A corporate financial analyst must calculate the value of an asset which produces year-end annual cash flows of $0 the first year, $2,000 the second year, $3,000 the third year, and $2,500 the fourth year. Assuming a discount rate of 15 percent, what is the value of this asset?

Question

A corporate financial analyst must calculate the value of an asset which produces year-end annual cash flows of $0 the first year, $2,000 the second year, $3,000 the third year, and $2,500 the fourth year.  Assuming a discount rate of 15 percent, what is the value of this asset?

BlackTom AI · Accepted Answer

We need the present value of the cash flows: year 2 = 2000, year 3 = 3000, year 4 = 2500, with a discount rate of 15% per year.

First, compute the present value factors:
- (1.15)^2 = 1.3225
- (1.15)^3 = 1.520875
- (1.15)^4 = 1.74900625

Now evaluate each cash flow:
- PV of year 2 cash flow: 2000 / 1.3225 ≈ 2000 ÷ 1.3225 ≈ 1512.0
- PV of year 3 cash flow: 3000 / 1.520875 ≈ 3000 ÷ 1.520875 ≈ 1972.0
- PV of year 4 cash flow: 2500 / 1.74900625 ≈ 2500 ÷ 1.74900625 ≈ 1429.0

Add these present values to obtain the asset’s value:
1512.0 + 1972.0 + 1429.0 ≈ 4913.0

Proceeding to compare with the given options:
- Option "$4,914": This is very close to the calculated ≈ $4,913; rounding differences in intermediate steps can produce this value.
- Option "$5,651": This would require substantially larger PVs for one or more cash flows, which is inconsistent with the 15% discounting.
- Option "$7,500": This would imply a much larger present value, impossible given the cash flows and high discount rate.
- Option "$5,708": Also higher than the computed total, suggesting a misestimation of present values or an incorrect discounting base.

In summary, the calculation aligns with the $4,914 choice, since the sum of discounted cash flows is about $4,913 to $4,914 depending on rounding during division steps. The other options overshoot the present value by a noticeable margin given the same cash flows and discount rate.

A corporate financial analyst must calculate the value of an asset which produces year-end annual cash flows of $0 the first year, $2,000 the second year, $3,000 the third year, and $2,500 the fourth year. Assuming a discount rate of 15 percent, what is the value of this asset?单项选择题

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