mba711 - answers to all chapter 7 problems

Capital Budgeting Process and Techniques 93

Chapter 7: Capital Budgeting Process and Techniques

Answers to questions

7-1. a. Type I error means rejecting a good project. Payback could lead to Type 1 errors when it rejects a good project that has large cash flows after the payback period cutoff. Payback ignores cash flows after the cutoff.

b. Type II error means accepting a project that should have been rejected. Type II errors occur when payback says to accept a project that doesn't return enough to compensate for the risk taken. This occurs because payback makes no adjustments for risk or time value of money.

c. If firms apply the payback rule with a fairly short cutoff period, then a type I error is more likelygood projects with higher cash flows in later years may be rejected. On the other hand, if firms apply the payback rule but use a long cutoff period, then a Type II error becomes more likely because the payback method makes no adjustment for the time value of money.

7-2. Discounted payback has a more severe biasdiscounted cash flows will be smaller, making it even harder for a project to pass the payback hurdle. For example, if the cutoff period is four years, then every project that satisfies the discounting payback rule will also satisfy payback, but the reverse is not true.

7-3. The NPV approach is consistent with shareholder maximization because it suggests that firms should only accept projects that earn returns above the opportunity costs of the firm’s investors. The NPV in effect measures the dollar contribution that the given project is expected to make to the firm’s overall value. If a firm invests in a project with NPV > $0, then the share price will rise. Conversely, a firm’s share price will fall if it invests in projects with NPV < $0.

7-4. It is true that long-term projections are more prone to error than are short-term projections. However, there are two reasons why this simple truth does not lead to the conclusion that the payback approach is superior to NPV. First, the payback approach itself implicitly makes long-term cash flow projections. Specifically, the payback approach forecasts zero cash flows beyond the payback horizon. The real question is not whether long-term forecasts are more or less accurate than short-term forecasts are, but whether a long-term forecast can be more accurate than a naïve guess of zero. Second, via discounting, the NPV approach makes an adjustment for the high degree of risk in long-term projections. The farther into the future that a given project’s cash flows arrive, the less valuable those cash flows are in an NPV calculation. NPV automatically adjusts for project time by using an exponentially smaller discount rate applied to later cash flows.

7-5. Any method can be manipulated. Smart managers must be aware of this and must be prepared to press analysts to justify their numbers. Opportunities to manipulate the numbers are not unique to the NPV approach and can therefore not be used to justify payback, accounting rate of return, or any other approach over NPV. It would be hard to argue that accounting numbers can’t be manipulated after all the accounting scandals, starting with Enron in late 2001. Managers should have incentives to provide the most accurate information possible.

7-6. a. A firm that consistently earns returns higher than its opportunity cost of capital is adding value to the firm, and its stock returns should increase. Stock returns should be well above average for companies of this risk level.

b. For the project returning 18%, as long as it returns enough to compensate for the risk of

94 Chapter 7

the project, it is adding value and shareholders will be happy about the decision to accept the project.

7-7. The IRR suffers from several problems. The IRR is not well suited to ranking projects with very different scales or projects with very different cash flow timing patterns due to the reinvestment assumption. The IRR method can also yield no solution or multiple solutions that are hard to interpret. Despite the flaws, the IRR method enjoys widespread use because in most investment situations it generates reliable accept/reject recommendations and it is easy to interpret intuitively. The MIRR method uses a more realistic reinvestment rate. Also, there can be only one MIRR for a project.

7-8. Because the discounted payback period equals the life of the projected, the sum of all of the discounted cash flows must equal the cost of the project. This indicates that the NPV must also be zero and that the IRR equals 10% because the NPV is zero.

7-9. The NPV is the most appropriate capital budgeting method because it yields correct accept/reject situations and correct project rankings. Nevertheless, it is somewhat less intuitive than the IRR. In projects with cash flow streams that switch signs, the IRR method can yield multiple solutions. In those cases, it is difficult for a firm to know whether to accept or reject a project based upon its IRR.

7-10. The NPV is calculated by discounting all of a project’s cash flows to the present. The IRR is calculated by finding the discount rate, which equates the NPV to zero. The profitability index is the ratio of the present value of a project’s cash flows (excluding the initial cash outflow) divided by the initial cash outflow. All three methods lead to the same accept/reject decision when evaluating a single project, but IRR and PI have problems when ranking projects. NPV generally overcomes these problems.

7-11. IRR, NPV, and PI can lead to different decisions when they are used to rank projects or to select between mutually exclusive projects. IRR and PI methods are not well suited to evaluating projects that vary in scale. The NPV method yields correct project rankings no matter what the scale of the project.

7-12. If an unlimited capital budget exists, firms should always accept every independent project with NPV > $0. When funds are limited, firms should select the group of projects which has the highest aggregate NPV yet stays within the budget constraint.

7-13. Project A recovers its cost in 2 years and Project B recovers its cost in 3 years. Consequently, the payback period for Project A is two years and the payback period for Project B is three years making Project A preferred based on the shortest payback period criteria. However, Project B is the better project because of the $10,000.00 cash flow in the fourth year. The problem with the payback criteria is that it does not encompass all of the cash flows of the project.

Answers to problems

7-1. a. If the computers are depreciated on a straight-line basis, depreciation will be $5,000 per year for 4 years. Contribution to net income will be:

Year 1 Year 2 Year 3 Year 4$7,500 $9,100 $9,100 $9,100


–5,000 –5,000 –5,000 –5,000$2,500 $4,100 $4,100 $4,100

The average net income is ($2,500 + $4,100 + $4,100 + $4,100)/4 = $3,700

b. The average book value of the investment is ($20,000 + 0)/2 = $10,000.

c. The average accounting rate of return = Average net income/Average book value of the investment = $3,700/$10,000 = .37 or 37%.

d. The payback period is 2.37 years, based on cash flow numbers, not net income.

e. This is not an appropriate method for evaluating capital budgeting projects. It does not take time value of money into account, nor does it look at cash flows. It also does not consider the risk of the project and what would be an appropriate discount rate in light of the project's cash flows.

7-2. a. Payback on this bond is 25 years. You pay $1,000; you receive $40 a year for 25 years, a total of $1,000.

b. The bond is not necessarily a bad investment. Payback does not take time value of money into account, nor does it account for cash flows received after the payback period. It is more appropriate to calculate the NPV of an investment. Given the risk level of the bond, is 4% a fair return? If the answer is yes, then the bond may be a good investment.

c. The discounted payback, using a 4% discount rate, is 30 years. This shows that unless the acceptable payback period is decreased when discounted payback is used, vs. regular payback, then projects that return money late in the life of the investment are even more disadvantaged under discounted payback than under regular payback. NPV is a more appropriate method to use to determine the value of an investment project. The general rule is that when a project’s discounted payback period is the same as its life, then the NPV must be zero.

7-3. a. Payback of Alpha = 3.5 years, payback of Beta = 2.5 years, payback of Gamma = 3.33 years

b. If the cutoff is 3 years, then only Beta is acceptable. If the cutoff is 4 years, then all of the projects are acceptable.

c. Beta has the fastest payback.

d. If the firm uses discounted payback with a cutoff of 4 years, then Alpha will payback in more than 5 years, Beta in just under 3 years and Gamma in between 4 and 5 years. This means only Beta is acceptable. Calculations are shown in the table that follows.

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Alpha ($1,500,000) Beta ($400,000) Gamma ($7,500,000)End of

YearCF PV of CF

@ 15% Cum PV CF PV of CF @ 15% Cum PV CF PV of CF

@ 15% Cum PV

1 300K $260,870 $260,870 100K $86,957 $86,957 2,000K $1,739,130 $1,739,1302 500K 378,072 638,942 200K 165,997 252,954 3,000K 226,8431 4,007,5613 500K 328,758 967,700 200K 151,229 404,183 2,000K 1,315,032 5,322,5934 400K 228,701 1,196,401 100K 68,887 473,070 1,500K 857,630 6,180,2235 300K 149,153 1,354,554 -200K -125,517 347,553 5,500K 2,734,472 8,914,695

Disc Pay-back

>5 yearsReject

>3 & 4 years <Accept

>4 & 5 years<Reject

e. Project Beta should be rejected. You must pay out a total of .6 million and take in .6 million. When there is a time value to money, in other words, a positive interest rate, this is unacceptable. If cash inflows and outflows are the same, this is a negative net present value project.

f. Project Gamma is rejected using discounted payback (as noted in d.), but even without discounting, seems to have a high dollar return for the investment. You pay $7.5 million and receive a total of $14 million in cash inflows. Unless the firm has a very high discount rate, greatly lowering the value of the last $5.5 million cash flow, this is likely to be an attractive investment.

7-4. a. To determine the accounting rate of return (AAR) we need to first determine the annual net income by subtracting the depreciation from the Cash Flow, as shown in the table below.

Asset A Asset B $200,000 ÷ 2 = $100,000 $180,000 ÷ 2 = $90,000

Year CF Depr.Net

Income CF Depr.Net

Income1 $70,000 $40,000 $30,000 $80,000 $36,000 $44,0002 $80,000 $40,000 $40,000 $90,000 $36,000 $54,0003 $90,000 $40,000 $50,000 $30,000 $36,000 $(6,000)4 $90,000 $40,000 $50,000 $40,000 $36,000 $4,0005 $100,000 $40,000 $60,000 $40,000 $36,000 $4,000

Average = $46,000 Average = $20,000

ARRA = $46,000 ÷ $100,000 = 46%ARRB = $20,000 ÷ $90,000 = 22.22%

Given that the minimum acceptable ARR is 30%, only Asset A is acceptable.

b.Asset A Asset B

Year Cash Flows Amount still to Cash Flows Amount still to


be recovered be recovered0 -$200,000 -$180,0001 $70,000 ($130,000) $80,000 ($100,000)2 $80,000 ($50,000) $90,000 ($10,000)3 $90,000 $30,000 4 $90,000 $40,000 5 $100,000 $40,000

Asset A has $50,000 left to be recovered after year 2, or 0.56 of year 3. Thus, Asset A’s payback is 2.56 years. Asset B has $10,000 to be recovered after year 2, or 0.33 of year 3. Asset B’s payback period is 2.33 years. According to the maximum payback period requirement of 2.5 years, only Asset B is acceptable.

c.

Year Asset A Asset BDiscounted Cash Flows

Amount still to be recovered

Discounted Cash Flows

Amount still to be recovered

0 ($200,000) ($180,000)1 $62,500 ($137,500) $71,429 ($108,571)2 $63,776 ($73,724) $71,747 ($36,824)3 $64,060 ($9,664) $21,353 ($15,471)4 $57,197 $25,421 5 $56,743 $22,697

After the third year, Asset A still has $9,664 left to be recovered. This represents 0.17 of the year; thus, Asset A’s discounted payback period is 3.17 years. Asset B still needs to recover $15,471 after the third year. This is 0.61 of the fourth year. Thus, Asset B’s discounted payback period is 3.61 years. Asset A is acceptable according to the firm’s maximum discounted payback period.

d. All the evaluation methods suffer from serious flaws. The firm should re-evaluate the projects using the NPV method or the MIRR method.

7-5. a. This project has CF0 = –$15,000, and 20 inflows of $13,000. At a 14% discount rate, its NPV is $71,100.70. This is a positive NPV and an acceptable project.

b. This project has CF0 = –$32,000 and 20 inflows of $4,000. At 14%, its NPV is –$5,507.48. This is a negative NPV and is not acceptable.

c. This project has CF0 = –$50,000, and 20 inflows of $8,500. At a 14% discount rate, its NPV is $6,296.61. This is a positive NPV and an acceptable project.

7-6. CF0 = –$19,000Cash flows of $4,000/year for 8 years.

a. NPV at 10% = $2,339.70, accept

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b. NPV at 12% = $870.56, accept

c. NPV at 14% = –$444.54, reject

Only positive NPV projects are acceptable. As the discount rate increases, NPV decreases. At some point, if the discount rate is high enough, a previously acceptable project at lower discount rates may become unacceptable.

7-7. Discount rate = 14%Project NPV Decision

A –$4,351.65 RejectB $67,678.24 AcceptC –$71,798.07 RejectD $98,189.82 AcceptE $8,548.44 Accept

7-8. Discount rate = 15%Project NPV Decision

A –$5,253.57 RejectB $2,424.27 AcceptC $17,992.95 Accept

Project C is the best, followed by Project B. Project A is the worst project, and is unacceptable.

7-9. NPV of project = $9,972,742Current firm value = $10 x 10,000,000 = $100,000,000New firm value = $100,000,000 + $9,972,742 = $109,972,742New stock price = $109,972,742 / 10,000,000 = $11.00 per shareThis project should add $10,000,000 or $1 per share to the firm’s overall value.

7-10. The NPV of Project LMN is $225.21: (-$10,000.00 + [$2,825.00 ÷ (1 + 12%)] + [$3,192.25 ÷ (1 + 12%)2] + [$3,607.24 ÷ (1 + 12%)3] + [$4,076.18 ÷ (1 + 12%)4] = $225.21).

The annual return is 8.19%: ([$13,700.67 ÷ $10,000.00]0.25 – 1 = 8.19%

Because the cash flows are not reinvested. This is contrary to an implicit reinvestment assumption in the NPV calculation. If the cash flows earned 12% interest upon receipt then the annual return would also be 12%.

7-11. Project IRRA 17.4%B 8.7%C 27.2%D 21.4%

7-12. a. Project A: IRR = 15.7%Project B: IRR = 17.3%


b. With a cost of capital of 15%, both projects are acceptable.

c. Project B has a higher IRR, and is preferred to Project A, based on the IRR criterion.

7-13. a. After three years of cash flows, only $426.87 of the fourth year cash flow is necessary to recover the cost of the project. Thus, the payback period is 3.3024 years ( 3 years + ($426.87 ÷ $1,411,48) years).

b. The discounted payback period is 4 years: (-$4,000.00 + [$1,090.00 ÷ (1 + 9%)] + [$1,188.10 ÷ (1 + 9%)2] + [$1,295.03 ÷ (1 + 9%)3] + [$1,411.58 ÷ (1 + 9%)4] = $0.00).

c&d. This is equivalent to an NPV of zero and an IRR of 9%.

7-14. The NPV for Project Z is $0.00: (-$6,000.00 + [$1,725.00 ÷ (1 + 15%)] + [$1,983.75 ÷ (1 + 15%)2] + [$2,281.31 ÷ (1 + 15%)3] + [$2,623.51 ÷ (1 + 15%)4] = $0.00). Because the NPV is zero, the profitability index is 1.0, the discounted payback period is 4 years (i.e. the life of the project), and the IRR is 15%.

7-15.Project NPV IRRRenovate $1,128,309 20.5%Replace $433,779 36.1%

The Renovate project has a higher NPV and the Replace project has a higher IRR.

a. Ranking on NPV: Renovate, Replace

b. Ranking on IRR: Replace, Renovate

c. The rankings provide mixed signals because of the differences in the site and timing of the cash flow patterns and initial investments of the two projects. Projects that have lower initial investments and return their cash flows earlier in the life of the project tend to have higher IRRs, as is the case with the Replace project.

d. The incremental project has the following cash flows:

Year Renovate Replace Renovate - Replace0 –$9,000,000 –$1,000,000 –$8,000,0001 3,500,000 600,000 2,900,0002 3,000,000 500,000 2,500,0003 3,000,000 400,000 2,600,0004 2,800,000 300,000 2,500,0005 2,500,000 200,000 2,300,000

The IRR of the incremental project is 18.7%. This is greater than the discount rate of 15%. For a conventional project, accept projects with IRRs greater than the hurdle rate. Since the incremental project is acceptable, this means the project on top (Renovate) – the one from which cash flows were subtracted, is the better project. This is consistent with the NPV criterion – accept the project with the highest NPV, in this case, the

100 Chapter 7

Renovate project.

7-16.

a.

Let

Using the quadratic formulaax2 + bx + c = 0

and

b. Because the undiscounted NPV of the project is positive (i.e.; $–20,000 + $50,000 – $10,000 = $20,000) the project will have a positive NPV at all discount rates between –78.07% and +127.27%. Therefore the firm can accept the project as long as its cost of capital falls between the two IRRs.

c. To determine the MIRR, solve for the interest rate that equates the present value of the outflows to the future value of the inflows, with the discount rate and compounding rate equal to the firm’s cost of capital.

Year CF FV @ 15% PV @ 15%0 -20000 ($20,000.00)1 50000 $57,500.00 2 -10000 ($7,561.44)

$57,500.00 ($27,561.44)

$27,561.44 = $57,500 ÷ [(1+i)2]

MIRR = I = 44.44%

–78.07%


The project is acceptable according to the MIRR.

7-17. a.

Let

Using the quadratic formulaax2 + bx + c = 0

and

b.Interest

Rate NPV0 $960,000.00

50 $337,777.78 100 $135,000.00 150 $49,920.00 200 $8,888.89 250 ($12,594.75)

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NPV Profile

($200,000.00)

$0.00

$200,000.00

$400,000.00

$600,000.00

$800,000.00

$1,000,000.00

$1,200,000.00

0 50 100 150 200 250 300

Interest Rate

NPV

c. Yes, because at 25% the NPV is positive.

d. To determine the MIRR, solve for the interest rate that equates the present value of the outflows to the future value of the inflows, with the discount rate and compounding rate equal to the firm’s cost of capital.

Year CF FV @ 15% PV @ 15%0 -480,000 ($480,000)1 1,560,000 $1,794,000 2 -120,000 ($90,737)

77% $1,794,000 ($570,737)

$570,737 = $1,794,000 ÷ [(1+i)2]

MIRR = I = 77.29%

The project is acceptable according to the MIRR.

7-18.a. Cost of Capital Project NPV

0 $05 $–1.35

10 015 $0.5620 025 $–0.67230 035 $3.4650 $41.48

b.


NPV Profile

-100

1020304050

0 20 40 60Cost of Capital

NPV

c. The project has an IRR at every point where it crosses the discount rate axis, in this case at 0%, 10%, 20% and 30%. The four IRRs correspond to the four changes in sign of the project’s cash flows.

d. This project is acceptable at discount rates between 10% and 20% and when the discount rate is greater than 30% in those cases the NPV is positive.

7-19. The PIs at the end of each project are listed below:

a. PI of Liquidate = $138,161 / $100,000 = 1.38PI of Recondition = $402,564 / $500,000 = 0.81PI of Replace = $1,141,613 / $1,000,000 = 1.14

b. Accept both Liquidate and Replace because both have a PI > 1.0

c. Accept Liquidate because it has the highest PI.

d. According to the NPV, the ranking would be Replace, Liquidate and then Recondition. If the projects are independent, Replace and Liquidate are acceptable, while Recondition is not viable. If the projects are mutually exclusive, Replace should be chosen.

Liquidate Recondition Replace

Year Cash FlowDiscounted

@ 15% Cash FlowDiscounted

@ 15% Cash FlowDiscounted

@ 15%0 $(100,000) $(100,000) $(500,000) $(500,000) $(1,000,000) $(1,000,000)1 $50,000 $43,478 $100,000 $86,957 $500,000 $434,7832 $60,000 $45,369 $200,000 $151,229 $500,000 $378,0723 $75,000 $49,314 $250,000 $164,379 $500,000 $328,758

NPV $38,161 $(97,436) $141,613

e. When the projects are mutually exclusive, the PI method and NPV method result in a dilemma, as PI argues for Liquidate while NPV argues for Replace. The reason for this dilemma is due to the large scale differences in the projects.

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7-20. a. NPV1 = –$4,000,000 + $1,000,000 x (1.12)-1 + $2,000,000 x (1.12)-2 + $3,000,000 x (1.12)-3 = $622,586NPV2 = –$5,000,000 + $2,000,000 x (1.12)-1 + $3,000,000 x (1.12)-2 + $3,000,000 x (1.12)-3 = $1,312,637NPV3 = –$10,000,000 + $4,000,000 x (1.12)-1 + $6,000,000 x (1.12)-2 + $5,000,000 x (1.12)-3 = $1,913,493 [highest NPV]

b. PI1 = $4,622,586 / $4,000,000 = 1.16PI2 = $6,312,637 / $5,000,000 = 1.26 [highest PI]PI3 = $11,913,493 / $10,000,000 = 1.19

c. Although Project # 2 provides “more bang for the buck” as represented by its higher PI, Project #3 should be accepted since it has the higher NPV and there are no other investments under consideration. It adds most to the firm.

7-21. The NPV of Project ABC is $818.18: (-$1,000.00 + [$2,000.00 ÷ (1 + 10%)] = $818.18. The NPV of Project QRS is $2,000.00: (-$10,000.00 + [$4,400.00 ÷ (1 + 10%)] + [$4,840.00 ÷ (1 + 10%)2] + [$5,324.00 ÷ (1 + 10%)3] = $2,000.00).

The profitability index of Project ABC is 1.818: ( 1 + [NPV ÷ Cost] = 1 + [$818.18 ÷ $1,000.00] = 1.818). The profitability index of Project QRS is 1.20: (1 + [$2,000.00 ÷ $10,000.00] = 1.20).

Based on NPV, Project QRS is considered better. Based on profitability index, Project ABC is better.

7-22. a. The discounted payback period for Project X is 3 years (36 months): (-$3,300.00 + [$1,232.00 ÷ (1 + 12%)] + [$1.379.84 ÷ (1 + 12%)2] + [$1,545.42 ÷ (1 + 12%)3] = $0.00). The discounted payback period for Project Y is 4 years (48 months): (-$5,000.00 + [$1,412.50 ÷ (1 + 13%)] + [$1,596.13 ÷ (1 + 13%)2] + [$1,803.62 ÷ (1 + 13%)3] + [$2,038.09 ÷ (1 + 13%)4] = $0.00).

b. Given the threshold of 42 months, Project X is the better project.

c. The NPV of Project X is $1,100.00: (-$3,300.00 + [$1,232.00 ÷ (1 + 12%)] + [$1.379.84 ÷ (1 + 12%)2] + [$1,545.42 ÷ (1 + 12%)3] + [$1,730.87 ÷ (1 + 12%)4] = $1,100.00). The NPV of Project Y is $1,250.00: (-$5,000.00 + [$1,412.50 ÷ (1 + 13%)] + [$1,596.13 ÷ (1 + 13%)2] + [$1,803.62 ÷ (1 + 13%)3] + [$2,038.09 ÷ (1 + 13%)4] + [$2,303.04 ÷ (1 + 13%)5]= $1,250.00). Using the NPV criteria, Project Y is better.

d. The profitability index of Project X is 1.333: ( 1 + [NPV ÷ Cost] = 1 + [$1,100.00 ÷ $3,300.00] = 1.333). The profitability index of Project Y is 1.250: ( 1 + [$1,250.00 ÷ $5,000.00] = 1.250). Based on the profitability index, Project X is better.

7-23. Project Cash Flows (in millions):

a. At Old Line's discount rate of 10%, this project has an NPV of about $474,000 and an


IRR of 15.9%. This project would be acceptable for Old Line.

c. At High Tech's 20% discount rate, the project NPV is about –$287,000. This makes the project unacceptable to High Tech due to its negative NPV.

c. The cost of capital is very important to the acceptance of a project. A firm that has a lower cost of capital will find more projects acceptable and, all other things equal, will potentially add more value for shareholders.

7-24.

a. At 10%, the NPV of the project is $1,421.04.

b. The IRR is 12.13%

c. This project is acceptable by both NPV and IRR criteria. It has a positive NPV and its IRR is greater than its hurdle rate of 10%.

7-25. a. The payback period is 3.56 years.

End of Year CF Cum CF

1 $18,000 $18,0002 22,500 45,0003 27,000 67,5004 31,500 99,0005 36,000 135,000

b. NPV is $8,672.54

c. IRR is 15.6%.

d. This project is acceptable by both NPV and IRR criteria. It has a positive NPV and its IRR of 15.6% is greater than its hurdle rate of 12%.

7-26.

Projecta.

Paybackb.

NPVc.

IRRX 2.96 years $14,965.24 20.4%Y 3.17 years $14,206.48 17.4%Z 3.37 years $6,240.94 14.75%

d. Ranking on Payback: X,Y,Z

Ranking on NPV: X,Y,Z

Ranking on IRR: X,Y,Z

106 Chapter 7

All measures agree that X is best, followed by Y, and then and Z. Since they are mutually exclusive projects, accept the project with the highest NPV, which is Project X.

7-27.Year All at once Gradual

0 –$5,000,000 –$1,000,0001 –$2,000,0002 –$2,000,0003 –$2,000,000

The NPV of the immediate program is –$5 million. The NPV of the phase-in program, at a discount rate of 15%, is –$5.57 million. It is cheaper to implement the immediate pollution control program.

7-28. All measures indicate project acceptability.NPV > 0IRR >11%PI > 1.00The * indicates the preferred project using each measure.

a. NPVSQ = $87,313.87 NPVHT = $142,254.07*b. IRRSQ = 16.07%* IRRHT = 15.17%c. PISQ = 1.13 PIHT = 1.15*

Asset A Asset B$200,000 $180,000

Year CFDiscounted

CF CFDiscounted

CF1 $70,000 $62,500 $80,000 $62,5002 $80,000 $63,776 $90,000 $63,7763 $90,000 $64,060 $30,000 $64,0604 $90,000 $57,197 $40,000 $57,1975 $100,000 $56,743 $40,000 $56,743

d. Timing issues result between the two projects because Project SQ receives a substantial amount of inflows early in its life while the bulk of Project HT’s cash flows do not arrive until later in its life. The reinvestment rate assumption of the IRR method leads to a conflict between project choices for the IRR method vs the NPV method. A scaling problem also exists in that SQ costs about 1.5 times that of HT.


NPV Profile

$(1,000,000)

$(500,000)

$-

$500,000

$1,000,000

0% 20% 40% 60%

Interest Rate

NPV

SQHT

e. The firm should choose Project HT. First, according to the NPV Profile, at the 11% discount rate, HT has the higher NPV. Secondly, according to the MIRR calculation, Project HT has the higher MIRR (MIRRSQ = 13.29%, MIRRHT = 13.64%).

7-29. a. NPV of Repackage is $0.384 million. NPV of Reformulate is $0.107. Choose the higher NPV, Repackage.

b. IRR of Repackage is 21.04%. IRR of Reformulate is 13.20%. Choose the higher IRR, Repackage.

c. PI of Repackage is PV of inflows divided by PV of outflows: $3,384,390/$3,000,000 = 1.13. PI of Reformulate is $25,102,163/$25,000,000 = 1.004. Choose the higher PI, Repackage.

d. At an interest rate of approximately 12% Reformulate becomes less desirable than Repackage. Also, it is clear from the Profile that Reformulate is far more sensitive to the discount rate than Repackage. A timing problem exists in the sense that Reformulate receives the bulk of its inflows early on. And, a scaling problem exists in that Repackage costs more than eight times Reformulate.

108 Chapter 7

NPV Profile

$(15,000,000)

$(10,000,000)

$(5,000,000)

$-

$5,000,000

$10,000,000

0% 10% 20% 30% 40% 50%

Interest Rate

NPV

RepackageReformulate

e. No, the rankings do not yield mixed signals. Repackage is better under all criteria.

f. The IRR of the incremental project:

Year Repackage Reformulate Repackage - Reformulate0 –$3,000,000 –$25,000,000 $22,000,0001 2,000,000 10,000,000 –8,000,0002 1,250,000 9,000,000 –7,750,0003 500,000 7,000,000 –6,500,0004 250,000 4,000,000 –3,750,0005 250,000 3.500,000 –3,250,000

The IRR of the incremental project is its compound annual costs of 12.38%. For a project of this type resulting from the smaller size of repackage versus reformulate, if the IRR is less than the discount rate, it is acceptable. Repackage is therefore the better project because its incremental cost is less than the cost of capital.

7-30. a., b., c.

Year A B A-B0 –$2.5 –$2.5 01 1.6 .35 1.252 1.6 .35 1.253 .35 –.35....

50 .35 –.35


Project NPV IRR PIA $276,860 18.16% $276,860/$2,500,000 = 1.11B $970,185 13.98% $3,470,185/$2,500,000 = 1.39

Rankings: B, A A, B B, A

The PI rankings agree with the rankings on NPV.

d. IRR and NPV yield mixed signals because of differences in the size and magnitude of their cash flows. Project A returns cash sooner than B, a pattern that generally has a higher IRR than one, like B, that returns cash flows over a longer period of time.

e. Lundblad should choose project A. The NPV of the incremental project is –$693,326, and its IRR is 13.1%. When a project has nonconventional cash flows (+ inflows followed by -outflows) its IRR is its compound annual costs. If this cost is greater than the hurdle rate, the project is unacceptable. In this case the cost of 13.1% is greater than the 10% cost of capital and therefore, Project A is inferior to Project B.

f. If the cost of capital is 13.5%, Project A has an NPV of $151,711 and an IRR of 18.16%. At a cost of capital of 16%, A has an NPV of $68,371. At a cost of capital of 13.5%, Project B has an NPV of $87,980 and at 16%, –$313,809. Project A is better than Project B at a discount rate of 13.5%. At 16%, Project A is the only acceptable project. At a cost of capital of 20%, Project A’s NPV is –$55,556 and Project B’s NPV is –$750,192; both projects should be rejected at this cost of capital.

7-31. Thomson One Business School Edition

7-32. Thomson One Business School Edition

Answers to mini-case

Payback period:

Poofy Puffs:

Initial outlay: $24,890,000Amount recovered in year 1: $12,950,000Amount remaining that needs to be recovered: $24,890,000 - $12,950,000 = 11,940,000Amount recovered in year 2: $10,923,000Amount remaining after year 2 that needs to be recovered: $11,940,000 - $10,923,000 = -1,017,000More than this amount is recovered in year 3, so we must calculate the fraction of year 3 it takes to recover the remaining $1,017,000. It takes 0.1236 ($1,017,000 ÷ $8,231,000) of a year to recover the remainder, or 1.5 months. Thus, the total payback for Poofy Puffs is 2 years and 1.5 months.

Filling Fiber:

Initial outlay: $13,500,000Amount recovered in year 1: $7,230,000Amount remaining that needs to be recovered after year 1: $13,500,000 - $7,230,000 = 6,270,000

110 Chapter 7

More than this amount is recovered in year 2, so we must calculate the fraction of year 2 it takes to recover the remaining $6,270,000. It takes 0.77 (6,270,000 ÷ 8,100,000) of a year to recover the remainder, or 9.29 months. Thus, the total payback for Filling Fiber is 1 year and 9.24 months.

Discounted Payback Period

DiscountedYear Poofy Puffs Filling Fiber Poofy Puffs Filling Fiber

0 $(24,890,000) $(13,500,000) $(24,890,000) $(13,500,000)1 $12,950,000 $7,230,000 $11,772,727 $6,572,7272 $10,923,000 $8,100,000 $9,027,273 $6,694,2153 $8,231,000 $8,629,000 $6,184,072 $6,483,0954 $7,242,000 $5,238,900 $4,946,383 $3,578,239

Poofy Puffs:

Initial outlay: $24,890,000Amount recovered in year 1 in discounted dollars: $11,772,727Amount remaining after year 1 that needs to be recovered: $24,890,000 - $11,772,727 = $13,117,273Amount recovered in year 2 in discounted dollars: $9,027,273Amount remaining after year 2 that needs to be recovered: $13,117,273 - $9,027,273 = $4,090,000More than this amount is recovered in year 3, so we must calculate the fraction of year 3 it takes to recover the remaining $4,090,000. It takes 0.66 (4,090,000 ÷ 6,184,072) of a year to recover the remainder, or 7.94 months. Thus, the total discounted payback for Poofy Puffs is 2 years and 8 months.

Filling Fiber:

Initial outlay: $13,500,000Amount recovered in year 1 in discounted dollars: $6,572,727Amount remaining that needs to be recovered: $13,500,000 - $6,572,727 = $6,927,273Amount recovered in year 2 in discounted dollars: $6,694,215Amount remaining after year 2 that needs to be recovered: $6,927,273 - $6,694,215 = $233,058More than this amount is recovered in year 3, so we must calculate the fraction of year 3 it takes to recover the remaining $233,058. It takes 0.04 ($233,058 ÷ 6,483,095) of a year to recover the remainder, or .4 months. Thus, the total discounted payback for Filling Fiber is 2 years and 0.4 months.

Accounting Rate of Return:

Poofy Puffs:The average book value of Poofy Puffs is $24,890,000 ÷ 2, or $12,445,000. The average net income for the project ($6,727,500 + $4,700,500 + $2,008,500 + $7,242,000) ÷ 4 = $5,169,625. Next, divide the average net income by the average book value of the project, or ($5,169,625 ÷ $12,445,000) = 0.4154 or 41.54%.

Filling Fiber: The average book value is $13,500,000 ÷ 2 = $6,750,000 while the average net income is $3,924,475, or ($3,855,000 + $4,725,000 + $5,254,000 + $1,863,900) ÷ 4 = $3,924,475. The project’s accounting rate of return is 58.14%, or $3,924,475 ÷ $6,750,000.


Net Present Value:

DiscountedYear Poofy Puffs Filling Fiber Poofy Puffs Filling Fiber

0 -24,890,000 -13,500,0001 12,950,000 7,230,000 $11,772,727 $6,572,7272 10,923,000 8,100,000 $9,027,273 $6,694,2153 8,231,000 8,629,000 $6,184,072 $6,483,0954 7,242,000 5,238,900 $4,946,383 $3,578,239

Sum = $31,930,456 $23,328,277

Poofy Puffs: NPV = PVinflows – PVoutflows = $31,930,456 – $24,890,000 = $7,040,456.Filling Fiber: NPV = $23,328,277 – $13,500,000 = $9,828,277.

Internal Rate of Return:

r = 24.09%

r = 41.54%

Profitability Index:

PI = PVinflows ÷ PVoutflows

PIPoofy Puffs = $31,930,456 ÷ $24,890,000 = 1.28PIFilling Fiber = $23,328,277 ÷ $13,500,000 = 1.73

Analysis: The minimum required payback period is 1.75 years, therefore both projects would be rejected using the payback and discounted payback period. From an accounting rate of return (AAR) perspective, both projects would be acceptable as they have ARRs above the required 15%. Based on the NPV method, both projects would be acceptable as the net present values are positive. Both projects are acceptable using the IRR method as well, as the IRRs are greater than 10%. Also, the profitability index (PI) is greater than 1.0 for both projects, thus both are acceptable using that criterion. Of course, since both of these projects are independent and ‘normal,’ one would not expect the NPV, IRR or PI methods to conflict.

Technically, there is not a scaling issue with these two projects as the NPV method and the IRR method rank Filling Fiber as the better project. Since the projects are independent, the firm should proceed with both of them.

mba711 - answers to all chapter 7 problems

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