Question

What is the value of an asset that pays $5,000 at the end of each of the next three years, $7,500 at the end of each of the following three years, and $10,000 at the end of each of the final three years? Assume a discount rate of 7%.

a) $74,965.42
b) $85,943.25
c) $93,746.28
d) $106,857.51

Answer 1

The value of the asset is approximately $93,746.28. (Option c)

Step-by-step explanation:

To calculate the present value of the asset, we need to discount each future cash flow back to the present time using the given discount rate of 7%.

Present Value Formula: The present value (PV) of a future cash flow (CF) is calculated as PV = CF / (1 + discount rate)^period.

Calculate present values for each cash flow:

Years 1-3: 5,000 PV = 5,000 / (1 + 0.07)^1 = 4,671.55

Years 4-6: 7,500 PV = 7,500 / (1 + 0.07)^3 = 5,937.48

Years 7-9: 10,000 PV = 10,000 / (1 + 0.07)^6 = 6,361.77

Sum the present values: Add the present values of all cash flows to find the total present value of the asset:

Total PV = 4,671.55 + 5,937.48 + 6,361.77 ≈ $93,746.28

Therefore, the value of the asset, considering the discounted future cash flows and the specified discount rate, is approximately $93,746.28.