Net Present Value Method—Annuity for a Service Company
Welcome Inn Hotels is considering the construction of a new hotel for $63 million. The expected life of the hotel is 8 years with no residual value. The hotel is expected to earn revenues of $19 million per year. Total expenses, including depreciation, are expected to be $13 million per year. Welcome Inn management has set a minimum acceptable rate of return of 11%. Assume straight-line depreciation.
a. Determine the equal annual net cash flows
from operating the hotel. Round to the nearest million
dollars.
$ million
| Present Value of an Annuity of $1 at Compound Interest | |||||||
| Periods | 8% | 9% | 10% | 11% | 12% | 13% | 14% |
| 1 | 0.92593 | 0.91743 | 0.90909 | 0.90090 | 0.89286 | 0.88496 | 0.87719 |
| 2 | 1.78326 | 1.75911 | 1.73554 | 1.71252 | 1.69005 | 1.66810 | 1.64666 |
| 3 | 2.57710 | 2.53129 | 2.48685 | 2.44371 | 2.40183 | 2.36115 | 2.32163 |
| 4 | 3.31213 | 3.23972 | 3.16987 | 3.10245 | 3.03735 | 2.97447 | 2.91371 |
| 5 | 3.99271 | 3.88965 | 3.79079 | 3.69590 | 3.60478 | 3.51723 | 3.43308 |
| 6 | 4.62288 | 4.48592 | 4.35526 | 4.23054 | 4.11141 | 3.99755 | 3.88867 |
| 7 | 5.20637 | 5.03295 | 4.86842 | 4.71220 | 4.56376 | 4.42261 | 4.28830 |
| 8 | 5.74664 | 5.53482 | 5.33493 | 5.14612 | 4.96764 | 4.79677 | 4.63886 |
| 9 | 6.24689 | 5.99525 | 5.75902 | 5.53705 | 5.32825 | 5.13166 | 4.94637 |
| 10 | 6.71008 | 6.41766 | 6.14457 | 5.88923 | 5.65022 | 5.42624 | 5.21612 |
b. Calculate the net present value of the new
hotel using the present value of an annuity of $1 table above.
Round to the nearest million dollars. If required, use the minus
sign to indicate a negative net present value.
Net present value of hotel project: $ million
c. Does your analysis support the purchase of
the new hotel?
, because the net present value is .
Answer to (a)
Straight Line Depreciation = (Cost – Residual Value) / Useful Life
Straight Line Depreciation = (63 – 0) / 8
Straight Line Depreciation per year = $7. 785 Million
Net Operating Income = Revenue – Expenses
Net Operating Income = $19 Million - $13 Million
Net Operating Income = $6 Million
Annual Net Cash Flow = Net Operating Income + Depreciation per year
Annual Net Cash Flow = $6 Million + $7. 875 Million
Annual Net Cash Flow = $13.875 million
Answer to (b)
Required Rate of Return = 11%
Life of Project = 8 years
Net Present Value = - Cost of Investment + Annual Net Cash Flow * PVA of $1 (11%, 8)
Net Present Value = -$63 million +( $13.875 million * 5.14612)
Net Present Value = -$63 million + $71.402million
Net Present Value = $8.402 million
Answer to (c)
Yes, because the Net Present Value is positive.
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