Decision #1: Which set of Cash Flows is worth more now? Assume that your grandmo

Question

Decision #1:   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 $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 4% 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 _______

Explanation / Answer

Solution - We need to find the present value of Option B & Option C ,as Present Value of Option A is $10000 and it will remain the same no matter what interest prevails in future - So we have

Lets Calulate Y ie Present value of Option C by using the below formula

PV = FV / (1+i)power n

Where PV = Present Value = To find

FV = Future Value = $20000 ( Given )

i = Interest Rate

n = Period = 10 Years ( Given )

So we have presnt Value of Option C as Below

Lets Calulate X ie Present value of Option B

Here we could use below formula to calculate Present Value of annual amount for n period

PV = P X ( 1-(1+r)Power(-n)/r   where P = Periodic Pament= $1600 , r= Interest Rate , n = Period = 10

Using the above formula we have the present value at three different interest rates as below

So below are the answers for each scenario

Particular Present Value Option A - Receive a one-time gift of $10,000 today 10000 Option B - Receive a $1600 gift each year for the next 10 years X Option C -Receive a one-time gift of $20,000 10 years from today Y

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