Question

Which set of Cash Flows is worth more now? Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive: Option A: Receive a one-time gift of $10,000 today. Option B: Receive a $1600 gift each year for the next 10 years. The first $1600 would be received 1 year from today. Option C: Receive a one-time gift of $20,000 10 years from today.

Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth ______ today. Option B would be worth _____ today. Option C would be worth _____ today. Financial theory supports choosing Option ____

Compute the Present Value of each of these options if you expect the interest rate to be 6% annually for the next 10 years. Which of these options does financial theory suggest you should choose?
Option A would be worth ____ today. Option B would be worth $_____ today. Option C would be worth $_____ today. Financial theory supports choosing Option ____

Compute the Present Value of each of these options if you expect to be able to earn 10% annually for the next 10 years. Which of these options does financial theory suggest you should choose?
Option A would be worth _____ today. Option B would be worth _____ today. Option C would be worth _____ today. Financial theory supports choosing Option _____

Answer 1

Answer a.

If interest rate is 3%:

Option 1:

Present Value = $10,000

Option 2:

Present Value = $1,600/1.03 + $1,600/1.03^2 + $1,600/1.03^3 + .... + $1,600/1.03^10
Present Value = $1,600 * (1 - (1/1.03)^10) / 0.03
Present Value = $1,600 * 8.530203
Present Value = $13,648

Option 3:

Present Value = $20,000/1.03^10
Present Value = $14,882

Option A would be worth $10,000 today. Option B would be worth $13,648 today. Option C would be worth $14,882 today. Financial theory supports choosing Option C.

Answer b.

If interest rate is 6%:

Option 1:

Present Value = $10,000

Option 2:

Present Value = $1,600/1.06 + $1,600/1.06^2 + $1,600/1.06^3 + .... + $1,600/1.06^10
Present Value = $1,600 * (1 - (1/1.06)^10) / 0.06
Present Value = $1,600 * 7.360087
Present Value = $11,776

Option 3:

Present Value = $20,000/1.06^10
Present Value = $11,168

Option A would be worth $10,000 today. Option B would be worth $11,776 today. Option C would be worth $11,168 today. Financial theory supports choosing Option B.

Answer c.

If interest rate is 10%:

Option 1:

Present Value = $10,000

Option 2:

Present Value = $1,600/1.10 + $1,600/1.10^2 + $1,600/1.10^3 + .... + $1,600/1.10^10
Present Value = $1,600 * (1 - (1/1.10)^10) / 0.10
Present Value = $1,600 * 6.144567
Present Value = $9,831

Option 3:

Present Value = $20,000/1.10^10
Present Value = $7,711

Option A would be worth $10,000 today. Option B would be worth $9,831 today. Option C would be worth $7,711 today. Financial theory supports choosing Option A.