expenses
R epa irs
R ecurr ing eventstha t p roducelong - lived asse ts
E xpenses
E xcep tion: recurr ing eventscan be expensed
C rea te an asse t tha tp roduces revenue
beyond 1 yea r
R epa ir + upg radeUpgrade is cap ita lized
C ap ita liza t ion
E xpend itures
Christopher B. Stone ‘01
Merger accounting
Based on BO O K (h istorical) valu es
Resu lts in h ig h er n et in com eon fu tu re b alan ce sh eets1) B ook va lue < F M V2) G oodw ill m us t be am ort ized
MUST b e u sed if an d on ly ifall 12 con d ition s are m et
Poolin g
Based on fair m arket valu e (F MV)
Pu rch ase
Meth od s of accou n tin g for b u sin ess com b in ation s
Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling
Common 550,000$ 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$