Question

Relationship between future value and present value: Mix stream. Using the information in the accompanying table, answer the questions that follow. Year Cash flow 0 $0 1 800 2 900 3 1000 4 1500 5 2000 a. Determine the present value of the mixed stream of cash flows, using a 5% discount rate. b. Suppose you had a lump sum equal to your answer in part (a) on hand today. If you invested this sum for 5 years and earned a 5% return each year, how much would you have after 5 years? c. Determine the future value 5 years from now of the mixed stream, using a 5% interest rate. Compare your answer here to your answer in part b. d. How much would you be willing to pay for this stream, assuming that you can at best earn 5% on your investments?

Answer 1

Answer a.

Cash Flows:
Year 1 = $800
Year 2 = $900
Year 3 = $1,000
Year 4 = $1,500
Year 5 = $2,000

Discount Rate = 5%

Present Value = $800/1.05 + $900/1.05^2 + $1,000/1.05^3 + $1,500/1.05^4 + $2,000/1.05^5
Present Value = $5,243.17

Answer b.

Amount Invested = $5,243.17
Return = 5%
Period = 5 years

Future Value = Amount Invested * (1 + Return)^Period
Future Value = $5,243.17 * 1.05^5
Future Value = $6,691.76

Answer c.

Future Value = $800*1.05^4 + $900*1.05^3 + $1,000*1.05^2 + $1,500*1.05 + $2,000
Future Value = $6,691.76

Both answer are same.

Answer d.

Maximum amount paid for this stream is $5,243.17