A company is wondering whether to invest £18,000 in a project which would make extra profits of £10,009 in the first year, £8,000 in the second year and £6,000 in the third year. It’s cost of capital is 10% (in other words, it would require a return of at least 10% on its investment). You are required to evaluate the project.



Answer to a math question A company is wondering whether to invest £18,000 in a project which would make extra profits of £10,009 in the first year, £8,000 in the second year and £6,000 in the third year. It’s cost of capital is 10% (in other words, it would require a return of at least 10% on its investment). You are required to evaluate the project.

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To evaluate the project, we can use the Net Present Value (NPV) method. NPV is the difference between the present value of cash inflows and the present value of cash outflows over a period of time, discounted at the company's cost of capital. The NPV formula is given by: NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - C_0 where: -CF_t is the net cash flow during the period t , - r is the discount rate (cost of capital), - n is the total number of periods, - C_0 is the initial investment cost. Given that: - Initial investment C_0 = £18,000, - Cash inflows in year 1 CF_1 = £10,009, - Cash inflows in year 2 CF_2 = £8,000, - Cash inflows in year 3 CF_3 = £6,000, - Cost of capital r = 0.10 (10%), Substitute these values into the NPV formula: NPV = \frac{£10,009}{(1 + 0.10)^1} + \frac{£8,000}{(1 + 0.10)^2} + \frac{£6,000}{(1 + 0.10)^3} - £18,000 Calculate the NPV to determine whether the project is a good investment or not. NPV \approx \frac{£10,009}{1.10} + \frac{£8,000}{(1.10)^2} + \frac{£6,000}{(1.10)^3} - £18,000 NPV \approx £9,099.09 + £6,611.57 + £4,507.89 - £18,000 NPV \approx £2,218.55 Since the NPV is positive (£2,218.55), the project is considered financially viable. A positive NPV suggests that the project is expected to generate more cash inflows than the initial investment, providing a return greater than the cost of capital (10%). Therefore, it may be advisable for the company to invest £18,000 in this project.

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