Question

You have a lot of uncles that are dying and leaving you inheritances. • Uncle 1 died today and left you $10,000. • Uncle 2 will die in 2 years and will leave you another $10,000. • Uncle 3 will die in 5 years and will leave you yet another $10,000. • Uncle 4 is doing fine but in the spirit of the others, has signed a will leaving you $10,000 to be given to you in 6 years from now . • Uncle 5 is also doing well. He will give you $25,000 in 8 years from now under the condition that today you donate $5,000 to a finance program . Assume these promises are good as gold in other words, you are certain that they will happen. Assume that the interest rate is 5% per year. Assume your aunt Petunia is willing you to front you a lump sum of money in exchange for all these inheritances. In other words, Petunia is going to buy these cash flows from you. What price should you charge Petunia? Solve this problem using both NPV and PV. Your answers should be positive numbers.

Answer 1

Aunt Petunia should pay $46,538.06 for the cash flows from the inheritances, calculated by finding the present value of each cash inflow and taking into account the $5,000 donation made today.

Step-by-step explanation:

To find the price Aunt Petunia should pay to buy the cash flows from the inheritances, we need to calculate the present value (PV) of each future cash inflow using the formula PV = FV / (1 + r)n, where FV is the future value, r is the interest rate, and n is the number of years until the cash flow occurs. We also need to take into account the $5,000 donation made today to receive the $25,000 from Uncle 5.

1. Uncle 1: $10,000 received today has a PV of $10,000 because it is already in present day terms.
2. Uncle 2: $10,000 received in 2 years has a PV of $10,000 / (1 + 0.05)2 = $9,070.29.
3. Uncle 3: $10,000 received in 5 years has a PV of $10,000 / (1 + 0.05)5 = $7,835.26.
4. Uncle 4: $10,000 received in 6 years has a PV of $10,000 / (1 + 0.05)6 = $7,472.25.
5. Uncle 5: $25,000 received in 8 years minus the $5,000 donation made today. The future value of $25,000 has a PV of $25,000 / (1 + 0.05)8 = $17,160.26. Since the $5,000 donation is made today, it does not need to be discounted, and the PV of the donation is simply $5,000.

Now, summing up the PV of all these cash inflows gives us the net present value (NPV) that Aunt Petunia should pay: $10,000 + $9,070.29 + $7,835.26 + $7,472.25 + $17,160.26 - $5,000 = $46,538.06.

Therefore, Aunt Petunia should pay $46,538.06 to buy the cash flows from the inheritances using a 5% discount rate.