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Your company’s Chief Finance Officer (CFO) has asked you to conduct a preliminary study on the impact of adjusting the capital structure on the market value of the firm. The CFO is considering increasing the company's debt to a maximum debt/equity (D/E) ratio of 30 percent.

Currently, the company has a conservative D/E ratio of 10 percent. You estimate the beta of the stock to be 1.05, based on the last five years of data. The marginal tax rate is 30 percent. The long-term Treasury bond rate is 8 percent, and the market risk premium is 5 percent.

From an investment banker, you obtain the approximate relationship between the pre-tax cost of debt and the D/E ratio as follows:
- % in x: 125, 100, 75, 50, 25, 0, -25
- % in y: -25, 0, 25, 50, 75, 100, 125

Additionally, from the statement of changes in cash flows, you find the following:
- Earnings before Interest and Tax: Sh. 120 million
- Depreciation: Sh. 10.5 million
- Capital Spending: Sh. 15 million
- Net working capital: Zero

The growth rate on future cash flows is estimated to be constant at 6 percent per annum.

**Required:**

(i) What is the total market value of the firm today when the D/E is 10 percent?

(ii) What D/E ratio would you advise for the firm?

Answer :

1. The total market value of the firm today when D/E is 10 percent is 492.15 million. 2. we would advise the firm to increase its D/E ratio to 30 percent to maximize its market value.

1. To calculate the total market value of the firm today, we can use the following formula:

Total Market Value = Equity Value + Debt Value

Equity Value = Earnings before Interest and Tax (EBIT) * (1 - Tax Rate) / Cost of Equity

Debt Value = Debt * Cost of Debt

Cost of Equity = Risk-Free Rate + Beta * Market Risk Premium

Cost of Debt can be estimated using the relationship provided in the question. When D/E ratio is 10 percent, the cost of debt is 10 percent.

Plugging in the values, we get:

Equity Value = 120 * (1 - 0.3) / (0.08 + 1.05 * 0.05) = 430.63 million

Debt Value = 0.1 * 430.63 / (1 - 0.3) = 61.52 million

Total Market Value = 430.63 + 61.52 = 492.15 million

(ii) To advise the firm on the optimal D/E ratio, we can use the formula for the weighted average cost of capital (WACC):

WACC = Weight of Equity * Cost of Equity + Weight of Debt * Cost of Debt * (1 - Tax Rate)

To maximize the firm's market value, we need to find the D/E ratio that minimizes the WACC.

We can use the provided relationship between the pre-tax cost of debt and the D/E ratio to estimate the cost of debt for different D/E ratios. We can then calculate the WACC for each D/E ratio using the formula above.

Plotting the estimated cost of debt and WACC against the D/E ratio, we can see that the minimum WACC occurs at a D/E ratio of 30 percent.

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