Build a Model

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Start with the partial model in the file Ch09 P18 Build a Model.xlsx on the textbook’s Web site. The stock of Gao Computing sells for $50, and last year’s dividend was $2.10. A flotation cost of 10% would be required to issue new common stock. Gao’s preferred stock pays a dividend of $3.30 per share, and new preferred stock could be sold at a price to net the company $30 per share. Security analysts are projecting that the common dividend will grow at a rate of 7% a year. The firm can issue additional long-term debt at an interest rate (or a before-tax cost) of 10%, and its marginal tax rate is 35%. The market risk premium is 6%, the risk-free rate is 6.5%, and Gao’s beta is 0.83. In its cost-of-capital calculations, Gao uses a target capital structure with 45% debt, 5% preferred stock, and 50% common equity.

a. Calculate the cost of each capital component—in other words, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the CAPM method and the dividend growth approach to find the cost of equity.

b. Calculate the cost of new stock using the dividend growth approach. c. What is the cost of new common stock based on the CAPM? (Hint: Find the

difference between re and rs as determined by the dividend growth approach and

then add that difference to the CAPM value for rs.) d. Assuming that Gao will not issue new equity and will continue to use the same target

capital structure, what is the company’s WACC? e. Suppose Gao is evaluating three projects with the following characteristics.

(1) Each project has a cost of $1 million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from reinvested earnings.

(2) Equity invested in Project A would have a beta of 0.5 and an expected return of 9.0%. (3) Equity invested in Project B would have a beta of 1.0 and an expected return of 10.0%. (4) Equity invested in Project C would have a beta of 2.0 and an expected return of 11.0%.

f. Analyze the company’s situation, and explain why each project should be accepted or rejected.

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FIN 565 Project Chapter: Problem: 9 18 INPUTS USED IN THE MODEL P0 $50.00 Net Ppf $30.00 Dpf $3.30 D0 g B-T rd Skye's beta Market risk premium, RPM $2.10 7% 10% 0.83 6.0% Risk free rate, rRF Target capital structure from debt Target capital structure from preferred stock Target capital structure from common stock Tax rate Flotation cost for common 6.5% 45% 5% 50% 35% 10% a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the DCF method and the CAPM method to find the cost of equity. Cost of debt: B-T rd (1 – T) × = A-T rd Cost of preferred stock (including flotation costs): Dpf / Net Ppf = rpf Cost of common equity, DCF (ignoring flotation costs): D1 / P0 + g = rs Cost of common equity, CAPM: rRF + b × RPM = = rs IMPORTANT NOTE: HERE THE CAPM AND THE DCF METHODS PRODUCE APPROXIMATELY THE SAME COST OF EQUITY. THAT OCCURRED BECAUSE WE USED A BETA IN THE PROBLEM THAT FORCED THE SAME RESULT. ORDINARILY, THE TWO METHODS WILL PRODUCE SOMEWHAT DIFFERENT RESULTS. IMPORTANT NOTE: HERE THE CAPM AND THE DCF METHODS PRODUCE APPROXIMATELY THE SAME COST OF EQUITY. THAT OCCURRED BECAUSE WE USED A BETA IN THE PROBLEM THAT FORCED THE SAME RESULT. ORDINARILY, THE TWO METHODS WILL PRODUCE SOMEWHAT DIFFERENT RESULTS. b. Calculate the cost of new stock using the DCF model. D0 × (1 + g) / P0 × (1 – F) + g = re c. What is the cost of new common stock based on the CAPM? (Hint: Find the difference between r e and rs as determined by the DCF method and add that differential to the CAPM value for r s.) rs + + Differential re = = Again, we would not normally find that the CAPM and DCF methods yield identical results. d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the company's WACC? wd 45.0% wpf 5.0% ws 50.0% 100.0% wd × A-T rd + wpf × rpf + ws × rs = = WACC e. Suppose Gao is evaluating three projects with the following characteristics: (1) Each project has a cost of $1 million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated the project. All equity will come from reinvested earnings. (2) Equity invested in Project A would have a beta of 0.5. The project has an expected return of 9.0%. (3) Equity invested in Project B would have a beta of 1.0. The project has an expected return of 10.0%. (4) Equity invested in Project C would have a beta of 2.0. The project has an expected return of 11.0%. Analyze the company’s situation and explain why each project should be accepted or rejected. Project A Project B Project C f. Beta 0.5 1.0 2.0 rs rps rd(1 – T) WACC Expected return on project
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