公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap005

CHAPTER 5

Net Present Value and Other Investment Criteria

Answers to Problem Sets

1. a. A = 3 years, B = 2 years, C = 3 years.

b. B

c. A, B, and C

d. B and C (NPV B = $3,378;NPV C = $2,405)

e. True. The payback rule ignores all cash flows after the cutoff date,

meaning that future years’ cash inflows are not considered. In addition, the

payback rule ignores the timing of cash inflows. For example, for a

payback rule set at two years, a project with a payback period of one year

is given equal weight as a project with a payback period of two years.

f. It will accept no negative-NPV projects, but will turn down some with

positive NPVs. A project can have positive NPV if all future cash flows are

considered but still do not meet the stated cutoff period.

Est. time: 6 – 10

2. Given the cash flows C0, C1, . . . , C T, IRR is defined by:

It is calculated by trial and error, by financial calculators, or by spreadsheet

programs.

Est. time: 1 – 5

3. a. $15,750; $4,250; $0

b. 100%

Est. time: 1 – 5

4. No (you are effectively “borrowing” at a rate of interest highe r than the

opportunity cost of capital).

Est. time: 1 – 5

5 a. Two. There are multiple internal rates of return for a project when there

are changes in the sign of the cash flows.

b. −50% and +50%. The NPV for the project using both of these IRRs is 0.

c. Yes, NPV = +14.6.

Est. time: 1 – 5

6. The incremental flows from investing in Alpha rather than Beta are −200,000;

+110,000; and 121,000. The IRR on the incremental cash flow is 10% (i.e., −200 + 110/1.10 + 121/1.102 = 0). The IRR on Beta exceeds the cost of capital and so does the IRR on the incremental investment in Alpha. Choose Alpha.

Est. time: 1 – 5

7. 1, 2, 4, and 6

The profitability index for each project is shown below:

Start with the project with the highest profitability index and go from there. Project

2 has the highest profitability index and has an initial investment of $5,000. The

next highest profitability index is for Project 1, which has an initial investment of $10,000. The next highest is Project 4, which will cost $60,000 up front. So far we have spent $75,000. Projects 5 and 6 both have profitability indexes of .2, but we only have $15,000 left to spend, so we will add Project 6 to our list. This gives us Projects 1, 2, 4, and 6.

Est. time: 1 – 5

8. a. $90.91.10)(1$10001000NPV A -=+

-=$ $4,044.7310)(1.$1000(1.10)$1000(1.10)$4000(1.10)$1000(1.10)$10002000NPV 5

432B +=+++++-=$ $39.4710)(1.$1000.10)(1$1000(1.10)$1000(1.10)$10003000NPV 542C +=++++

-=$ Projects B and C have positive NPVs.

b. Payback A = one year

Payback B = two years

Payback C = four years

c. A and B

d.

$909.09.10)(1$1000PV 1A == The present value of the cash inflows for Project A never recovers the initial

outlay for the project, which is always the case for a negative NPV project.

The present values of the cash inflows for Project B are shown in the third

row of the table below, and the cumulative net present values are shown

in the fourth row:

C 0

C 1 C 2 C 3 C 4 C 5 -2,000.00

+1,000.00 +1,000.00 +4,000.00 +1,000.00 +1,000.00 -2,000.00

909.09 826.45 3,005.26 683.01 620.92 -1,090.91 -264.46 2,740.80 3,423.81 4,044.73

Since the cumulative NPV turns positive between year 2 and year 3, the discounted payback period is:

years 2.093,005.26

264.462=+

The present values of the cash inflows for Project C are shown in the third row of the table below, and the cumulative net present values are shown in the fourth row:

C 0 C 1 C 2 C 3 C 4 C 5

-3,000.00 +1,000.00 +1,000.00

0.00 +1,000.00 +1,000.00 -3,000.00 909.09 826.45

0.00 683.01 620.92 -2,090.91 -1,264.46 -1,264.46 -581.45 39.47

Since the cumulative NPV turns positive between year 4 and year 5, the

discounted payback period is: