a. The profitability index is the present value of the future cash flows divided by the initial cost

So, for Project Alpha, the profitability index is:

PIAlpha = [$300 / 1.10 + $700 / 1.10² + $600 / 1.10³] / $500 = 2.604 And for Project Beta the profitability index is:

PIBeta = [$300 / 1.10 + $1,800 / 1.10² + $1,700 / 1.10³] / $2,000 = 1.519

b. According to the profitability index, you would accept Project Alpha. However, remember the profitability index rule can lead to incorrect decision when ranking mutually exclusive projects.

Intermediate

11. a. To have a payback equal to the project’s life, given C is a constant cash flow for N years:

C = I/N

b. To have a positive NPV, I < C (PVIFAR%, N). Thus, C > I / (PVIFAR%, N).

c. Benefits = C (PVIFAR%, N) = 2 × costs = 2I C = 2I / (PVIFAR%, N)

12. a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)² + C3 / (1 + IRR)³ + C4 / (1 + IRR)⁴ 0 = ₩5,000 – ₩2,500 / (1 + IRR) – ₩2,000 / (1 + IRR)² – ₩1,000 / (1 + IRR)³

– ₩1,000 / (1 +IRR)⁴

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 13.99%

b. This problem differs from previous ones because the initial cash flow is positive and all future cash flows are negative. In other words, this is a financing-type project, while previous projects were investing-type projects. For financing situations, accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate.

IRR = 13.99%

Discount Rate = 12%

IRR > Discount Rate

Reject the offer when the discount rate is less than the IRR.

c. Using the same reason as part b., we would accept the project if the discount rate is 20 percent.

IRR = 13.99%

Discount Rate = 19%

IRR < Discount Rate

Accept the offer when the discount rate is greater than the IRR.

d. The NPV is the sum of the present value of all cash flows, so the NPV of the project if the discount rate is 10 percent will be:

NPV = ₩5,000 – ₩2,500 / 1.12 – ₩2,000 / 1.12² – ₩1,000 / 1.12³ – ₩1,000 / 1.12⁴ NPV = –₩173.83

When the discount rate is 12 percent, the NPV of the offer is –₩359.95. Reject the offer.

And the NPV of the project is the discount rate is 19 percent will be:

NPV = ₩5,000 – ₩2,500 / 1.19 – ₩2,000 / 1.19² – ₩1,000 / 1.19³ – ₩1,000 / 1.19⁴ NPV = ₩394.75

When the discount rate is 19 percent, the NPV of the offer is ₩466.82. Accept the offer.

e. Yes, the decisions under the NPV rule are consistent with the choices made under the IRR rule since the signs of the cash flows change only once.

13. a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is:

Deepwater Fishing IRR:

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)² + C3 / (1 + IRR)³

0 = –$600,000 + $270,000 / (1 + IRR) + $350,000 / (1 + IRR)² + $300,000 / (1 + IRR)³

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 24.30%

Submarine Ride IRR:

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)² + C3 / (1 + IRR)³

0 = –$1,800,000 + $1,000,000 / (1 + IRR) + $700,000 / (1 + IRR)² + $900,000 / (1 + IRR)³

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 21.46%

Based on the IRR rule, the deepwater fishing project should be chosen because it has the higher IRR.

b. To calculate the incremental IRR, we subtract the smaller project’s cash flows from the larger project’s cash flows. In this case, we subtract the deepwater fishing cash flows from the submarine ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are:

Year 0 Year 1 Year 2 Year 3

Submarine Ride –$1,800,000 $1,000,000 $700,000 $900,000 Deepwater Fishing –600,000 270,000 350,000 300,000 Submarine – Fishing –$1,200,000 $730,000 $350,000 $600,000

Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)² + C3 / (1 + IRR)³

0 = –$1,200,000 + $730,000 / (1 + IRR) + $350,000 / (1 + IRR)² + $600,000 / (1 + IRR)³ Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

Incremental IRR = 19.92%

For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 19.92%, is greater than the required rate of return of 15 percent, choose the submarine ride project. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem.

That is, the submarine ride has a greater initial investment than does the deepwater fishing project. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.

c. The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be:

Deepwater fishing:

NPV = –$600,000 + $270,000 / 1.15 + $350,000 / 1.15² + $300,000 / 1.15³ NPV = $96,687.76

Submarine ride:

NPV = –$1,800,000 + $1,000,000 / 1.15 + $700,000 / 1.15² + $900,000 / 1.15³ NPV = $190,630.39

Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishing project, choose the submarine ride project. The incremental IRR rule is always consistent with the NPV rule.

14. a. The profitability index is the PV of the future cash flows divided by the initial investment. The cash flows for both projects are an annuity, so:

PII = 元 15,000(PVIFA10%,3 ) / 元 30,000 = 1.243 PIII = 元 2,800(PVIFA10%,3) / 元 5,000 = 1.393

The profitability index decision rule implies that we accept project II, since PIII is greater than the PII.

b. The NPV of each project is:

NPVI = – 元 30,000 + 元 15,000(PVIFA10%,3) = 元 7,302.78 NPVII = – 元 5,000 + 元 2,800(PVIFA10%,3) = 元 1,963.19

The NPV decision rule implies accepting Project I, since the NPVI is greater than the NPVII. c. Using the profitability index to compare mutually exclusive projects can be ambiguous when

the magnitudes of the cash flows for the two projects are of different scale. In this problem, project I is roughly 3 times as large as project II and produces a larger NPV, yet the profit-ability index criterion implies that project II is more acceptable.

15. a. The equation for the NPV of the project is:

NPV = – ₦28,000,000 + ₦53,000,000/1.11 – ₦8,000,000/1.11² = ₦13,254,768.28 The NPV is greater than 0, so we would accept the project.

b. The equation for the IRR of the project is:

0 = –₦28,000,000 + ₦53,000,000/(1+IRR) – ₦8,000,000/(1+IRR)²

From Descartes rule of signs, we know there are two IRRs since the cash flows change signs twice. From trial and error, the two IRRs are:

IRR = 72.75%, –83.46%

When there are multiple IRRs, the IRR decision rule is ambiguous. Both IRRs are correct; that is, both interest rates make the NPV of the project equal to zero. If we are evaluating whether or not to accept this project, we would not want to use the IRR to make our decision.

16. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment.

Board game:

Cumulative cash flows Year 1 = MXN 400 = MXN 400 Payback period = MXN 300 / MXN 400 = .75 years

CD-ROM:

Cumulative cash flows Year 1 = MXN 1,100 = MXN 1,100

Cumulative cash flows Year 2 = MXN 1,100 + 800 = MXN 1,900 Payback period = 1 + (MXN 1,500 – MXN 1,100) / MXN 800 Payback period = 1.50 years

Since the board game has a shorter payback period than the CD-ROM project, the company should choose the board game.

b. The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be:

Board game:

NPV = –MXN 300 + MXN 400 / 1.10 + MXN 100 / 1.10² + MXN 100 / 1.10³ NPV = MXN 221.41

CD-ROM:

NPV = –MXN 1,500 + MXN 1,100 / 1.10 + MXN 800 / 1.10² + MXN 400 / 1.10³ NPV = MXN 461.68

Since the NPV of the ROM is greater than the NPV of the board game, choose the CD-ROM.

c. The IRR is the interest rate that makes the NPV of a project equal to zero. So, the IRR of each project is:

Board game:

0 = –MXN 300 + MXN 400 / (1 + IRR) + MXN 100 / (1 + IRR)² + MXN 100 / (1 + IRR)³ Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 65.61%

CD-ROM:

0 = –MXN 1,500 + MXN 1,100 / (1 + IRR) + MXN 800 / (1 + IRR)² + MXN 400 / (1 + IRR)³ Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 30.09%

Since the IRR of the board game is greater than the IRR of the CD-ROM, IRR implies we choose the board game.

d. To calculate the incremental IRR, we subtract the smaller project’s cash flows from the larger project’s cash flows. In this case, we subtract the board game cash flows from the CD-ROM cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are:

Year 0 Year 1 Year 2 Year 3

CD-ROM –MXN 1,500 MXN

1,100

MXN 800 MXN 400

Board game –300 400 100 100

CD-ROM – Board game –MXN 1,200 MXN 700 MXN 700 MXN 300 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)² + C3 / (1 + IRR)³

0 = –MXN 1,200 + MXN 700 / (1 + IRR) + MXN 700 / (1 + IRR)² + MXN 300 / (1 + IRR)³ Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

Incremental IRR = 22.57%

For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 22.57%, is greater than the required rate of return of 10 percent, choose the CD-ROM project. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem. That is, the CD-ROM has a greater initial investment than does the board game. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.

17. a. The profitability index is the PV of the future cash flows divided by the initial investment. The profitability index for each project is:

PICDMA = [25,000,000 / 1.10 + 15,000,000 / 1.10² + 5,000,000 / 1.10³] / 10,000,000 = 3.89 PIG4 = [20,000,000 / 1.10 + 50,000,000 / 1.10² + 40,000,000 / 1.10³] / 20,000,000 = 4.48 PIWi-Fi = [20,000,000 / 1.10 + 40,000,000 / 1.10² + 100,000,000 / 1.10³] / 30,000,000 = 4.21 The profitability index implies we accept the G4 project. Remember this is not necessarily correct because the profitability index does not necessarily rank projects with different initial investments correctly.

b. The NPV of each project is:

NPVCDMA = –10,000,000 + 25,000,000 / 1.10 + 15,000,000 / 1.10² + 5,000,000 / 1.10³ NPVCDMA = 28,880,540.95

NPVG4 = –20,000,000 + 20,000,000 / 1.10 + 50,000,000 / 1.10² + 40,000,000 / 1.10³ NPVG4 = 69,556,724.27

PIWi-Fi = –30,000,000 + 20,000,000 / 1.10 + 40,000,000 / 1.10² + 100,000,000 / 1.10³ PIWi-Fi = 96,371,149.51

NPV implies we accept the Wi-Fi project since it has the highest NPV. This is the correct decision if the projects are mutually exclusive.

c. We would like to invest in all three projects since each has a positive NPV. If the budget is limited to 30 million, we can only accept the CDMA project and the G4 project, or the Wi-Fi project. NPV is additive across projects and the company. The total NPV of the CDMA project and the G4 project is:

NPVCDMA and G4 = 28,880,540.95 + 69,556,724.27 NPVCDMA and G4 = 98,437,265.21

This is greater than the Wi-Fi project, so we should accept the CDMA project and the G4 project.

18. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment.

AZM Mini-SUV:

Cumulative cash flows Year 1 = €200,000 = €200,000 Payback period = €200,000 / €200,000 = 1 year

AZF Full-SUV:

Cumulative cash flows Year 1 = €200,000 = €200,000 Cumulative cash flows Year 2 = €200,000 + 300,000 = €500,000 Payback period = 2 years

Since the AZM has a shorter payback period than the AZF, the company should choose the AZF. Remember the payback period does not necessarily rank projects correctly.

b. The NPV of each project is:

NPVAZM = –€200,000 + €200,000 / 1.10 + €150,000 / 1.10² + €150,000 / 1.10³ NPVAZM = €218,482.34

NPVAZF = –€500,000 + €200,000 / 1.10 + €300,000 / 1.10² + €300,000 / 1.10³ NPVAZF = €155,146.51

The NPV criteria implies we accept the AZM because it has the highest NPV.

c. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of each AZM is:

0 = –€200,000 + €200,000 / (1 + IRR) + €150,000 / (1 + IRR)² + €150,000 / (1 + IRR)³

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRAZM = 70.04%

And the IRR of the AZF is:

0 = –€500,000 + €200,000 / (1 + IRR) + €300,000 / (1 + IRR)² + €300,000 / (1 + IRR)³

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRAZF = 25.70%

The IRR criteria implies we accept the AZM because it has the highest NPV. Remember the IRR does not necessarily rank projects correctly.

d. Incremental IRR analysis is not necessary. The AZM has the smallest initial investment, and the largest NPV, so it should be accepted.

19. a. The profitability index is the PV of the future cash flows divided by the initial investment. The profitability index for each project is:

PIA = [R$70,000 / 1.12 + R$70,000 / 1.12²] / R$100,000 = 1.18 PIB = [R$130,000 / 1.12 + R$130,000 / 1.12²] / R$200,000 = 1.10 PIC = [R$75,000 / 1.12 + R$60,000 / 1.12²] / R$100,000 = 1.15 b. The NPV of each project is:

NPVA = –R$100,000 + R$70,000 / 1.12 + R$70,000 / 1.12² NPVA = R$18,303.57

NPVB = –R$200,000 + R$130,000 / 1.12 + R$130,000 / 1.12² NPVB = R$19,706.63

NPVC = –R$100,000 + R$75,000 / 1.12 + R$60,000 / 1.12² NPVC = R$14,795.92

c. Accept projects A, B, and C. Since the projects are independent, accept all three projects because the respective profitability index of each is greater than one.

d. Accept Project B. Since the Projects are mutually exclusive, choose the Project with the highest PI, while taking into account the scale of the Project. Because Projects A and C have the same initial investment, the problem of scale does not arise when comparing the profitability indices.

Based on the profitability index rule, Project C can be eliminated because its PI is less than the PI of Project A. Because of the problem of scale, we cannot compare the PIs of Projects A and B. However, we can calculate the PI of the incremental cash flows of the two projects, which are:

Project C0 C1 C2

B – A –R$100,000 R$60,000 R$60,000

When calculating incremental cash flows, remember to subtract the cash flows of the project with the smaller initial cash outflow from those of the project with the larger initial cash outflow. This procedure insures that the incremental initial cash outflow will be negative. The incremental PI calculation is:

PI(B – A) = [R$60,000 / 1.12 + R$60,000 / 1.12²] / R$100,000 PI(B – A) = 1.014

The company should accept Project B since the PI of the incremental cash flows is greater than one.

e. Remember that the NPV is additive across projects. Since we can spend R$300,000, we could take two of the projects. In this case, we should take the two projects with the highest NPVs, which are Project B and Project A.

20. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment.

Akita:

Cumulative cash flows Year 1 = ¥600,000 = ¥600,000 Cumulative cash flows Year 2 = ¥600,000 + 400,000 = ¥1,000,000 Payback period = 2 years

Fukui:

Cumulative cash flows Year 1 = ¥300,000 = ¥300,000 Cumulative cash flows Year 2 = ¥300,000 + 500,000 = ¥800,000 Payback period = 1 year

Since the Fukui has a shorter payback period than the Akita, the company should choose the Fukui. Remember the payback period does not necessarily rank projects correctly.

b. The NPV of each project is:

NPVAkita = –¥1,000,000 + ¥600,000 / 1.10 + ¥400,000 / 1.10² + ¥1,000,000 / 1.10³ NPVAkita = ¥627,347.86

NPVFukui = –¥500,000 + ¥300,000 / 1.10 + ¥500,000 / 1.10² + ¥100,000 / 1.10³ NPVFukui = ¥261,081.89

The NPV criteria implies accepting the Akita because it has the highest NPV.

c. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of each Akita is:

0 = –¥1,000,000 + ¥600,000 / (1 + IRR) + ¥400,000 / (1 + IRR)² + ¥1,000,000 / (1 + IRR)³ Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRAkita = 39.79%

And the IRR of the Fukui is:

0 = –¥500,000 + ¥300,000 / (1 + IRR) + ¥500,000 / (1 + IRR)² + ¥100,000 / (1 + IRR)³

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRFukui = 40.99%

The IRR criteria implies accepting the Fukui because it has the highest NPV. Remember the IRR does not necessarily rank projects correctly.

d. Incremental IRR analysis is necessary. The Fukui has a higher IRR, but is relatively smaller in terms of investment and NPV. In calculating the incremental cash flows, we subtract the cash flows from the project with the smaller initial investment from the cash flows of the project with the large initial investment, so the incremental cash flows are:

Year 0 Year 1 Year 2 Year 3

Akita –¥1,000,000 ¥600,000 ¥400,000 ¥1,000,000

Fukui –500,000 300,000 500,000 100,000

Akita – Fukui –¥500,000 ¥300,000 –¥100,000 ¥900,000

Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:

0 = –¥500,000 + ¥300,000 / (1 + IRR) – ¥100,000 / (1 + IRR)² + ¥900,000 / (1 + IRR)³

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

Incremental IRR = 38.90%

For investing-type projects, we accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 38.90%, is greater than the required rate of return of 10 percent, we choose the Akita. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem. That is, the Akita has a greater initial investment than does the Fukui. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.

By the way, as an aside: The cash flows for the incremental IRR change signs three times, so we would expect up to three real IRRs. In this particular case, however, two of the IRRs are not real numbers. For the record, the other IRRs are:

IRR = [1/(–.30442 + .08240i)] – 1 IRR = [1/(–.30442 – .08240i)] – 1 21. a. The NPV of each project is:

NPVNP-30 = –€100,000 + €40,000{[1 – (1/1.15)⁵ ] / .15 } NPVNP-30 = €34,086.20

NPVNX-20 = –€30,000 + €20,000 / 1.15 + €23,000 / 1.15² + €26,450 / 1.15³ + €30,418 / 1.15⁴ + €34,980 / 1.15⁵

NPVNX-20 = €56,956.75

The NPV criteria implies accepting the NX-20.

b. The IRR is the interest rate that makes the NPV of the project equal to zero, so the IRR of each project is:

NP-30:

0 = –€100,000 + €40,000({1 – [1/(1 + IRR)⁵ ]} / IRR)

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRNP-30 = 28.65%

And the IRR of the NX-20 is:

0 = –€30,000 + €20,000 / (1 + IRR) + €23,000 / (1 + IRR)² + €26,450 / (1 + IRR)³ + €30,418 / (1 + IRR)⁴ + €34,980 / (1 + IRR)⁵

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRNX-20 = 73.02%

The IRR criteria implies accepting the NX-20.

c. Incremental IRR analysis is not necessary. The NX-20 has a higher IRR, and but is relatively smaller in terms of investment, with a larger NPV. Nonetheless, we will calculate the incremental IRR. In calculating the incremental cash flows, we subtract the cash flows from the project with the smaller initial investment from the cash flows of the project with the large initial investment, so the incremental cash flows are:

Year

Incremental cash flow

0 –€70,000

1 20,000

2 17,000

3 13,550

4 9,582

5 5,020

Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:

0 = –€70,000 + €20,000 / (1 + IRR) + €17,000 / (1 + IRR)² + €13,550 / (1 + IRR)³ + €9,582 / (1 + IRR)⁴ + €5,020 / (1 + IRR)⁵

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

Incremental IRR = –2.89%

For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, –2.89%, is less than the required rate of return of 15 percent, choose the NX-20.

d. The profitability index is the present value of all subsequent cash flows, divided by the initial investment, so the profitability index of each project is:

PINP-30 = (€40,000{[1 – (1/1.15)⁵ ] / .15 }) / €100,000 PINP-30 = 1.341

PINX-20 = [€20,000 / 1.15 + €23,000 / 1.15² + €26,450 / 1.15³ + €30,418 / 1.15⁴ + €34,980 / 1.15⁵] / €30,000

PINX-20 = 2.899

The PI criteria implies accepting the NX-20.

22. a. The NPV of each project is:

NPVA = –$100,000 + $50,000 / 1.15 + $50,000 / 1.15² + $40,000 / 1.15³ + $30,000 / 1.15⁴ + $20,000 / 1.15⁵

NPVA = $34,682.23

NPVB = –$200,000 + $60,000 / 1.15 + $60,000 / 1.15² + $60,000 / 1.15³ + $100,000 / 1.15⁴ + $200,000 / 1.15⁵

NPVB = $93,604.18

The NPV criteria implies accepting Project B.

b. The IRR is the interest rate that makes the NPV of the project equal to zero, so the IRR of each project is:

Project A:

0 = –$100,000 + $50,000 / (1 + IRR) + $50,000 / (1 + IRR)² + $40,000 / (1 + IRR)³ + $30,000 / (1 + IRR)⁴ + $20,000 / (1 + IRR)⁵

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRA = 31.28%

And the IRR of the Project B is:

0 = –$200,000 + $60,000 / (1 + IRR) + $60,000 / (1 + IRR)² + $60,000 / (1 + IRR)³ + $100,000 / (1 + IRR)⁴ + $200,000 / (1 + IRR)⁵

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRRB = 29.54%

The IRR criteria implies accepting Project A.

c. Incremental IRR analysis is not necessary. The NX-20 has a higher IRR, and but is relatively smaller in terms of investment, with a larger NPV. Nonetheless, we will calculate the incremental IRR. In calculating the incremental cash flows, we subtract the cash flows from the project with the smaller initial investment from the cash flows of the project with the large initial investment, so the incremental cash flows are:

Year

Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:

0 = –$100,000 + $10,000 / (1 + IRR) + $10,000 / (1 + IRR)² + $20,000 / (1 + IRR)³ + $70,000 / (1 + IRR)⁴ + $180,000 / (1 + IRR)⁵

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

Incremental IRR = 28.60%

For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 28.60%, is greater than the required rate of return of 15 percent, choose the Project B.

d. The profitability index is the present value of all subsequent cash flows, divided by the initial investment, so the profitability index of each project is:

d. The profitability index is the present value of all subsequent cash flows, divided by the initial investment, so the profitability index of each project is:

在文檔中 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions (頁 151-168)