2. Cost of Capital (WACC). Suppose your company has decided to use a divisional

Question

2. Cost of Capital (WACC). Suppose your company has decided to use a divisional WACC approach to analyze projects. The firm currently has 2 divisions, A and B, with betas for each division of 0.5 and 1.5, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 5%) is 18% and the after-tax yield on the company's bonds is 6%, what are the WACCs for divisions A and B? Hint: First Solve for Market Risk Premium (MRP). MRP = (Km-Rf)

Explanation / Answer

Solution 1 Retirement age (in years) 60 Time to retirement (in years) 15 Current assets in retirement plans $250,000 Other investments $90,000 Per year contribution in retirement plans $30,000 Per year contribution to other investments $6,000 a. Calculation of money available at the age of 60 Per year growth rate of assets 9% Calculation future value of current assets and investments Total amount in current assets and investments = $250,000 + $90,000 Total amount in current assets and investments = $340,000 Future value = $340,000*((1+9%)^15) Future value = $1,238,444.04 Calculation of future value of per year contribution in retirement plans and other investments Total per year contribution = $30,000+$6,000 Total per year contribution = $36,000 Future value = Total per year contribution *((((1+growth rate)^time)-1)/growth rate) Future value = $36,000*((((1+9%)^15)-1)/9%) Future value = $1,056,992.98 Money available at the age of 60 = $1,238,444.04+$1,056,992.98 Money available at the age of 60 = $2,295,437.02 b. Calculation of annual payments Rate of return 6% Time (in years) 30 Calculation of the amount of annual payment Present Value = Annual payment * ((1-(1/((1+rate of return)^time)))/rate of return) $2,295,437.02 = Annual payment * ((1-(1/((1+6%)^30)))/6%) Annual payment = 2295437.02/((1-(1/((1+6%)^30)))/6%) Annual payment = $166,761.00 Solution 2 Division A beta 0.5 Division B beta 1.5 Proportion of debt in the capital structure 0.5 Proportion of equity in the capital structure 0.5 Risk free rate 5% Current cost of equity 16% Average firm beta 1 After tax cost of debt 6% Calculation of market risk premium Current cost of equity = Risk free rate + Market risk premium*Average firm beta 16% = 5%+Market risk premium*1 Market risk premium = 16%-5% Market risk premium = 11% a. Division A WACC Cost of Division A equity = Risk free rate + Market risk premium *Division A beta Cost of Division A equity = 5% + 11% * 0.5 Cost of Division A equity = 10.50% Source of financing Weight Cost of capital Weight*Cost of capital Equity 0.5 10.50% 0.0525 Debt 0.5 6.00% 0.0300 Total 1 0.0825 Division A WACC = Weight of equity * cost of equity + weight of debt * cost of debt Division A WACC = 8.25% b. Division B WACC Cost of Division B equity = Risk free rate + Market risk premium *Division B beta Cost of Division B equity = 5% + 11% * 1.5 Cost of Division B equity = 21.50% Source of financing Weight Cost of capital Weight*Cost of capital Equity 0.5 21.50% 0.1075 Debt 0.5 6% 0.0300 Total 1 0.1375 Division B WACC = Weight of equity * cost of equity + weight of debt * cost of debt Division B WACC = 13.75%

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