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 $1400 gift each year for the next 10 years. The first $1400 would be received 1 year from today.   

Option C: Receive a one-time gift of $17,000 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 9% 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

We need to calculate the PV of all the options today, with option A already at PV, option B is an ordinary annuity and option C is a lumpsum received at future date

Interest Rate = 3%

Option A - PV = $10,000

Option B - PV of ordinary annuity can be calculated using mathematical relation:

PV = 1400 * 8.53

PV = $11,942.28

Option C - This is a lumpsum amount

PV = FV/(1 + r)ⁿ

PV = 17000/(1 + 3%)¹⁰

PV = $12,649.60

Hence, with highest PV, OPTION C is the best.

Interest Rate = 6%

Option A - PV = $10,000

Option B - PV of ordinary annuity can be calculated using mathematical relation:

PV = 1400 * 7.36

PV = $10,304.12

Option C - This is a lumpsum amount

PV = FV/(1 + r)ⁿ

PV = 17000/(1 + 6%)¹⁰

PV = $9,492.71

Hence, with highest PV, OPTION B is the best.

Interest Rate = 9%

Option A - PV = $10,000

Option B - PV of ordinary annuity can be calculated using mathematical relation:

PV = 1400 * 6.42

PV = $8,984.72

Option C - This is a lumpsum amount

PV = FV/(1 + r)ⁿ

PV = 17000/(1 + 9%)¹⁰

PV = $7,180.98

Hence, with highest PV, OPTION A is the best.