Financial Management Chapter 09 IM 10th Ed

8/2/2019 Financial Management Chapter 09 IM 10th Ed

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Prof. Rushen Chahal

CHAPTER 9

Capital Budgeting DecisionCriteria

CHAPTER ORIENTATION

Capital budgeting involves the decision making process with respect to the investment infixed assets; specifically, it involves measuring the incremental cash flows associated with

investment proposals and evaluating the attractiveness of these cash flows relative to theproject's costs. This chapter focuses on the various decision criteria.

CHAPTER OUTLINE

I. Methods for evaluating projects

A. The payback period method

1. The payback period of an investment tells the number of yearsrequired to recover the initial investment. The payback period iscalculated by adding the cash inflows up until they are equal to the

initial fixed investment.

2. Although this measure does, in fact, deal with cash flows and is easyto calculate and understand, it ignores any cash flows that occur afterthe payback period and does not consider the time value of moneywithin the payback period.

3. To deal with the criticism that the payback period ignores the timevalue of money, some firms use the discounted payback periodmethod. The discounted payback period method is similar to thetraditional payback period except that it uses discounted free cashflows rather than actual undiscounted free cash flows in calculating

the payback period.4. The discounted payback period is defined as the number of years

needed to recover the initial cash outlay from the discounted free cashflows.

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B. Present-value methods

1. The net present value of an investment project is the present value ofits free cash flows less the investments initial outlay

NPV = tt

n

1t k)(1

FCF

+= - IO

where:

FCFt = the annual free cash flow in time period t (this

can take on either positive or negative values)

k = the required rate of return or appropriatediscount rate or cost of capital

IO = the initial cash outlay

n = the project's expected life

a. The acceptance criteria are

accept if NPV 0

reject if NPV < 0

b. The advantage of this approach is that it takes the time valueof money into consideration in addition to dealing with cashflows.

2. The profitability index is the ratio of the present value of the expectedfuture free cash flows to the initial cash outlay, or

profitability index =

IO

k)(1

FCF

tt

n

1t +=

a. The acceptance criteria are

accept if PI 1.0

reject if PI < 1.0

b. The advantages of this method are the same as those for the net

present value.

c. Either of these present-value methods will give the sameaccept-reject decisions to a project.

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C. The internal rate of return is the discount rate that equates the present value ofthe project's future net cash flows with the project's initial outlay. Thus theinternal rate of return is represented by IRR in the equation below:

IO =t

tn

1t IRR)(1

FCF

+=1. The acceptance-rejection criteria are:

accept if IRR required rate of return

reject if IRR< required rate of return

The required rate of return is often taken to be the firm's cost ofcapital.

2. The advantages of this method are that it deals with cash flows andrecognizes the time value of money; however, the procedure is rathercomplicated and time-consuming. The net present value profile

allows you to graphically understand the relationship between theinternal rate of return and NPV. A net present value profile is simplya graph showing how a projects net present value changes as thediscount rate changes. The IRR is the discount rate at which the NPVequals zero.

3. The primary drawback of the internal rate of return deals with thereinvestment rate assumption it makes. The IRR implicitly assumesthat the cash flows received over the life of the project can bereinvested at the IRR while the NPV assumes that the cash flows overthe life of the project are reinvested at the required rate of return.Since the NPV makes the preferred reinvestment rate assumption it is

the preferred decision technique. The modified internal rate of return(MIRR) allows the decision maker the intuitive appeal of the IRRcoupled with the ability to directly specify the appropriatereinvestment rate.

a. To calculate the MIRR we take all the annual free tax cashinflows, ACIFt's, and find their future value at the end of the

project's life compounded at the required rate of return - this iscalled the terminal value or TV. All cash outflows, ACOFt,

are then discounted back to present at the required rate ofreturn. The MIRR is the discount rate that equates the present

value of the free cash outflows with the present value of theproject's terminal value.

b. If the MIRR is greater than or equal to the required rate ofreturn, the project should be accepted.

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ANSWERS TOEND-OF-CHAPTER QUESTIONS

9-1. Capital budgeting decisions involve investments requiring rather large cash outlays at

the beginning of the life of the project and commit the firm to a particular course ofaction over a relatively long time horizon. As such, they are costly and difficult toreverse, both because of: (1) their large cost and (2) the fact that they involve fixedassets, which cannot be liquidated easily.

9-2. The criticisms of using the payback period as a capital budgeting technique are:

(1) It ignores the timing of the free cash flows that occur during the paybackperiod.

(2) It ignores all free cash flows occurring after the payback period.

(3) The selection of the maximum acceptable payback period is arbitrary.

The advantages associated with the payback period are:

(1) It deals with cash flows rather than accounting profits, and therefore focuseson the true timing of the project's benefits and costs.

(2) It is easy to calculate and understand.

(3) It can be used as a rough screening device, eliminating projects whose returnsdo not materialize until later years.

These final two advantages are the major reasons why it is used frequently.

9-3. Yes. The payback period eliminates projects whose returns do not materialize untillater years and thus emphasizes the earliest returns, which in a country experiencingfrequent expropriations would certainly have the most amount of uncertainty

surrounding the later returns. In this case, the payback period could be used as arough screening device to filter out those riskier projects, which have long lives.

9-4. The three, discounted cash flow capital budgeting criteria are the net present value,the profitability index, and the internal rate of return. The net present value methodgives an absolute dollar value for a project by taking the present value of the benefitsand subtracting out the present value of the costs. The profitability index comparesthese benefits and costs through division and comes up with a measure of theproject's relative valuea benefit/cost ratio. On the other hand, the internal rate ofreturn tells us the rate of return that the project earns. In the capital budgeting area,these methods generally give us the same accept-reject decision on projects but manytimes rank them differently. As such, they have the same general advantages and

disadvantages, although the calculations associated with the internal rate of returnmethod can become quite tedious and it assumes cash flows over the life of the life ofthe project are reinvested at the IRR. The advantages associated with thesediscounted cash flow methods are:

(1) They deal with cash flows rather than accounting profits.

(2) They recognize the time value of money.

(3) They are consistent with the firm's goal of shareholder wealth maximization.

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9-5 The advantage of using the MIRR, as opposed to the IRR technique is that the MIRRtechnique allows the decision maker to directly input the reinvestment rateassumption. With the IRR method it is implicitly assumed that the cash flows overthe life of the project are reinvested at the IRR.

SOLUTIONS TOEND-OF-CHAPTER PROBLEMS

Solutions to Problem Set A

9-1A. (a) IO = FCFt [PVIFIRR%,t yrs]

$10,000 = $17,182 [PVIFIRR%,8 yrs]

0.582 = PVIFIRR%,8 yrs

Thus, IRR = 7%

(b) $10,000 = $48,077 [PVIFIRR%,10 yrs]


Thus, IRR = 17%

(c) $10,000 = $114,943 [PVIFIRR%,20 yrs]


Thus, IRR = 13%

(d) $10,000 = $13,680 [PVIFIRR%,3 yrs]

.731 = PVIFIRR%,3 yrs

Thus, IRR = 11%

9-2A. (a) I0 = FCFt [PVIFAIRR%,t yrs]

$10,000 = $1,993 [PVIFAIRR%,10 yrs]

5.018 = PVIFAIRR%,10 yrs

Thus, IRR = 15%

(b) $10,000 = $2,054 [PVIFAIRR%,20 yrs]


Thus, IRR = 20%

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(c) $10,000 = $1,193 [PVIFAIRR%,12 yrs]


Thus, IRR = 6%

(d) $10,000 = $2,843 [PVIFAIRR%,5 yrs]


Thus, IRR = 13%

9-3A. (a) $10,000 =1IRR)(1

$2,000

++ 2IRR)(1

$5,000

++ 3IRR)(1

$8,000

+

Try 18%:

$10,000 = $2,000(0.847) + $5,000 (0.718) + $8,000 (0.609)= $1,694 + $3,590 + $4,872

= $10,156

Try 19%

$10,000 = $2,000 (0.840) + $5,000 (0.706) + $8,000 (0.593)

= $1,680 + $3,530 + $4,744

= $9,954

Thus, IRR = approximately 19%

(b) $10,000 = 1IRR)(1

$8,000

++ 2IRR)(1

$5,000

++ 3IRR)(1

$2,000

+

Try 30%

$10,000 = $8,000 (0.769) + $5,000 (0.592) + $2,000 (0.455)

= $6,152 + $2,960 + $910

= $10,022

Try 31%:

$10,000 = $8,000 (0.763) + $5,000 (0.583) + $2,000 (0.445)

= $6,104 + $2,915 + $890

= $9,909


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(c) $10,000 = t

5

1t IRR)(1

$2,000

+=

+ 6)IRR1(

000,5$

+

Try 11%

$10,000 = $2,000 (3.696) + $5,000 (0.535)= $7,392 + $2,675

= $10,067

Try 12%

$10,000 = $2,000 (3.605) + $5,000 (0.507)

= $7,210 + $2,535

= $9,745


9-4A. (a) NPV = t6

1t .09)(1$450,000

+=

- $1,950,000

= $450,000 (4.486) - $1,950,000

= $2,018,700 - $1,950,000 = $68,700

(b) PI =000,950,1$

700,018,2$

= 1.0352

(c) $1,950,000 = $450,000 [PVIFAIRR%,6 yrs]


IRR = about 10% (10.1725%)

(d) Yes, the project should be accepted.

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9-5A. (a) Payback Period = $80,000/$20,000 = 4 years

Discounted Payback Period Calculations:

CumulativeUndiscounted Discounted Discounted

Year Cash Flows PVIF10%,n Cash Flows Cash Flows

0 -$80,000 1.000 -$80,000 -$80,000

1 20,000 .909 18,180 -61,820

2 20,000 .826 16,520 -45,300

3 20,000 .751 15,020 -30,280

4 20,000 .683 13,660 -16,620

5 20,000 .621 12,420 -4,200

6 20,000 .564 11,280 7,080

Discounted Payback Period = 5.0 + 4,200/11,280 = 5.37 years.

(b) NPV = t

6

1t .10)(1

$20,000

+=

- $80,000

= $20,000 (4.355) - $80,000

= $87,100 - $80,000 = $7,100

(c) PI =000,80$

100,87$

= 1.0888(d) $80,000 = $20,000 [PVIFAIRR%,6 yrs]


IRR = about 13% (12.978%)

9-6A. (a) NPVA = t

6

1t .12)(1

$12,000

+=

- $50,000

= $12,000 (4.111) - $50,000

= $49,332 - $50,000 = -$668

NPVB = t

6

1t .12)(1

$13,000

+=

- $70,000

= $13,000 (4.111) - $70,000

= $53,443 - $70,000 = -$16,557

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(b) PIA =000,50$

332,49$

= 0.9866

PIB = 000,70$

443,53$

= 0.7635

(c) $50,000 = $12,000 [PVIFAIRR%,6 yrs]


IRRA = 11.53%

$70,000 = $13,000 [PVIFAIRR%,6 yrs]

5.3846 = PVIFAIRR%,6 yrsIRRB = 3.18%

Neither project should be accepted.

9-7A. (a) Project A:

Payback Period = 2 years + $100/$200 = 2.5 years

Project A:




0 -$1,000 1.000 -$1,000 -$1,000

1 600 .909 545 -455

2 300 .826 248 -207

3 200 .751 150 -57

4 100 .683 68 11

5 500 .621 311 322

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Discounted Payback Period = 3.0 + 57/68 = 3.84 years.

Project B:

Payback Period = 2 years + $2,000/$3,000 = 2.67 years

Project B:




0 -$10,000 1.000 -$10,000 -$10,000

1 5,000 .909 4,545 -5,455

2 3,000 .826 2,478 -2,977

3 3,000 .751 2,253 -724

4 3,000 .683 2,049 1,325

5 3,000 .621 1,863 3,188

Discounted Payback Period = 3.0 + 724/2,049 = 3.35 years.

Project C:


Project C:

Discounted Payback Period Calculations:Cumulative

Undiscounted Discounted DiscountedYear Cash Flows PVIF10%,n Cash Flows Cash Flows

0 -$5,000 1.000 -$5,000 -$5,000

1 1,000 .909 909 -4,091

2 1,000 .826 826 -3,265

3 2,000 .751 1,502 -1,763

4 2,000 .683 1,366 -397

5 2,000 .621 1,242 845

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Discounted Payback Period = 4.0 + 397/1,242 = 4.32 years.

Project Traditional Payback Discounted Payback

A Accept Reject

B Accept Reject

C Reject Reject

9-8A. NPV9% = t

8

1t .09)(1

$1,000,000

+=

- $5,000,000

= $1,000,000 (5.535) - $5,000,000

= $5,535,000 - $5,000,000 = $535,000

NPV11% = t

8

1t .11)(1

$1,000,000

+=

- $5,000,000

= $1,000,000 (5.146) - $5,000,000

= $5,146,000 - $5,000,000 = $146,000

NPV13% = +=

8

1t .13)t(1

$1,000,000- $5,000,000

= $1,000,000 (4.799) - $5,000,000

= $4,799,000 - $5,000,000 = -$201,000

NPV15% = t

8

1t .15)(1

$1,000,000

+=

- $5,000,000

= $1,000,000 (4.487) - $5,000,000

= $4,487,000 - $5,000,000 = -$513,000

9-9A. Project A:

$50,000 =1A )IRR(1

$10,000

++

2A )IRR(1

$15,000

++

3A )IRR(1

$20,000

+

+ 4A )IRR(1

$25,000

++ 5

A )IRR(1

$30,000

+

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Try 23%

$50,000 = $10,000(.813) + $15,000(.661) + $20,000(.537)

+ $25,000(.437) + $30,000(.355)

= $8,130 + $9,915 + $10,740 + $10,925 + $10,650

= $50,360

Try 24%

$50,000 = $10,000(.806) + $15,000(.650) +$20,000(.524)

+ $25,000(.423) + $30,000(.341)

= $8,060 + $9,750 + $10,480 + $10,575 + $10,230

= $49,095

Thus, IRR = just over 23%

Project B:$100,000 = $25,000 [PVIFAIRR%,5 yrs]


Thus, IRR = 8%

Project C:

$450,000 = $200,000 [PVIFAIRR%,3 yrs]


Thus, IRR = 16%

9-10A. (a) NPV = t

10

1t .10)(1

$18,000

+=

- $100,000

= $18,000(6.145) - $100,000

= $110,610 - $100,000

= $10,610

(b) NPV = t

10

1t .15)(1

$18,000

+=

- $100,000

= $18,000(5.019) - $100,000

= $90,342 - $100,000

= -$9,658

(c) If the required rate of return is 10% the project is acceptable as in part (a).

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(d) $100,000 = $18,000 [PVIFAIRR%,10 yrs]


IRR = Between 12% and 13% (12.41%)

9-11A. (a) tt

n

0t k)(1

ACOF

+=

=n

tntn

0t

MIRR)(1

k)(1ACIF

+

+ =

$10,000,000 = 1010%10years

MIRR)(1

)(FVIFA$3,000,000

+

$10,000,000 = 10)MIRR1(

)937.15(000,000,3$

+

$10,000,000 =10)MIRR1(

000,811,47$

+MIRR = 16.9375%

(b) $10,000,000 = 1012%10years

MIRR)(1

)(FVIFA$3,000,000

+

$10,000,000 = 10)MIRR1(

)549.17(000,000,3$

+

$10,000,000 = 10)MIRR1(

000,647,52$

+

MIRR = 18.0694%

(c) $10,000,000 = 10years10%14

)MIRR1(

)FVIFA(000,000,3$

+

$10,000,000 = 10)MIRR1(

)337.19(000,000,3$

+

$10,000,000 = 10)MIRR1(

000,011,58$

+

MIRR = 19.2207%

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SOLUTION TO INTEGRATIVE PROBLEM

1. Capital budgeting decisions involve investments requiring rather large cash outlays atthe beginning of the life of the project and commit the firm to a particular course ofaction over a relatively long time horizon. As such, they are both costly and difficult

to reverse, both because of: (1) their large cost; (2) the fact that they involve fixedassets which cannot be liquidated easily.

2. Axiom 5: The Curse of Competitive MarketsWhy It's Hard to Find ExceptionallyProfitable Projects deals with the problems associated with finding profitableprojects. When we introduced that axiom we stated that exceptionally successfulinvestments involve the reduction of competition by creating barriers to entry eitherthrough product differentiation or cost advantages. In effect, without barriers toentry, whenever extremely profitable projects are found competition rushes in,driving prices and profits down unless there is some barrier to entry.

3. Payback periodA

= 3 years +000,50

000,20years = 3.4 years

Payback PeriodB =000,40

000,110years = 2.75 years

Project B should be accepted while project A should be rejected.

4. The disadvantages of the payback period are: 1) ignores the time value of money,2)ignores cash flows occurring after the payback period, 3)selection of the maximumacceptable payback period is arbitrary.

5. Discounted Payback Period Calculations, Project A:



0 -$110,000 1.000 -$110,000 -$110,000

1 20,000 .893 17,860 -92,140

2 30,000 .797 23,910 -68,230

3 40,000 .712 28,480 -39,750

4 50,000 .636 31,800 -7,950

5 70,000 .567 39,690 31,740


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Discounted Payback Period Calculations, Project B:



0 -$110,000 1.000 -$110,000 -$110,000

1 40,000 .893 35,720 -74,280

2 40,000 .797 31,880 -42,400

3 40,000 .712 28,480 -13,920

4 40,000 .636 25,440 11,520

5 40,000 .567 22,680 34,200


Using the discounted payback period method and a 3-year maximum acceptableproject hurtle, neither project should be accepted.

6. The major problem with the discounted payback period comes in setting the firm'smaximum desired discounted payback period. This is an arbitrary decision thataffects which projects are accepted and which ones are rejected. Thus, while thediscounted payback period is superior to the traditional payback period, in that itaccounts for the time value of money in its calculations, its use should be limited dueto the problem encountered in setting the maximum desired payback period. Ineffect, neither method should be used.

7. NPVA =t

tn

1t k)(1

FCF

+=- IO

= $20,000(PVIF12%, 1 year) + $30,000 (PVIF12%, 2 years)

+ $40,000(PVIF12%, 3 years) + $50,000 (PVIF12%, 4 years)

+ $70,000(PVIF12%, 5 years) - $110,000

= $20,000(.893) + $30,000 (.797) + $40,000 (.712) + $50,000

(.636) + $70,000 (.567) - $110,000

= $17,860 + $23,910 + $28,480 + $31,800 + $39,690 - $110,000

= $141,740-$110,000

= $31,740

NPVB = $40,000(PVIFA12%, 5 years) - $110,000

= $40,000(3.605) - $110,000

= $144,200-$110,000

= $34,200

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Both projects should be accepted

8. The net present value technique discounts all the benefits and costs in terms of cashflows back to the present and determines the difference. If the present value of thebenefits outweighs the present value of the costs, the project is accepted, if not, it isrejected.

9. PIA =

IO

k)(1

FCF

t

t

n

1t

+

=

=000,110$

740,141$

= 1.2885

PIB =000,110$

200,144$

= 1.3109

Both projects should be accepted

10. The net present value and the profitability index always give the same accept rejectdecision. When the present value of the benefits outweighs the present value of thecosts the profitability index is greater than one, and the net present value is positive.In that case, the project should be accepted. If the present value of the benefits is lessthan the present value of the costs, then the profitability index will be less than one,and the net present value will be negative, and the project will be rejected.

11. For both projects A and B all of the costs are already in present dollars and, as such,will not be affected by any change in the required rate of return or discount rate. Allthe benefits for these projects are in the future and thus when there is a change in therequired rate of return or discount rate their present value will change. If the requiredrate of return increased, the present value of the benefits would decline which wouldin turn result in a decrease in both the net present value and the profitability index foreach project.

12. IRR A = 20.9698%

IRRB = 23.9193%13. The required rate of return does not change the internal rate of return for a project,

but it does affect whether a project is accepted or rejected. The required rate of returnis the hurdle rate that the project's IRR must exceed in order to accept the project.

14. The net present value assumes that all cash flows over the life of the project arereinvested at the required rate of return, while the internal rate of return implicitlyassumes that all cash flows over the life of the project are reinvested over the

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remainder of the project's life at the IRR. The net present value method makes themost acceptable, and conservative assumption and thus is preferred.

15. Project A:

t

tn

0t k)(1

ACOF

+= = n

n

0t

tn

t

MIRR)(1

k)(1ACIF

+

+

=

$110,000 =

5

A

12%12%

12%12%

)MIRR(1

$70,000

year)1,IF$50,000(FVyears)2,IF$40,000(FV

years)3,IF$30,000(FVyears)4,IF$20,000(FV

++

+++

$110,000 =5

A )MIRR(1

000,70$)120.1(000,50$)254.1(000,40$)405.1(000,30$)574.1(000,20$

+

++++

$110,000 = 5A )MIRR(1

000,70$000,56$160,50$150,42$480,31$

+++++

$110,000 = 5A )MIRR1(

790,249$

+

MIRRA = 17.8247%

Project B:

$110,000 =5

B

,5years12%

)MIRR(1

)IFA$40,000(FV

+

$110,000 = 5B)MIRR(1

353)$40,000(6.

+

$110,000 = 5B)MIRR(1

$254,120

+

MIRRB = 18.2304%

Both projects should be accepted because their MIRR exceeds the required rate of return.The modified internal rate of return is superior to the internal rate of return method becauseMIRR assumes the reinvestment rate of cash flows is the required rate of return.

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Solutions to Problem Set B

9-1B. (a) IO = FCFt [PVIFIRR%,t yrs]

$10,000 = $19,926[PVIFIRR%,8 yrs]


Thus, IRR = 9%

(b) $10,000 = $20,122[PVIFIRR%,12 yrs]


Thus, IRR = 6%

(c) $10,000 = $121,000[PVIFIRR%,22 yrs]


Thus, IRR = 12%

(d) $10,000 = $19,254 [PVIFIRR%,5 yrs]


Thus, IRR = 14%

9-2B. (a) IO = FCFt [PVIFAIRR%,t yrs]

$10,000 = $2,146 [PVIFAIRR%,10 yrs]


Thus, IRR = 17%

(b) $10,000 = $1,960 [PVIFAIRR%,20 yrs]


Thus, IRR = 19%

(c) $10,000 = $1,396 [PVIFAIRR%,12 yrs]

7.163 = PVIFAIRR%,12 yrs]

Thus, IRR = 9%

(d) $10,000 = $3,197 [PVIFAIRR%,5 yrs]


Thus, IRR = 18%

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9-3B. (a) $10,000 =1IRR)(1

$3,000

++ 2IRR)(1

$5,000

++ 3IRR)(1

$7,500

+

Try 21%:

$10,000 = $3,000(0.826) + $5,000 (0.683) + $7,500 (0.564)= $2,478+ $3,415 + $4,230

= $10,123

Try 22%

$10,000 = $3,000 (0.820) + $5,000 (0.672) + $7,500 (0.551)

= $2,460 + $3,360 + $4,132.50

= $9,952.50


(b) $12,000 = 1IRR)(1

$9,000

++ 2IRR)(1

$6,000

++ 3IRR)(1

$2,000

+

Try 25%

$12,000 = $9,000 (0.800) + $6,000 (0.640) + $2,000 (0.512)

= $7,200 + $3,840 + $1,024

= $12,064

Try 26%:

$12,000 = $9,000 (0.794) + $6,000 (0.630) + $2,000 (0.500)

= $7,146 + $3,780 + $1,000

= $11,926

Thus, IRR = nearest percent is 25%

(c) $8,000 =t

5

1t IRR)(1

$2,000

+=

+ 6IRR)(1

$5,000

+

Try 18%

$8,000 = $2,000 (3.127) + $5,000 (0.370)

= $6,254 + $1,850= $8,104

Try 19%

$8,000 = $2,000 (3.058) + $5,000 (0.352)

= $6,116 + $1,760

= $7,876

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Thus, IRR = nearest percent is 18%

9-4B. (a) NPV = t

6

1t .11)(1

$750,000

+=

- $2,500,000

= $750,000 (4.231) - $2,500,000

= $3,173,250 - $2,500,000

= $673,250

(b) PI =000,500,2$

250,173,3$

= 1.2693

(c) $2,500,000 = $750,000 [PVIFAIRR%,6 yrs]


IRR = about 20% (19.90%)

(d) Yes, the project should be accepted.

9-5B. (a) Payback Period = $160,000/$40,000 = 4 years

(b) NPV = t

6

1t .10)(1

$40,000

+=

- $160,000

= $40,000 (4.355) - $160,000

= $174,200 - $160,000 = $14,200

(c) PI =000,160$200,174$

= 1.0888

(d) $160,000 = $40,000 [PVIFAIRR%,6 yrs]


IRR = about 13% (12.978%)

9-6B. (a) NPVA = t

6

1t .12)(1

$12,000

+=

- $45,000

= $12,000 (4.111) - $45,000

= $49,332 - $45,000 = $4,332

NPVB = t

6

1t .12)(1

$14,000

+=

- $70,000

= $14,000 (4.111) - $70,000

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= $57,554 - $70,000 = -$12,446

(b) PIA =000,45$

332,49$

= 1.0963

PIB =000,70$

554,57$

= 0.822

(c) $45,000 = $12,000 [PVIFAIRR%,6 yrs]


IRRA = 15.34%

$70,000 = $14,000 [PVIFAIRR%,6 yrs]


IRRB = 5.47%

Project A should be accepted.

9-7B. (a) Project A:

Payback Period = 2 years

Project B:


Project C:Payback Period = 3 years + $1,000/$2,000 = 3.5 years

Project Payback Period Method

A Accept

B Accept

C Reject

9-8B. NPV9% = t

8

1t .09)(1

$2,500,000

+= - $10,000,000

= $2,500,000 (5.535) - $10,000,000

= $13,837,500 - $10,000,000 = $3,837,500

NPV11% = t

8

1t .11)(1

$2,500,000

+=

- $10,000,000

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= $2,500,000 (5.146) - $10,000,000

= $12,865,000 - $10,000,000 = $2,865,000

NPV13% = t

8

1t .13)(1

$2,500,000

+=

- $10,000,000

= $2,500,000 (4.799) - $10,000,000

= $11,997,500 - $10,000,000 = $1,997,500

NPV15% = t

8

1t .15)(1

$2,500,000

+=

- $10,000,000

= $2,500,000 (4.487) - $10,000,000

= $11,217,500 - $10,000,000 = $1,217,500

9-9B. Project A:

$75,000 =1

A )IRR(1$10,000+

+ 2A )IRR(1

$10,000+

+ 3A )IRR(1

$30,000+

+ 4A )IRR(1

$25,000

++ 5

A )IRR(1

$30,000

+

Try 10%

$75,000 = $10,000(.909) + $10,000(.826) + $30,000(.751)

+ $25,000(.683) + $30,000(.621)

= $9,090 + $8,260 + $22,530 + $17,075 + $18,630

= $75,585

Try 11%

$75,000 = $10,000(.901) + $10,000(.812) +$30,000(.731)

+ $25,000(.659) + $30,000(.593)

= $9,010 + $8,120 + $21,930+ $16,475 + $17,790

= $73,325

Thus, IRR = just over 10%

Project B:

$95,000 = $25,000 [PVIFAIRR%,5 yrs]


Thus, IRR = just below 10%

Project C:

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$395,000 = $150,000 [PVIFAIRR%,3 yrs]


Thus, IRR = just below 7%

9-10B. (a) NPV = t

10

1t .09)(1$25,000+= - $150,000

= $25,000(6.418) - $150,000

= $160,450 - $150,000

= $10,450

(b) NPV = t

10

1t .15)(1

$25,000

+=

- $150,000

= $25,000(5.019) - $150,000

= $125,475 - $150,000

= -$24,525

(c) If the required rate of return is 9% the project is acceptable in part (a). Itshould be rejected in part (b) with a negative NPV.

(d) $150,000 = $25,000 [PVIFAIRR%,10 yrs]


IRR = Between 10% and 11% (10.558%)

9-11B. (a) ttn

0 k)(1

ACOF+

=t

=n

t-nt

n

0t

MIRR)(1

k)(1ACIF

+

+=

$8,000,000 =8

,8years10%

MIRR)(1

)(FVIFA$2,000,000

+

$8,000,000 = 8MIRR)(1

(11.436)$2,000,000

+

$8,000,000 = 8MIRR)(1

$22,872000

+MIRR = 14.0320%

b) $8,000,000 =8

,8years12%

MIRR)(1

)(FVIFA$2,000,000

+

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Prof. Rushen Chahal

$8,000,000 = 8MIRR)(1

(12.300)$2,000,000

+

$8,000,000 = 8MIRR)(1

0$24,600,00

+

MIRR = 15.0749%

c) $8,000,000 =8

,8years14%

MIRR)(1

)(FVIFA$2,000,000

+

$8,000,000 = 8MIRR)(1

(13.233)$2,000,000

+

$8,000,000 = 8MIRR)(1

0$26,466,00

+

MIRR = 16.1312%

FORD'S PINTO(Ethics in Capital Budgeting)

OBJECTIVE: To force the students to recognize the role ethical behavior plays in allareas of Finance.

DEGREE OF DIFFICULTY: Easy

Case Solution:

With ethics cases there are no right or wrong answers - just opinions. Try to bring outas many opinions as possible without being judgmental.

Documents

Financial Management Chapter 09 IM 10th Ed