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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%