A firm is considering a project with annual cash flows of £75,000. The project would have a 7-year life, and the company uses a discount rate of 10 per cent. What is the maximum amount the company could invest in the project and the project still be acceptable?

Question

Quizplus · Accepted Answer

To find the maximum amount the company can invest and still have a positive net present value, we have to calculate the present value of the cash flows and subtract it from the initial investment. 
The present value of the cash flows can be calculated as follows:

PV = CF/(1+r)^n

Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods.

Using the formula, we can find the present value of the annual cash flows:

PV = £75,000/(1+0.10)^1 + £75,000/(1+0.10)^2 + £75,000/(1+0.10)^3 + £75,000/(1+0.10)^4 + £75,000/(1+0.10)^5 + £75,000/(1+0.10)^6 + £75,000/(1+0.10)^7 
PV = £424,718.32

Now, we can calculate the maximum investment by subtracting the present value of the cash flows from the initial investment:

Max investment = PV - initial investment 
Max investment = £424,718.32 - X

We want the net present value to be zero or higher, so: 
0 ≤ PV - initial investment 
0 ≤ £424,718.32 - X 
X ≤ £424,718.32

Therefore, the maximum amount the company could invest in the project and the project still be acceptable is £365,100 (option B). Any investment higher than that would result in a negative net present value.

A Firm Is Considering a Project with Annual Cash Flows