Question
In: Finance
You will receive the following cash payments as a retirement settlement: Year 1 2 3 4...
You will receive the following cash payments as a retirement settlement: Year 1 2 3 4 5 Amount $10,000 $20,000 $50,000 $50,000 $75,000 In place of the above you are offered a check today for $178,000. Assuming an interest rate of 4%, which would you choose? If an interest rate of 3% was used would this change your selection? Explain.
Solutions
Expert Solution
Assuming an interest rate of 4% present value of cash flows is $176,941.06 which is less than the cash receipt of $178,000 received today. Hence, a check today of $178,000 will be present due to higher value of discounted cash flows.
However if the the interest rate is 3%, the present value of cash flows is $183,437.75 which is more than $178,000 received today. Hence, the stream of cash payments over 5 years must be preferred to a check today.
Workings:
| Year | Amount | PV Factor @4% | Present value |
| 1 | 10,000 | 0.961538462 | 9615.384615 |
| 2 | 20,000 | 0.924556213 | 18491.12426 |
| 3 | 50,000 | 0.888996359 | 44449.81793 |
| 4 | 50,000 | 0.854804191 | 42740.20955 |
| 5 | 75,000 | 0.821927107 | 61644.53301 |
| Present value of cash flows at 4% interest rate | 176941.0694 |
| Year | Amount | PV Factor @3% | Present value |
| 1 | 10,000 | 0.970873786 | 9708.737864 |
| 2 | 20,000 | 0.942595909 | 18851.91818 |
| 3 | 50,000 | 0.915141659 | 45757.08297 |
| 4 | 50,000 | 0.888487048 | 44424.3524 |
| 5 | 75,000 | 0.862608784 | 64695.65883 |
| Present value of cash flows at 3% interest rate | 183437.7502 |
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