12-16. Solution:
Skyline Corporation
Present Value of Inflows
Find the present value of a deferred annuity
Discount from beginning of the third period (end of second
period to present):
The net present value is positive and the project should be
undertaken.
Calculator Solution:
Using a financial calculator,
17. Net present value and internal rate of return methods (LO12-4) The Hudson
Corporation makes an investment of $24,000 that provides the following cash flow:
Year Cash Flow
1…………….. $ 13,000
2…………….. 13,000
3…………….. 4,000
a. What is the net present value at an 8 percent discount rate?
b. What is the internal rate of return?
c. In this problem, would you make the same decision under both parts a and b?
12-17. Solution:
Hudson Corporation
a. Net Present Value
Year Cash Flow × 8% PVIF Present Value
b. Internal Rate of Return
We will average the inflows to arrive at an assumed annuity
value.
12-17. (Continued)
We divide the investment by the assumed annuity value.
IFA
$24,000 2.400 PV
10,000 =
Using Appendix D for n = 3, the first approximation appears
to fall between 12 percent and 14 percent. Since the heavy
inflows are in the early years, we will try 14 percent.
Year Cash Flow × 14% PVIF Present Value
Since 14 percent is not high enough to get $24,000 as the
present value, we will try 16 percent. (We could have only
Year Cash Flow × 16%PVIF Present Value
The correct answer must fall between 14 percent and 16
percent. We interpolate.
$98
14% (2%) 14% .15 (2%) 14% .30% 14.30%
$669
+ = + = + =
As an alternative answer, students who use 15 percent as the
second trial and error rate will show the following:
Year Cash Flow × 15%PVIF Present Value
The correct answer falls between 14 percent and 15 percent.
We interpolate.
$98
14% (1%) 14% .30 (1%) 14% .30% 14.30%
$328
+ = + = + =
c. Yes. Both the NPV is greater than 0 and the IRR is greater
than the cost of capital.
Calculator Solution:
(a)
Press down arrow; calculator shows NPV = 0.00
Press CPT; calculator shows NPV = 2,357.77, which is the net present value of the project.
(b)
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 24,000 +|– key, press Enter.
Answer: IRR = 14.29%
18. Net present value and internal rate of return methods (LO12-4) The Pan American
Bottling Co. is considering the purchase of a new machine that would increase the speed of
bottling and save money. The net cost of this machine is $60,000. The annual cash flows
have the following projections:
Year Cash Flow
1…..……. $23,000
2………… 26,000
3………… 29,000
4………… 15,000
5………… 8,000
a. If the cost of capital is 13 percent, what is the net present value of selecting a new
machine?
b. What is the internal rate of return?
c. Should the project be accepted? Why?
12-18. Solution:
Pan American Bottling Co.
a. Net Present Value
Year Cash Flow × 13% PVIF Present Value
12-18. (Continued)
b. Internal Rate of Return
We will average the inflows to arrive at an assumed annuity.
We divide the investment by the assumed annuity value.
IFA
$60,000 2.97 PV
$20, 200 =
Using Appendix D for n = 5, 20 percent appears to be a
reasonable first approximation (2.991). We try 20 percent.
Year Cash Flow × 20% PVIF Present Value
Present Value of Inflows $64,440
Since 20 percent is not high enough, we try the next highest
rate at 25 percent.
Year Cash Flow × 25% PVIF Present Value
12-18. (Continued)
The correct answer must fall between 20 and 25 percent. We
interpolate.
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 60,000 +|– key, press Enter.
Press CPT; calculator shows NPV = 14,356.11, which is the net present value of the
project.
(b)
Calculator Solution:
Find the IRR using a financial calculator:
Press IRR; calculator shows IRR = 0.
Press CPT; calculator shows IRR = 23.77%, which is the IRR of the project.
19. Use of profitability index (LO12-4) You are asked to evaluate the following two projects
for the Norton Corporation. Using the net present value method combined with the
profitability index approach described in footnote 2 of this chapter, which project would
you select? Use a discount rate of 14 percent.
Project X (Videotapes
of the Weather Report)
($20,000 Investment)
Project Y (Slow-Motion
Replays of Commercials)
($40,000 investment)
Year Cash Flow Year Cash Flow
1……………………. $10,000 1
………………………….…. $20,000
2……………………. 8,000 2
………………………….…. 13,000
3……………………. 9,000 3
………………………….…. 14,000
4……………………. 8,600 4
………………………….…. 16,000
12-19. Solution:
Norton Corporation
NPV for Project X
Year Cash Flow × PVIF at 14% Present Value
Present Value of Inflows $26,088
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 20,000 +|– key, press the Enter key.
Profitability Index = Present Value of Inflows / Present Value of Outflows
Present Value of Inflows = NPV + Outflows
(b)
Find NPV using a financial calculator:
Press the following keys: 2nd, CF, 2nd, Clear.
Press NPV; calculator shows I = 0; enter 14 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Profitability Index = $46,469.82/40,000 = 1.16
20. Reinvestment rate assumption in capital budgeting (LO12-4) Turner Video will invest
$58,500 in a project. The firm’s cost of capital is 12 percent. The investment will provide
the following inflows:
Year Inflow
1…………….. $15,000
2…………….. 17,000
3…………….. 21,000
4…………….. 25,000
5…………….. 29,000
The internal rate of return is 11 percent.
a. If the reinvestment assumption of the net present value method is used, what will be
the total value of the inflows after five years? (Assume the inflows come at the end of
each year.)
b. If the reinvestment assumption of the internal rate of return method is used, what will
be the total value of the inflows after five years?
c. Generally is one investment assumption likely to be better than another?