Question

Martin Technologies Inc., a large electronics company, is evaluating the possible acquisition of Columbia Electronics, a regional electronics company. Martin’s analysts project the following post-merger data for Columbia (in millions of dollars): 2015 2016 2017 2018 Net sales $300 $425 $475 $550 Selling and administrative expense 40 50 60 75 Interest 25 30 35 40 Tax rate after merger 35% Cost of goods sold as a percent of sales 75% Beta after merger 1.2000 Risk-free rate 4% Market risk premium 5% Continuing growth rate of cash flow available to Martin 4% If the acquisition is made, it will occur on January 1, 2015. All cash flows shown in the income statements are assumed to occur at the end of the year. Columbia currently has a capital structure of 40% debt, but Martin would increase that to 50% if the acquisition were made. Columbia, if independent, would pay taxes at 20%; but its income would be taxed at 35% if it were consolidated. Columbia’s current market-determined beta is 1.15, and its investment bankers think that its beta would rise to 1.2000 if the debt ratio were increased to 50%. The cost of goods sold is expected to be 75% of sales, but it could vary somewhat. Depreciation-generated funds would be used to replace worn-out equipment, so they would not be available to Martin’s shareholders. The risk-free rate is 4%, and the market risk premium is 5%. What is the appropriate discount rate for valuing the acquisition? % (to 4 decimals)

Answer 1

As Martin Technologies is yet to acquire Columbia Electronics, the former needs to look at pre-merger data of FCFs, Dividends, etc to value the latter. All available data is for the post-merger scenario and hence is irrelevant to the act of determining the appropriate pre-merger fair value of Columbia Electronics. However, we have data regarding Columbia's pre-merger capital structure, equity beta, tax rate and cost of debt. The same can be used to determine the firm's WACC which in turn would be the appropriate discount rate for determining the firm's pre-merger fair value. This is true because the firm's WACC(the pre-merger one) incorporates the risks associated with the firm's pre-merger capital structure, tax rate, and equity beta, thereby naturally being the WACC (or discount rate) of choice for discounting the firm's pre-merger cash flows.

The firm's initial equity beta is 1.15, which increases to 1.2 upon introduction of more debt thereby proving that the debt is not default risk-free. This, in turn, would mean that the risk-free rate is not an appropriate measure of the firm's cost of debt.

Let the firm's cost of debt be kd

Risk-Free Rate = Rf = 4% and Market Risk Premium = MRP = 5% , Equity Beta = Levered Beta = Bl = 1.15

Debt to Equity Ratio = D/E = (2/3) and Tax Rate = t = 20%

Therefore, Unlvered Beta = Levered Beta / [1+(1-t) x D/E] = 1.15 / [1+(1-0.2) x (2/3)] = 0.75

Unlvered Cost of Equity = ko = Rf + Unlevered Beta x MRP = 4 + 0.75 x 5 = 7.75 %

Levered Cost of Equity = ke = Rf + Bl x MRP = 4 + 1.15 x 5 = 9.75%

Therefore, ke = ko + (D/E) x (1-t) x (ko - kd)

9.75 = 7.75 + (2/3) x (1-0.2) x (7.75 - kd)

2 x (3/2) x (1/0.8) = (7.75 - kd)

kd = 4 %

Therefore, company's pre-merger WACC = kd x (1-t) x (D/V) + ke x (E/V) = 4 x (1-0.2) x (0.4) + 9.75 x (0.6) = 7.13 %

The appropriate discount rate for valuing the acquisition is the company's pre-merger WACC which is 7.13 %.