What is the maximum that should be invested in a project at time zero if the inflows are estimated at $25,000 annually for four years, and the cost of capital is 9%?[Fill in the blank]单项选择题
A
a. $25,000.00
B
b. $19,007.00
C
c. $91,743.12
D
d. $80,993.00

Question

What is the maximum that should be invested in a project at time zero if the inflows are estimated at $25,000 annually for four years, and the cost of capital is 9%?[Fill in the blank]

BlackTom AI · Accepted Answer

We need the maximum amount to invest at time zero given a 9% cost of capital and four annual inflows of 25,000. This is the present value of an ordinary annuity with payment PMT = 25,000, i = 9%, n = 4.

Option a: $25,000.00
- This would imply that the project’s present value equals one year’s inflow, which ignores three additional future inflows and the time value of money. It is far too small.

Option b: $19,007.00
- This value is not consistent with the PV of four payments of 25,000 at 9%. It represents neither a correct PV calculation nor a meaningful breakpoint in relation to the given cash flows.

Option c: $91,743.12
- This is higher than the true PV of the four 25,000 inflows at 9%. It would correspond to a higher discount factor or misapplied formula. The standard PV of an ordinary annuity at 9% for 4 years is smaller than this, so this overstates the correct PV.

Option d: $80,993.00
- This aligns closely with the precise present value: PV = 25,000 × [(1 − (1+0.09)^(−4)) / 0.09]. Computing (1.09)^4 ≈ 1.4116, so (1+0.09)^(−4) ≈ 0.708; 1 − 0.708 ≈ 0.292; 0.292 / 0.09 ≈ 3.244; 25,000 × 3.244 ≈ 81,100. The value 80,993 is the closest compatible PV to the standard calculation, reflecting rounding differences.

In summary, the maximum time-zero investment is the present value of the four inflows discounted at 9%. The options show common misinterpretations (a and b) and a miscalculation (c); option d correctly reflects the PV with typical rounding.}

What is the maximum that should be invested in a project at time zero if the inflows are estimated at $25,000 annually for four years, and the cost of capital is 9%?[Fill in the blank]单项选择题

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