Question

Use what you have learned about the time value of money to analyze each of the following decisions: (PLEASE SHOW WORK)

Decision #1:   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.

1. 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? (PLEASE SHOW WORK)

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

2. 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? (PLEASE SHOW WORK)

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

3. 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? (PLEASE SHOW WORK)

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