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

jeff jeffy answered 1 year ago

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