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 $ 7500 today.

Option B: Receive a $1000 gift each year for the next 10 years. The first $1000 would be received 1 year from today.

Option C: Receive a one-time gift of $15,000 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 7% 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

1)

Present value of option A = $7,500

Present value of option B = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of option B = 1,000 * [1 - 1 / (1 + 0.03)¹⁰] / 0.03

Present value of option B = 1,000 * 8.530203

Present value of option B = $8,530.20

Present value of option C = FV / (1 + r)ⁿ

Present value of option C = 15,000/ (1 + 0.03)¹⁰

Present value of option C = 15,000/ 1.343916

Present value of option C = $11,161.41

Financial theory supports choosing Option C as it has the higher present value

2)

Present value of option A = $7,500

Present value of option B = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of option B = 1,000 * [1 - 1 / (1 + 0.07)¹⁰] / 0.07

Present value of option B = 1,000 * 7.023582

Present value of option B = $7,023.58

Present value of option C = FV / (1 + r)ⁿ

Present value of option C = 15,000/ (1 + 0.07)¹⁰

Present value of option C = 15,000/ 1.967151

Present value of option C = $7,625.24

Financial theory supports choosing Option C as it has the higher present value

3)

Present value of option A = $7,500

Present value of option B = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of option B = 1,000 * [1 - 1 / (1 + 0.1)¹⁰] / 0.1

Present value of option B = 1,000 * 6.144567

Present value of option B = $6,144.57

Present value of option C = FV / (1 + r)ⁿ

Present value of option C = 15,000/ (1 + 0.1)¹⁰

Present value of option C = 15,000/ 2.593742

Present value of option C = $5,783.15

Financial theory supports choosing Option C as it has the higher present value