Principles of Corporate Finance: Net Present Value and Other Investment Criteria
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 (NPVB = $3,378; NPVC = $2,405)
e. True
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.
2. Given the cash flows C0, C1, . . . , CT, IRR is defined by:
It is calculated by trial and error, by financial calculators, or by spreadsheet programs.
3. a. $15,750; $4,250; $0
b. 100%.
4. No (you are effectively “borrowing” at a rate of interest higher than the opportunity cost of capital).
5. a. Two
b. -50% and +50%
c. Yes, NPV = +14.6.
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.
7. 1, 2, 4, and 6
8. a.
b. Payback A = 1 year
Payback B = 2 years
Payback C = 4 years
c. A and B
d.
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:
C0
C1
C2
C3
C4
C5
-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 two and year three, the discounted payback period is:
The present values of the cash inflows for Project C are shown in the third row of the table below, and the cumulative net
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 (NPVB = $3,378; NPVC = $2,405)
e. True
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.
2. Given the cash flows C0, C1, . . . , CT, IRR is defined by:
It is calculated by trial and error, by financial calculators, or by spreadsheet programs.
3. a. $15,750; $4,250; $0
b. 100%.
4. No (you are effectively “borrowing” at a rate of interest higher than the opportunity cost of capital).
5. a. Two
b. -50% and +50%
c. Yes, NPV = +14.6.
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.
7. 1, 2, 4, and 6
8. a.
b. Payback A = 1 year
Payback B = 2 years
Payback C = 4 years
c. A and B
d.
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:
C0
C1
C2
C3
C4
C5
-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 two and year three, the discounted payback period is:
The present values of the cash inflows for Project C are shown in the third row of the table below, and the cumulative net