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

1) When Interest rate is 3 % annually

Option A : Present Value for option A would be 10,000

Option B : The Present Value of the cash flow would be 1,400/1.03 + 1400/1.03^2 + 1400/1.03^3.....1400/1.03^10

{ PV = FV/(1+ i )^N} = 1400 * [1-(1/1.03)^10]/ 0.3 = 1400 * 8.530 = 11942

Option C : The present Value of Gift given after 10 year worth 17,000 = 17000/1.03^10 = 12650

Therefore option C is worth 12650 today and option C should be availed from your grandmother as its the most sound financial choice.

2) Now what if the interest rate annually is 6 %

Option A = Gift would be having the same present value at 10,000

Option B The present value of cash flow for the next 10 years at discounted rate of 6 % would be 1,400/1.06 + 1400/1.06^2 + 1,400/1.06^3....1400/1.06^10

= 1400 * [1-(1/1.06)^10]/0.06 = 1400 * 7.360 = 10,304

Option C = 17,000 / 1.06^10 = 9,493

Here we must go for the option B as its value 10,304 which is highest among all options and you must tell your grandmother to give you 1,400 as gift each year for next 10 year.

3) Now, the interest rates annually is 9 % let's see how its affects our options now.

Option A : Present Value remains the same as 10,000 as you are recieving it immediately.

Option B The Present Value of cashflows for the next 10 years at interest or discounted rate of 9 % would be as 1,400/1.09 +1,400/1.09^2 + 1,400/1.09^3 + 1,400/1.09^4......1,400/1.09^10

= 1400* [ 1-(1/1.09)^10]/0.09 = 1400 * 6.417 = 8,989

Option C : 17,000/ 1.09^10 = 7,181

As per financial theory we must go for option A as it gives the highest prevent value of 10,000 which is more than other options, so you must tell your grandmother to give you 10,000 as a giftb immediately.