A project that provides annual cash flows of $18,300 for ten years costs $89,000
ID: 2723885 • Letter: A
Question
A project that provides annual cash flows of $18,300 for ten years costs $89,000 today.
What is the NPV for the project if the required return is 9 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 9 percent, should the firm accept this project? Accept Reject What is the NPV for the project if the required return is 21 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 21 percent, should the firm accept this project? Accept Reject At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Discount rate %
Explanation / Answer
1
Calculation of NPV for the project if the required return is 9 percent:
Annual Cash Flows
$ 18,300.00
Number of years
10
Required Rate
9%
Present value of Annuity $1 (10 Periods, 9%)
6.41766
Present value of Cash flows = 18300*6.41766 =
$ 117,443.14
Less: Initial Cost
$ (89,000.00)
NPV =
$ 28,443.14
Decision:
Accept. Firm should accept the project, because it has positive NPV.
2
Calculation of NPV for the project if the required return is 21 percent:
Annual Cash Flows
$ 18,300.00
Number of years
10
Required Rate
21%
Present value of Annuity $1 (10 Periods, 21%)
4.05408
Present value of Cash flows = 18300*4.05408 =
$ 74,189.63
Less: Initial Cost
$ (89,000.00)
NPV =
$ (14,810.37)
Decision:
Reject. Firm should reject the project, because it has negative NPV.
3
Indifferent Rate for the project shall be its Internal Rate of Return (IRR):
Calculation of IRR:
Year
Cash Flows
0
$ (89,000.00)
1
$ 18,300.00
2
$ 18,300.00
3
$ 18,300.00
4
$ 18,300.00
5
$ 18,300.00
6
$ 18,300.00
7
$ 18,300.00
8
$ 18,300.00
9
$ 18,300.00
10
$ 18,300.00
IRR =
15.83%
(Using excel formula "=IRR()"
Hence Indifferent rate shall be 15.83%
1
Calculation of NPV for the project if the required return is 9 percent:
Annual Cash Flows
$ 18,300.00
Number of years
10
Required Rate
9%
Present value of Annuity $1 (10 Periods, 9%)
6.41766
Present value of Cash flows = 18300*6.41766 =
$ 117,443.14
Less: Initial Cost
$ (89,000.00)
NPV =
$ 28,443.14
Decision:
Accept. Firm should accept the project, because it has positive NPV.
2
Calculation of NPV for the project if the required return is 21 percent:
Annual Cash Flows
$ 18,300.00
Number of years
10
Required Rate
21%
Present value of Annuity $1 (10 Periods, 21%)
4.05408
Present value of Cash flows = 18300*4.05408 =
$ 74,189.63
Less: Initial Cost
$ (89,000.00)
NPV =
$ (14,810.37)
Decision:
Reject. Firm should reject the project, because it has negative NPV.
3
Indifferent Rate for the project shall be its Internal Rate of Return (IRR):
Calculation of IRR:
Year
Cash Flows
0
$ (89,000.00)
1
$ 18,300.00
2
$ 18,300.00
3
$ 18,300.00
4
$ 18,300.00
5
$ 18,300.00
6
$ 18,300.00
7
$ 18,300.00
8
$ 18,300.00
9
$ 18,300.00
10
$ 18,300.00
IRR =
15.83%
(Using excel formula "=IRR()"
Hence Indifferent rate shall be 15.83%
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