30.03.2023 - 17:58

Midwest Electric Company (MEC) uses only debt and common equity. It can borrow unlimited amounts at an interest rate of r_d = 10% as long as it finances at its target capital structure, which calls for 45% debt and 55% common equity. Its last dividend (D_

Midwest Electric Company (MEC) uses only debt and common equity. It can borrow unlimited amounts at an interest rate of {eq}r_d {/eq} = 10% as long as it finances at its target capital structure, which calls for 45% debt and 55% common equity. Its last dividend {eq}(D_0) {/eq} was $2.70, its expected growth rate is 4%, and its common stock sells for $22. MEC’s tax rate is 40%. Two projects are available: Project A has a rate of return of 13%, while Project B’s return is 10%. These two projects are equally risky and about as risky as the firm’s existing assets.

a) What is its cost of common equity? Round your answer to two decimal places.

b) What is the WACC? Round your answer to two decimal places.

c) Which projects should Midwest accept?

Answers (1)
  • doberman-69
    April 9, 2023 в 05:52

    a) The cost of common equity can be calculated using the CAPM formula:

    {eq}r_e = r_f + beta_e (r_m - r_f) {/eq}

    where {eq}r_f {/eq} is the risk-free rate, {eq}beta_e {/eq} is the equity beta, and {eq}r_m {/eq} is the market return.

    We are not given the equity beta directly, but we can calculate it using the target debt-to-equity ratio and the unlevered beta. Assuming the unlevered beta for MEC's assets is the same as the beta for the two projects, which are equally risky as the firm's existing assets, we have:

    {eq}beta_u = beta_A = beta_B = 1 {/eq}

    Using the formula for the levered beta, we get:

    {eq}beta_e = beta_u [1 + (1 - t) \frac{D}{E}] = 1 [1 + (1 - 0.4) \frac{0.45}{0.55}] = 1.36 {/eq}

    Assuming the risk-free rate is 2.5% and the market return is 8%, we can plug in the numbers to get:

    {eq}r_e = 2.5% + 1.36(8% - 2.5%) \approx 11.34% {/eq}

    Therefore, the cost of common equity for MEC is 11.34%.

    b) The weighted average cost of capital (WACC) can be calculated as:

    {eq}WACC = w_d r_d (1 - t) + w_e r_e {/eq}

    where {eq}w_d {/eq} and {eq}w_e {/eq} are the weights of debt and equity, respectively.

    Using the target capital structure, we have:

    {eq}w_d = 0.45 {/eq}

    {eq}w_e = 0.55 {/eq}

    {eq}r_d = 10% {/eq}

    {eq}t = 0.4 {/eq}

    {eq}r_e = 11.34% {/eq}

    Plugging in the numbers, we get:

    {eq}WACC = 0.45times10%times(1-0.4) + 0.55times11.34% \approx 8.43% {/eq}

    Therefore, the WACC for MEC is 8.43%.

    c) To determine which projects MEC should accept, we need to calculate the net present value (NPV) of each project using the WACC as the discount rate. The NPV formula is:

    {eq}NPV = sum_{t=1}^n \frac{CF_t}{(1 + WACC)^t} - C_0 {/eq}

    where {eq}CF_t {/eq} is the cash flow in year t, {eq}n {/eq} is the number of years, and {eq}C_0 {/eq} is the initial investment.

    For Project A, we have:

    {eq}CF_1 = 1000times13% = 130 {/eq}

    {eq}CF_t = CF_1times(1+4%)^{t-1} = 130times(1+4%)^{t-1} {/eq}

    {eq}C_0 = 1000 {/eq}

    Assuming the project lasts for 5

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