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CHAPTER 14
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• This chapter examines tools used to evaluate potential projects/investments
• Accountants
–Simple Rate of Return (SRR)
• Based on NI
• AKA � Accounting Rate of Return
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• Financiers
–Don’t like NI
• Too much discretion
• Prefer ATCF to NI
–Use PBP, NPV, and IRR
–Concept of ATCF is discussed in Appendix 14C
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• SRR & PBP are non-discounting models
–Don’t use PV
• NPV & IRR are discounting models
–Use PV
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Present Value
(Appendix 14A)
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• Instinctively, you know $1 in future ≠ $1 today
• You can put $1 in bank:
–Earn interest on deposit
–Have $1 + interest in future
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7• PV tells you what you put in bank
today to have $1 in future:
PVIF =
__1___
(1+ d)n
• “d” – interest rate
• “n” – number of periods
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• E.g., $1 received at end of 1 year–10% interest compounded annually–Deposit following at start of year:
PVIF = (1/(1.10)1)PVIF = 90.909¢
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You can test this:
One Year's Interest (.1 x 90.909¢ )
= 9.0909¢
Original Principal = 90.9090¢
After 1 Year: 99.9999¢
Off due to rounding
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10• E.g., $1 is received at end of 2 years
• 10% interest compounded annually
• Deposit following at start of period:
PVIF = (1/(1.10)2)
PVIF = 82.6446¢
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1st Year's Interest(.1 x 82.6446¢)
= 8.26446¢
Original Principal = 82.64460¢
After 1 year: 90.90906¢
2nd Year's Interest(.1 x 90.90906¢)
= 9.090906¢
Balance At Start of Year = 90.909060¢
After 2 years: 99.999966¢
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• If you get $1 a year for a number of years
– “Annuity”
– You could calculate PV of each $1 to be received
– Or use PV of Annuity formula:
PVIFannuity = 1/d ( 1- [ __1___
])(1+d)n
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• E.g., $1 received at end of each year for 2 years
– 10% interest compounded annually
– Deposit following:
PV of $1 received 1 year from now: 90.9090¢
PV of $1 received 2 years from now: 82.6446¢
$1.735536
• Using PVA formula:
PVIFannuity = [1-(1/(1.10)2]/.1
PVIFannuity = $ 1.73553719
14 • If you deposit $1.73553719@ 10% interest• You can withdraw $1 at end of each year for 2
years:
Initial Deposit: $1.735537190
1st Year’s Interest: 17.355372¢
Balance after 1 Year: $1.909091
Withdrawal of $1: -$1.000000
Balance Remaining: 90.9091¢
2nd Year’s Interest: 9.0909¢
Balance after 2 Years: $1.000000
Withdrawal of $1: -$1.000000
Balance after Withdrawal of $1: 0
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Net Present Value
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• Problem with evaluating investment
–You invest present $s & receive future $s
–Like comparing apples & oranges
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• NPV
– Convert payoff into PV & subtract investment
• Now comparing apples & apples
– If positive � receiving return > discount factor
18• Discount rate �minimum return required
• Traditionally � weighted average cost of capital of firm
– Weights are % capital coming from a particular source of capital
• E.g., 20% from equity vs. 80% from debt
– Cost of capital is after-tax cost of capital:
• interest is deductible
• dividends are not deductible
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• NPV payoff is in ATCF (not NI)
– Difference between NI & ATCF �depreciation & other non-cash expenses
• We will assume that:
– Investment made on 1st day of investment &
– Payoffs received at end of each year
20Depreciation Tax Shield (Appx 14C)• Depreciation is not a cash expense
– Not directly part of ATCF
• But depreciation is tax deduction– Taxes are a cash expense & included in calculation
of ATCF
• For tax purposes, Depreciation follows MACRS– Unless you are told otherwise, we will assume S/L
method
21 • Most Books:
A Revenue: $100K
B Less: Cash Expenses: -40K
C BTCF (A-B): $60K $60K
D x Tax Rate: X .4
E Taxes (CxD): -$24K
F Prelim ATCF (B-E): $36K
G Depreciation: $10K
H x Tax Rate: X .4
I Tax Shield (GxH): +$4K
J ATCF (F+I): $40K
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22 • My Approach � Same Result:
A Revenue: $100K
B Less: Cash Expenses: -40K
C BTCF (A-B): $60K $60K
D Depreciation: -10K
E OP (C-D): $50K
F x Tax Rate: X .4
G Taxes (ExF): -$20K
H ATCF (C-G): $40K
23 • E.g., Co. considering new project• Investment of $420,000• no salvage value• tax rate � 40%• required minimum return � 10%• S/L depreciation with no SV
Cash Flow
1 $ 100K 4 150K
2 200K 5 100K
3 250K 6 100K
$ 900K
24 • Depreciation Tax Shield approach– Assume depreciation deduction is
$70,000/year ($420,000/6)::
CF - Taxes(.4) +Tx Shd ATCF
1 $ 100K - $40K + $28K 88K
2 200K - $80K + 28K 148K
3 250K - 100K + 28K 178K
4 150K - 60K + 28K 118K
5 100K - 40K + 28K 88K
6 100K - 40K + 28K 88K
$ 900K $708K
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25 • Alternative approach:
(A) (B) (C=A-B) (D=.4C)
BTCF Dep TI Tx Rt Taxes
1 $ 100K - $70K = $30K x.4= 12K
2 200K - $70K = 130K x.4= 52K
3 250K - $70K = 180K x.4= 72K
4 150K - $70K = 80K x.4= 32K
5 100K - $70K = 30K x.4= 12K
6 100K - $70K = 30K x.4= 12K
$ 900K $420K $480K $192K
26 • Next, subtract taxes from BTCF:
(A) (D) (A-D)
BTCF -Taxes ATCF
1 $ 100K 12K 88K
2 200K 52K 148K
3 250K 72K 178K
4 150K 32K 118K
5 100K 12K 88K
6 100K 12K 88K
$ 900K $708K
27 • Now, Calculate PV of ATCF:
ATCF x PVIF PV of CF
1 88K x .90909 $ 80,000
2 148K x .82645 122,315
3 178K x .75131 133,733
4 118K x .68301 80,595
5 88K x .62092 54,641
6 88K x .56447 49,673
$708K $520,957
Less Investment: -420,000
NPV: $100,957
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• If NPV > 0 � Co. receiving > minimum required return
–You don’t know actual return
–Turns out you are receiving 18.1% return
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How Do You Handle Salvage Value in NPV?
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• Treat the Salvage Value as an additional cash flow in the last year of the investment.
– It can be a separate line, but it has the same PVIF as the last year’s payoff
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• Remember that the payoffs are ATCF
• You need to subtract the taxes from the assumed sale of the Salvage Value.
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• Are there any taxes on the assumed sale of the Salvage Value?
• This depends on whether there is a gain from the assumed sale.
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• If you used accounting depreciation, then you never depreciated the asset below its salvage value.
• Thus, it still has a BV equal to its salvage value, and the sale produces no gain:
Sale Proceeds – BV = Gain
Salvage Value – Salvage Value = 0 gain
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• If you used MACRS, then you depreciated the asset below its salvage value.
• Thus, it has no BV on the assumed sale
• You therefore have a gain on the assumed sale:
• Sale Proceeds – BV = gain
• Salvage Value – 0 = Salvage Value (gain)
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• If you used MACRS, you have to assume that the Salvage Value taxable
• Thus, you have to reduce it by the tax amount in order to have the ATCF
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Internal Rate of Return
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• IRR is same analysis as NPV � with following modifications:
–Assume NPV = 0
–Solve for discount (interest) rate
• IRR is very popular in business world
• Academics don’t like IRR
• NPV is not used much
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Using Excel To Calculate IRR & NPV
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• Major problem using Excel in calculating NPV
– Excel assumes: “The initial cost [investment] … occurs at the end of the 1st period”
– Excel also assumes that 1st payoff is received at end of 2nd year of investment
– Not traditional assumptions
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• Set up Investment (as negative number) & AFTC as shown below:
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• =NPV (Required Rate of Return, CellsContaining Investment and ATCF)
42 • If you cannot remember NPV notation
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• Excel will give you an NPV of$91,780
• When we did it by hand �
$100,957
• The difference is due to:
–Excel pushes all the cash flowsback 1 year.
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• To correct this, Excel says calculate NPV onpayoff
• Leave off investment
• Then subtract investment.
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46 • Or you can increase each payoff by 1 year’s interest
• to make up for being pushed back one year.
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• IRR
=IRR(cells containing investment & ATCF, guess of the IRR)”
48 • If you cannot remember IRR function:
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50• IRR function gives correct answer.
• Doesn’t matter if you put everything back one year
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Payback Period
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• Simple tool
• Does not use PVs
• PBP reflects feeling that if you get your money back quickly � there is very little risk
• E.g., you can refinance a loan at lower interest rate
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• With PBP, you state how long it takes to recoup your investment
• Many managers are not interested in making investments with LT return
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• If ATCF is same every year, PBP is calculated as follows:
PBP =Original Investment
Annual ATCF
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• E.g., investment is $420K & generates ATCF of $100K/year:
PBP = $420K/$100K = 4.2 years
• If ATCF is uneven �examine cumulative ATCF
56 • Using our previous example:
ATCF Cumulative ATCF
Needed ATCF
1 88K $ 88K $332K
2 148K 236K 184K
3 178K 414K 6K
4 118K 532K
5 88K
6 88K
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• $118K received over entire 4th year
• We need $6K of the $118K:
Portionof Year
=Cash Needed
=$6K
= .05085Total Cash $118K
• PBP is 3.05 years
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Simple Rate of Return(AKA Accounting Rate of Return)
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• SRR uses NI (not ATCF)
• There is a different SRR each year of investment � Average them
SRR =Average Annual NI
Investment
60 • SRR for our previous example
• 1st calculate Average NI:
(A)BTCF
(B)Depr.
(C=A-B) (D=.4C)Taxes
(E=C-D)NI
1 $ 100K - $70K = $30K - 12K = 18K
2 200K - $70K = 130K - 52K = 78K
3 250K - $70K = 180K - 72K = 108K
4 150K - $70K = 80K - 32K = 48K
5 100K - $70K = 30K - 12K = 18K
6 100K - $70K = 30K - 12K = 18K
$900K $420K $480K $192K $288K
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SRR:
Aver Annual NI = $288,000 / 6
Aver Annual NI = $48,000
SRR = Aver NI / Orig Investment
SRR = $48K / $420K
SRR = 11.4%