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

Ans:- In this question, first we will find the PV of all the options and compare them, the option with the highest PV needs to be chosen as per the Financial theory.

Option A;- PV of option A is $10,000.

Option B:- This is a case of an ordinary annuity. PV of an ordinary annuity is given by

P * [ 1 - (1 + r)^-n] / r, where P is the Periodic Payment, r is the rate of return and n is the number of periods

= $1600 * [ 1 - (1 + 0.02) ^-10] / 0.02 = $14,372.16

Option C:- PV, in this case, will be given by CF / ( 1 +r )^n, where CF is the cash flow, r is the annual rate and n is the time period.

= $20,000 / (1 + 0.02 )^10 = $16,406.97.

From the above it is clear that Option C has the highest Present Value, therefore Option (c) should be chosen as per the Financial theory.

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