Finance Chapter 5 Homework Year Cash Flow 240000104 249600 So The

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

the initial investment.

NP-30:

Cumulative cash flows Year 1 = $239,000 = $239,000

NX-20:

Cumulative cash flows Year 1 = $130,000 = $130,000

NP-30. Remember the payback period does not necessarily rank projects correctly.

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 = –$735,000 + $239,000({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 = 18.74%

c. 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 = ($239,000{[1 – (1/1.15)5]/.15})/$735,000

PINP-30 = 1.090

d. The NPV of each project is:

NPVNP-30 = –$735,000 + $239,000{[1 – (1/1.15)5]/.15}

NPVNP-30 = $66,165.07

20. The MIRRs for the project with all three approaches is:

Discounting approach:

In the discounting approach, we find the value of all negative cash outflows at Time 0, while any

positive cash inflows remain at the time at which they occur. So, discounting the cash outflows to

Time 0, we find:

Time 0 cash flow = –$47,000 – $9,500/1.105

Time 0 cash flow = –$52,898.75

So, the MIRR using the discounting approach is:

So, the MIRR using the reinvestment approach is:

0 = –$47,000 + $95,040.59/(1 + MIRR)5

$95,040.59/$47,000 = (1 + MIRR)5

21. With different discounting and reinvestment rates, we need to make sure to use the appropriate interest

rates. The MIRRs for the project with all three approaches are:

Discounting approach:

In the discounting approach, we find the value of all cash outflows at Time 0 at the discount rate, while

any cash inflows remain at the time at which they occur. So, discounting the cash outflows to Time 0,

In the reinvestment approach, we find the future value of all cash flows except the initial cash flow at

the end of the project using the reinvestment rate. So, reinvesting the cash flows to Time 5, we find:

Time 5 cash flow = $16,900(1.084) + $20,300(1.083) + $25,800(1.082) + $19,600(1.08) – $9,500

Time 5 cash flow = $90,325.54

So, the MIRR using the discounting approach is:

Time 5 cash flow = $16,900(1.084) + $20,300(1.083) + $25,800(1.082) + $19,600(1.08)

Time 5 cash flow = $99,825.54

So, the MIRR using the discounting approach is:

0 = –$52,637.79 + $99,825.54/(1 + MIRR)5

$99,825.54/$52,637.79 = (1 + MIRR)5

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

0 = –$75,000 + $155,000/(1 + IRR) – $65,000/(1 + IRR)2

From Descartes’ Rule of Signs, we know there are either zero IRRs or two IRRs since the cash flows

change signs twice. We can rewrite this equation as:

0 = –$75,000 + $155,000X – $65,000X2

X =

)000,65(2

−

X =

)000,65(2

0004,525,000,000,155

−

−

X =

000,130

12.268,67000,155

−

−

To find the maximum (or minimum) of a function, we find the derivative and set it equal to zero. The

derivative of this IRR function is:

0 = –$155,000(1 + IRR)–2 + $130,000(1 + IRR)–3

–$155,000(1 + IRR)–2 = $130,000(1 + IRR)–3

–$155,000(1 + IRR)3 = $130,000(1 + IRR)2

23. Given the six-year payback, the worst case is that the payback occurs at the end of the sixth year. Thus,

the worst case:

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

0 = –$6,048 + $34,344/(1 + IRR) – $72,840/(1 + IRR)2 + $68,400/(1 + IRR)3

25. a. Here the cash inflows of the project go on forever, which is a perpetuity. Unlike ordinary

perpetuity cash flows, the cash flows here grow at a constant rate forever, which is a growing

perpetuity. The PV of the future cash flows from the project is:

PV of cash inflows = C1/(R – g)

b. Here we want to know the minimum growth rate in cash flows necessary to accept the project.

The minimum growth rate is the growth rate at which we would have a zero NPV. The equation

for a zero NPV, using the equation for the PV of a growing perpetuity is:

26. a. The project involves three cash flows: the initial investment, the annual cash inflows, and the

abandonment costs. The mine will generate cash inflows over its 11-year economic life. To

express the PV of the annual cash inflows, apply the growing annuity formula, discounted at the

IRR and growing at eight percent.

b. Yes. Since the mine’s IRR exceeds the required return of 13 percent, the mine should be opened.

27. First, we need to find the future value of the cash flows for the one year in which they are blocked by

the government. So, reinvesting each cash inflow for one year, we find:

Year 2 cash flow = $295,000(1.04) = $306,800

Year 3 cash flow = $325,000(1.04) = $338,000

IRR = 10.37%

While this may look like an MIRR calculation, it is not an MIRR, rather it is a standard IRR

28. a. We can apply the growing perpetuity formula to find the PV of Stream A. The perpetuity formula

values the stream as of one year before the first payment. Therefore, the growing perpetuity

formula values the stream of cash flows as of Year 2. Next, discount the PV as of the end of Year

2 back two years to find the PV as of today, Year 0. Doing so, we find:

b. If we combine the cash flow streams to form Project C, we get:

Project A = [C3/(r – g)]/(1 + r)2

Project B = [C2/r]/(1 + r)

c. The correct decision rule for an investing-type project is to accept the project if the discount rate

29. To answer this question, we need to examine the incremental cash flows. To make the projects equally

attractive, Project Billion must have a larger initial investment. We know this because the subsequent

cash flows from Project Billion are larger than the subsequent cash flows from Project Million. So,

subtracting the Project Million cash flows from the Project Billion cash flows, we find the incremental

cash flows are:

Incremental

Year cash flows

0 –Io + $1,200

30. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of the project

is:

0 = $20,000 – $26,000/(1 + IRR) + $13,000/(1 + IRR)2

Even though it appears there are two IRRs, a spreadsheet, financial calculator, or trial and error will

not give an answer. The reason is that there is no real IRR for this set of cash flows. If you examine

Calculator Solutions

1. b.

Project A

CFo

–$15,000

CFo

–$19,000

C01

$10,400

C01

$12,700

1

C02

$5,900

C02

$6,100

1

C03

$2,100

C03

$5,300

1

I = 15%

NPV CPT

–$114.49

$140.79

5.

CFo

–$27,000

C01

$13,100

1

C02

$17,200

1

C03

$8,400

F03

1

IRR CPT

21.80%

6.

Project A

Project B

CFo

–$7,300

CFo

–$4,390

C01

$3,940

C01

$2,170

F01

1

F01

1

C02

$3,450

C02

$2,210

1

C03

$2,480

C03

$1,730

1

IRR CPT

18.24%

19.31%

7.

CFo

0

10.

CFo

$8,700

C01

–$3,900

1

C02

–$2,900

1

C03

–$2,300

F03

1

C04

F04

1

IRR CPT

11.21%

CFo

$8,700

CFo

$8,700

C01

–$3,900

C01

–$3,900

F01

1

F01

1

C02

F02

1

F02

1

C03

F03

1

F03

1

C04

–$1,800

C04

–$1,800

1

I = 10%

I = 20%

NPV CPT

–$199.60

$1,237.04

11. a.

Deepwater fishing

Submarine ride

CFo

–$725,000

CFo

–$1,450,000

C01

$270,000

C01

$820,000

F01

1

F01

1

C02

$420,000

C02

$650,000

F02

1

F02

1

C03

$380,000

C03

$540,000

1

IRR CPT

20.96%

19.87%

C01

$67,000

7

I = 13%

NPV CPT

$296,314.90

b.

CFo

–$725,000

C01

$550,000

F01

1

c.

Deepwater fishing

Submarine ride

CFo

–$725,000

CFo

–$1,450,000

C01

$270,000

C01

$820,000

F01

1

F01

1

C02

$420,000

C02

$650,000

F02

1

F02

1

C03

$380,000

C03

$540,000

F03

1

F03

1

I = 14%

NPV CPT

$91,507.64

$133,936.76

12.

Project I

CFo

$0

CFo

–$45,000

C01

$23,200

C01

$23,200

F01

3

F01

3

I = 10%

NPV CPT

$57,694.97

$12,694.97

CFo

$0

CFo

–$19,800

C01

$11,700

C01

$11,700

F01

3

F01

3

I = 10%

NPV CPT

$29,096.17

$9,296.17

C02

$230,000

F02

1

C03

$160,000

F03

1

IRR CPT

18.40%

13.

CFo

–$65,000,000

CFo

–$65,000,000

C01

$92,000,000

C01

$92,000,000

14. b.

Board game

DVD

CFo

–$850

CFo

–$1,700

C01

$670

C01

$1,300

1

C02

$510

C02

$750

1

C03

$90

C03

$350

1

I = 10%

NPV CPT

$248.20

$364.61

c.

Board game

DVD

CFo

–$850

CFo

–$1,700

C01

$670

C01

$1,300

1

C02

$510

C02

$750

1

C03

$90

C03

$350

1

IRR CPT

30.86%

24.96%

d.

CFo

–$850

C01

$630

1

C02

$240

1

C03

$260

1

IRR CPT

19.29%

1

C02

–$11,000,000

C02

1

I = 10%

IRR CPT

NPV CPT

28.35%

$9,545,454.55

15. a.

CDMA

G4

Wi–Fi

CFo

0

CFo

0

CFo

0

C01

$23,000,000

C01

$21,000,000

C01

$39,000,000

F01

1

F01

1

F01

1

C02

$16,000,000

C02

$51,000,000

C02

$66,000,000

b.

CDMA

G4

Wi–Fi

CFo

–$18,000,000

CFo

–$25,000,000

CFo

–$43,000,000

C01

$23,000,000

C01

$21,000,000

C01

$39,000,000

F01

C02

$16,000,000

C02

$51,000,000

C02

$66,000,000

F02

C03

F03

1

F03

1

F03

1

I = 10%

NPV CPT

$20,640,120.21

$67,043,576.26

$78,555,221.64

16. b.

AZM

AZF

CFo

–$575,000

CFo

–$980,000

C01

$373,000

C01

$395,000

F01

1

F01

1

C02

$219,000

C02

$477,000

F02

1

F02

1

C03

$185,000

C03

$339,000

F03

1

F03

1

I = 10%

NPV CPT

$84,075.88

$28,001.50

c.

AZM

AZF

CFo

–$575,000

CFo

–$980,000

C01

$373,000

C01

$395,000

F01

1

F01

1

C02

$219,000

C02

$477,000

F02

1

F02

1

C03

$185,000

C03

$339,000

F03

1

F03

1

IRR CPT

19.36%

11.65%

F02

1

F02

1

F02

1

C03

$6,000,000

C03

$41,000,000

C03

$42,000,000

F03

1

F03

1

F03

1

I = 10%

NPV CPT

$38,640,120.21

$92,043,576.26

$121,555,221.64

17. a.

Project A

Project B

Project C

CFo

0

CFo

0

CFo

0

C01

$165,000

C01

$300,000

C01

$180,000

F01

1

F01

1

F01

1

b.

Project A

Project B

Project C

CFo

–$225,000

CFo

–$450,000

CFo

–$225,000

C01

$165,000

C01

$300,000

C01

$180,000

F01

1

F01

1

F01

1

C02

$165,000

C02

$300,000

C02

$135,000

F02

1

F02

1

F02

1

I = 12%

NPV CPT

$53,858.42

$57,015.31

$43,335.46

18. b.

Dry prepeg

Solvent prepeg

CFo

–$1,500,000

CFo

–$650,000

C01

$900,000

C01

$345,000

F01

1

F01

1

C02

$700,000

C02

$570,000

F02

1

F02

1

C03

$725,000

C03

$360,0000

F03

1

F03

1

I = 8%

NPV CPT

$508,998.88

$443,907.18

c.

Dry prepeg

Solvent prepeg

CFo

–$1,500,000

CFo

–$650,000

C01

$900,000

C01

$345,000

F01

1

F01

1

C02

$700,000

C02

$570,000

F02

1

F02

1

C03

$725,000

C03

$360,0000

F03

1

F03

1

IRR CPT

26.84%

42.16%

C02

$165,000

C02

$300,000

C02

$135,000

F02

1

F02

1

F02

1

I = 12%

NPV CPT

$278,858.42

$507,015.31

$268,335.46

d.

CFo

–$850,000

12.68%

19. b.

NP-30

NX-20

CFo

–$735,000

CFo

–$460,000

C01

$239,000

C01

$130,000

F01

5

F01

1

C02

$143,000

F02

1

$157,300

F03

1

$173,030

F04

1

C05

$190,333

F05

1

IRR CPT

18.74%

19.87%

c.

NP-30

NX-20

CFo

0

CFo

0

C01

$239,000

C01

$130,000

F01

5

F01

1

C02

$143,000

F02

1

$157,300

F03

1

$170,030

F04

1

C05

$190,333

F05

1

I = 15%

NPV CPT

$801,165.07

$518,158.93

$555,000

F01

1

C02

$130,000

F02

1

C03

$365,000

F03

1

IRR CPT

d.

NP-30

NX-20

CFo

–$735,000

CFo

–$460,000

30.

CFo

$20,000

–$26,000

1

$13,000

1

IRR CPT

ERROR 7

$239,000

$130,000

5

1

$143,000

1

$157,300

1

$173,030

1

$190,333

1

I = 15%

NPV CPT

$66,165.07

$58,158.93