Suppose that UK Motors Ltd. is considering an investment of £30 million to develop a newfactory. Assume that the company’s stockholders require a 22% rate of return, that thecompany’s bondholders require a 9% rate of return, that the UK corporate tax rate is 40%,that 35% of the project will be financed by debt, and that 65% of the project will be financedwith equity. What must be the annual income from the project if it is to be a zero net presentvalue investment?
Question
Suppose that UK Motors Ltd. is considering an investment of £30 million to develop a newfactory. Assume that the company’s stockholders require a 22% rate of return, that thecompany’s bondholders require a 9% rate of return, that the UK corporate tax rate is 40%,that 35% of the project will be financed by debt, and that 65% of the project will be financedwith equity. What must be the annual income from the project if it is to be a zero net presentvalue investment?
Solution
To calculate the annual income from the project for it to be a zero net present value investment, we need to first calculate the weighted average cost of capital (WACC).
The WACC is the average rate of return a company is expected to pay its investors; the weights are the proportion of debt and equity in the company's capital structure.
The formula for WACC is:
WACC = (E/V * Re) + ((D/V * Rd) * (1 - Tc))
Where: E = market value of equity V = total market value of equity and debt Re = cost of equity D = market value of debt Rd = cost of debt Tc = corporate tax rate
Given in the problem: E/V = 65% or 0.65 (equity financing) Re = 22% or 0.22 (required return on equity) D/V = 35% or 0.35 (debt financing) Rd = 9% or 0.09 (required return on debt) Tc = 40% or 0.40 (corporate tax rate)
Substituting these values into the formula, we get:
WACC = (0.65 * 0.22) + ((0.35 * 0.09) * (1 - 0.40)) WACC = 0.143 + 0.0189 WACC = 0.1619 or 16.19%
This is the return that the project needs to generate to satisfy the investors.
To find the annual income that would make the project a zero net present value investment, we need to divide the initial investment by the WACC.
So, £30 million / 0.1619 = £185,179,211.
Therefore, the project must generate an annual income of approximately £185.18 million to be a zero net present value investment.
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