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]

Question

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]

View Explanation

Log in for full answers

Similar Questions

If you receive $99 each quarter for 8 years and the discount rate is 0.1, what is the present value?

If you receive $102 each month for 4 years and the discount rate is 0.06, what is the present value?

If you receive $223 each month for 12 months and the discount rate is 0.11, what is the present value?

If you receive $58 each quarter for 15 years and the discount rate is 0.09, what is the present value?

If you receive $193 each month for 12 months and the discount rate is 0.05, what is the present value?

What is the present value (to the nearest dollar) of a six-period annuity of $300 per year that begins three years from today if the discount rate is 8%?[Fill in the blank]

If you receive $197 each month for 21 years and the discount rate is 0.03, what is the present value?

If you receive $172 each quarter for 15 years and the discount rate is 0.11, what is the present value?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler