Question
In: Accounting
Internal Rate of Return Method for a Service Company The Riverton Company, announced a $608,580 million...
Internal Rate of Return Method for a Service Company
The Riverton Company, announced a $608,580 million expansion of lodging properties, ski lifts, and terrain in Park City, Utah. Assume that this investment is estimated to produce $98,000 million in equal annual cash flows for each of the first eight 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 eight years, using the present value of
an annuity of $1 table above.
%
Solutions
Expert Solution
| Solution : | ||||||
| IRR : IRR Means with a particular Percentage rate , At that point the present value of future cash inflow become the zero | ||||||
| CALCULATION OF IRR OF THE INVESTMENT | ||||||
| CALCULATION OF PRESENT VALUE OF INVESTMENT WITH PVF OF $ 1 @ 6% | ||||||
| Cash Flow | "x" | Annuity Factor @ 6% for 8th Year | "=" | Present Value | ||
| Total present value of cash inflow | $ 98,000.0 | "x" | 6.210 | "=" | $ 6,08,580 | |
| Less: Amount to be invested | $ -6,08,500 | |||||
| Net Present Value | $ 80 | |||||
| CALCULATION OF PRESENT VALUE OF INVESTMENT WITH PVF OF $ 1 @ 10% | ||||||
| Cash Flow | "x" | Annuity Factor @ 10% for 8th Year | "=" | Present Value | ||
| Total present value of cash inflow | $ 98,000.0 | "x" | 5.335 | "=" | $ 5,22,830.0 | |
| Less: Amount to be invested | $ -6,08,500 | |||||
| Net Present Value | $ -85,670.0 | |||||
| CALCULATION OF PRESENT VALUE OF INVESTMENT WITH PVF OF $ 1 @ 12% | ||||||
| Cash Flow | "x" | Annuity Factor @ 12% for 8th Year | "=" | Present Value | ||
| Total present value of cash inflow | $ 98,000.0 | "x" | 4.968 | "=" | $ 4,86,864.0 | |
| Less: Amount to be invested | $ -6,08,500 | |||||
| Net Present Value | $ -1,21,636.0 | |||||
| CALCULATION OF PRESENT VALUE OF INVESTMENT WITH PVF OF $ 1 @ 15% | ||||||
| Cash Flow | "x" | Annuity Factor @ 15% for 8th Year | "=" | Present Value | ||
| Total present value of cash inflow | $ 98,000.0 | "x" | 4.487 | "=" | $ 4,39,726.0 | |
| Less: Amount to be invested | $ -6,08,500 | |||||
| Net Present Value | $ -1,68,774.0 | |||||
| CALCULATION OF PRESENT VALUE OF INVESTMENT WITH PVF OF $ 1 @ 20% | ||||||
| Cash Flow | "x" | Annuity Factor @ 20% for 8th Year | "=" | Present Value | ||
| Total present value of cash inflow | $ 98,000.0 | "x" | 3.837 | "=" | $ 3,76,026.0 | |
| Less: Amount to be invested | $ -6,08,500 | |||||
| Net Present Value | $ -2,32,474.0 | |||||
| Present value become zero( $80 Ignorable) with interest rate 6 % it means IRR is 6% | ||||||
| Answer = IRR of the Investment is 6% | ||||||
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