Question

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 $ 10,000 today. Option B would be worth $__________ today. Option C would be worth $__________ today. Financial theory supports choosing Option _______

Answer 1

Step 1 : Identifying the available options

• 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.

Expected interest rate = 2% pa

Step 2 : Calculate the present worth of all the options

In order to calculate which set of cash flows will provide the most benefit. We should calculate the present worth of all the available options.

(i) Option A (As the money is received today itself no adjustment is required)

Present Value of gift = $ 10,000

(ii) Option B In case of Annual payments of $1600 received at the end of each year.

where
A = Annuity receipt every year
r = rate of return
n = Time period

PV = $1600 * PVAF (2%,10)

PV = $1600 * 8.98258501

PV of gift = $14,372.14

(iii) Option C: Receiving future value after 10 years = $20,000

where
FV = Future value  
r = rate of return
n = Time period

PV = $20,000 * PVF(2%,10)

PV = $20,000 * 0.82034830

PV of gift = $16,406.97

ANS :

Option A would be worth $ 10,000 today

Option B would be worth $14,372.14 today

Option C would be worth $16,406.97 today

Decision: Since the present worth of option C is highest we should choose option C.

Financial theory supports choosing Option is Expectations Theory

In Expectations theory, we forecast the future or expected rate of interest and apply the rate of interest on future projected cash flows in order to calculate their present worth.