12-10. Solution:
X-treme Vitamin Company
a. Payback Method
b. Net Present Value Method
Project A
Year Cash Flow PVIFA Present Value
1 $12,000 .909 $10,908
Project B
Year Cash Flow PVIFA Present Value
3 $16,000 .751 $12,016
Under the net present value method, you should select
Project B because of the higher net present value.
c. A company should normally have more confidence in answer
Calculator Solution:
(b-1)
Project A using a financial calculator:
Use the NPV keys by pressing and entering the following:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 10,000 +|– key, press the Enter key.
Press down arrow, enter 12,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 8,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 6,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 10 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 12,028.55, which is the net present value of Project A.
(b-2)
Project B Using Financial Calculator
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 10,000 +|– key, press the Enter key.
Press down arrow, enter 10,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 6,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 16,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 10 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 16,070.62, which is the net present value of Project B.
Under the net present value method, you should select Project B because of the higher net present
value.
11. Internal rate of return (LO12-4) You buy a new piece of equipment for $16,230, and you
receive a cash inflow of $2,500 per year for 12 years. What is the internal rate of return?
12-11. Solution:
Appendix D
IFA
$16, 230
PV 6.492
$2,500
= =
IRR = 11%
For n = 12, we find 6.492 under the 11% column.
Calculator Solution:
Using a financial calculator,
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 16,230 +|– key, press the Enter key.
Answer: IRR = 11%
12. Internal rate of return (LO12-4) King’s Department Store is contemplating the purchase
of a new machine at a cost of $22,802. The machine will provide $3,500 per year in cash
flow for nine years. King’s has a cost of capital of 10 percent. Using the internal rate of
return method, evaluate this project and indicate whether it should be undertaken.
12-12. Solution:
King’s Department Store
Calculator Solution:
(a)
Using a financial calculator,
Press the following keys: 2nd, CF, 2nd, CLR WORK.
Answer: IRR = 7%
13. Internal rate of return (LO12-4) Home Security Systems is analyzing the purchase of
manufacturing equipment that will cost $50,000. The annual cash inflows for the next three
years will be
Year Cash Flow
1…………………… $25,000
2…………………… 23,000
3…………………… 18,000
a. Determine the internal rate of return.
b. With a cost of capital of 18 percent, should the machine be purchased?
12-13. Solution:
Home Security Systems
a. Step 1 Average the inflows.
$25,000
23,000
18,000
$66,000 / 3 $22,000=
Step 2 Divide the inflows by the assumed annuity in Step 1.
Investment $50,000 2.273
Annuity 22,000
= =
Step 3 Go to Appendix D for the first approximation.
Step 4 Try a first approximation of discounting back the
Year Cash Flow PVIF at 16% Present Value
$50,177
12-13. (Continued)
Year Cash Flow PVIF at 17% Present Value
Because the NPV is now below $50,000, we know the IRR
is between 16 and 17 percent. We will interpolate.
16% + ($177/$757) (1%)
14% + .234 (1%) = 16.23% IRR
The IRR is 16.23%
$ 48,651
12-13. (Continued)
16% + ($177/$1,526) (2%)
16% + (.12)(2%) = 16.24%
This answer is very close to the previous answer, the
b. Since the IRR of 16.23 percent (or 16.24 percent) is less than
Calculator Solution:
Alternatively, use a financial calculator as follows to obtain the correct answer rather than an
approximation.
Press IRR; calculator shows IRR = 0.00.
Press CPT; calculator shows IRR = 16.23.
14. Net present value method (LO12-4) Aerospace Dynamics will invest $110,000 in a
project that will produce the following cash flows. The cost of capital is 11 percent. Should
the project be undertaken? (Note that the fourth year’s cash flow is negative.)
Year Cash Flow
1…………….. $36,000
2…………….. 44,000
3…………….. 38,000
4…………….. (44,000)
5…………….. 81,000
12-14. Solution:
Aerospace Dynamics
Year Cash Flow PVIF at 11% Present Value
The net present value is positive and the project should be
undertaken.
Calculator Solution:
Using a financial calculator,
The net present value is positive and the project should be undertaken.
15. Net present value method (LO12-4) The Horizon Company will invest $60,000 in a
temporary project that will generate the following cash inflows for the next three years.
Year Cash Flow
1…………….. $15,000
2…………….. 25,000
3…………….. 40,000
The firm will also be required to spend $10,000 to close down the project at the end of the
three years. If the cost of capital is 10 percent, should the investment be undertaken?
12-15. Solution:
Horizon Company
Present Value of Inflows
Year Cash Flow × PVIF at 10% Present Value
Present Value of Outflows
Present Value of Inflows $64,325
The net present value is negative and the project should not be
undertaken.
Calculator Solution:
Using a financial calculator,
Press CPT; calculator shows NPV = –3,163.04, which is the net present value of the project.
Note, the $10,000 outflow in year 3 has been subtracted from the $40,000 inflow in the third year,
and thus the year 3 net cash flow is $30,000.
16. Net present value method (LO12-4) Skyline Corp. will invest $130,000 in a project that
will not begin to produce returns until after the 3rd year. From the end of the 3rd year until
the end of the 12th year (10 periods), the annual cash flow will be $34,000. If the cost of
capital is 12 percent, should this project be undertaken?