Mr. Hall wants to receive $45,000 at the end of each year in today's dollars for the next 15 years. He is concerned about inflation and wants you to determine the lump sum he would need if the annual rate of inflation averages four percent and he could earn nine percent on his investment.

Question

Quizplus · Accepted Answer

To determine the lump sum Mr. Hall would need to receive $45,000 at the end of each year for the next 15 years, we can use the present value of an annuity formula:

PV = C [(1 - (1 + r)^-n) / r]

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of periods.

First, we need to calculate the inflation-adjusted cash flow for each year. The first year's payment is already given as $45,000, but we need to adjust it for inflation in the following years. In year two, this payment will be worth $45,000 / (1 + 0.04) = $43,269.23 in today's dollars. In year three, it will be worth $43,269.23 / (1 + 0.04) = $41,870.69, and so on. We can create a table to calculate the inflation-adjusted cash flow for each year:

Year	Cash Flow	Inflation-adjusted Cash Flow
1	$45,000	$45,000
2	$45,000	$43,269.23
3	$45,000	$41,870.69
4	$45,000	$40,758.16
5	$45,000	$39,889.54
6	$45,000	$39,229.65
7	$45,000	$38,748.09
8	$45,000	$38,419.19
9	$45,000	$38,220.98
10	$45,000	$38,136.23
11	$45,000	$38,150.41
12	$45,000	$38,251.63
13	$45,000	$38,430.54
14	$45,000	$38,679.34
15	$45,000	$38,991.76

Next, we can use the formula to calculate the present value of these cash flows. We'll use a discount rate of 9%, since Mr. Hall could earn 9% on his investment:

PV = $45,000 [(1 - (1 + 0.09)^-15) / 0.09] = $470,094.70

However, this is the present value of the cash flows without considering inflation. We need to adjust this amount for inflation by dividing it by (1 + 0.04)^15:

Inflation-adjusted PV = $470,094.70 / (1 + 0.04)^15 = $495,967.26

Therefore, Mr. Hall would need a lump sum of approximately $495,967 in today's dollars to receive $45,000 at the end of each year for the next 15 years, given an average inflation rate of 4% and an investment return of 9%. The best choice is B.

Mr Hall Wants to Receive $45,000 at the End of Each