You work for the CEO of a new company that plans to manufacture and sell a new product,a watch that has an embedded TV set and a magnifying glass crystal.The issue now is how to finance the company,with only equity or with a mix of debt and equity.Expected operating income is $180,000.The company is small,so it is not subject to the interest deduction limitation.Other data for the firm are shown below.How much higher or lower will the firm's expected ROE be if it uses some debt rather than all equity,i.e. ,what is ROE_L - ROE_U? Do not round your intermediate calculations.

Question

Quizplus · Accepted Answer

To calculate the expected ROE with only equity (S1U) we use the formula:

ROES1U = NI / E

where NI = expected operating income - taxes, and E = equity

Using the data given:

NI = (0.6 * $180,000) - (0.4 * 0.35 * $180,000) = $64,800

E = $1,000,000

ROES1U = $64,800 / $1,000,000 = 6.48%

To calculate the expected ROE with a mix of debt and equity (S1U1B), we use the formula:

ROES1U1B = (NI - I) / E

where I = interest expense and E = equity

To find the interest expense, we need to first calculate the amount of debt the company should use.

Using the information given, we know that the company is not subject to the interest deduction limitation, so it can use as much debt as it wants. However, we don't want to use too much debt and increase the risk of bankruptcy.

To decide the optimal debt level, we can use the formula for the weighted average cost of capital (WACC):

WACC = (E / (E + D)) * Re + (D / (E + D)) * Rd * (1 - T)

where Re is the cost of equity, Rd is the cost of debt, T is the corporate tax rate, and E and D are the amounts of equity and debt, respectively.

Since we don't have the cost of equity and debt, let's assume a cost of equity of 10% and a cost of debt of 5%. Also, let's assume a corporate tax rate of 35%.

Plugging in these assumptions, we get:

WACC = (1,000,000 / (1,000,000 + D)) * 0.1 + (D / (1,000,000 + D)) * 0.05 * (1 - 0.35)

Simplifying:

WACC = 0.1 - 0.0175D / (1,000,000 + D)

To find the optimal debt level, we need to find the value of D that minimizes WACC. We can do this graphically or using calculus. Using calculus, we first take the derivative of WACC with respect to D:

dWACC / dD = 0.0175 * (1,000,000 - D) / (1,000,000 + D)^2

Setting this equal to zero and solving for D, we get D = 1,000,000, which means the company should use no debt.

Therefore, the expected ROE with a mix of debt and equity (S1U1B) is the same as the expected ROE with only equity (S1U):

ROES1U1B = ROES1U = 6.48%

The difference in ROE between using all equity and using a mix of debt and equity is 0%.

Therefore, the best choice is to finance the company with only equity.

You Work for the CEO of a New Company That