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# 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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## 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.

Clarabelle
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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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