Question
In: Accounting
Internal Rate of Return Method for a Service Company The Riverton Company, a ski resort, recently...
Internal Rate of Return Method for a Service Company
The Riverton Company, a ski resort, recently announced a $368,830 expansion to lodging properties, lifts, and terrain. Assume that this investment is estimated to produce $110,000 in equal annual cash flows for each of the first five years of the project life.
| Present Value of an Annuity of $1 at Compound Interest | |||||
| Year | 6% | 10% | 12% | 15% | 20% |
| 1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2 | 1.833 | 1.736 | 1.690 | 1.626 | 1.528 |
| 3 | 2.673 | 2.487 | 2.402 | 2.283 | 2.106 |
| 4 | 3.465 | 3.170 | 3.037 | 2.855 | 2.589 |
| 5 | 4.212 | 3.791 | 3.605 | 3.353 | 2.991 |
| 6 | 4.917 | 4.355 | 4.111 | 3.785 | 3.326 |
| 7 | 5.582 | 4.868 | 4.564 | 4.160 | 3.605 |
| 8 | 6.210 | 5.335 | 4.968 | 4.487 | 3.837 |
| 9 | 6.802 | 5.759 | 5.328 | 4.772 | 4.031 |
| 10 | 7.360 | 6.145 | 5.650 | 5.019 | 4.192 |
a.
Determine the expected internal rate of return of this project for
five years, using the present value of an annuity of $1 table
above. If required, round your final answer to the nearest whole
percent.
Solutions
Expert Solution
Correct Answer:
IRR = 15%
Working:
IRR =R1+ NPV1/ (NPV1-NPV2) * (R2-R1)
|
Cash inflow(outflow) |
PV of annuity @ 12% |
Present value |
|
|
Cash outflow |
$ (368,830.00) |
1 |
$ (368,830.00) |
|
Cash inflow |
$ 110,000.00 |
3.605 |
$ 396,550.00 |
|
NPV 1 |
$ 27,720.00 |
|
Cash inflow(outflow) |
PV of annuity @ 20% |
Present value |
|
|
Cash outflow |
$ (368,830.00) |
1 |
$ (368,830.00) |
|
Cash inflow |
$ 110,000.00 |
2.991 |
$ 329,010.00 |
|
NPV 2 |
$ (39,820.00) |
|
A |
R1 |
12% |
|
B |
R1 |
20% |
|
C |
NPV1 |
$ 27,720.00 |
|
D |
NPV2 |
$ (39,820.00) |
|
E =C-D |
NPV1-NPV2 |
$ 67,540.00 |
|
F =C/D |
NPV1/NPV1-NPV2 |
0.41042 |
|
G = A-B |
R2-R1 |
8% |
|
H =F*G |
NPV1/(NPV1-NPV2) * (R2-R1) |
0.03 |
|
I = A+H |
IRR |
15% |
End of answer.
Thanks.
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