Question

Use what you have learned about the time value of money to analyze each of the following decisions:

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 2% 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 5% 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 8% 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

If interest rate is 2%:

Option 1:

Present Value = $10,000

Option 2:

Present Value = $1,600/1.02 + $1,600/1.02^2 + …. + $1,600/1.02^9 + $1,600/1.02^10
Present Value = $1,600 * (1 - (1/1.02)^10) / 0.02
Present Value = $1,600 * 8.982585
Present Value = $14,372

Option 3:

Present Value = $20,000/1.02^10
Present Value = $16,407

Option A would be worth $10,000 today.
Option B would be worth $14,372 today.
Option C would be worth $16,407 today.
Financial theory supports choosing Option 3

If interest rate is 5%:

Option 1:

Present Value = $10,000

Option 2:

Present Value = $1,600/1.05 + $1,600/1.05^2 + …. + $1,600/1.05^9 + $1,600/1.05^10
Present Value = $1,600 * (1 - (1/1.05)^10) / 0.05
Present Value = $1,600 * 7.721735
Present Value = $12,355

Option 3:

Present Value = $20,000/1.05^10
Present Value = $12,278

Option A would be worth $10,000 today.
Option B would be worth $12,355 today.
Option C would be worth $12,278 today.
Financial theory supports choosing Option 2

If interest rate is 8%:

Option 1:

Present Value = $10,000

Option 2:

Present Value = $1,600/1.08 + $1,600/1.08^2 + …. + $1,600/1.08^9 + $1,600/1.08^10
Present Value = $1,600 * (1 - (1/1.08)^10) / 0.08
Present Value = $1,600 * 6.710081
Present Value = $10,736

Option 3:

Present Value = $20,000/1.08^10
Present Value = $9,264

Option A would be worth $10,000 today.
Option B would be worth $10,736 today.
Option C would be worth $9,264 today.
Financial theory supports choosing Option 2