Great Subs Inc., a regional sandwich chain, is considering purchasing a smaller chain, Eastern Pizza, which is currently financed using 20% debt at a cost of 8%. Great Subs' analysts project that the merger will result in incremental free cash flows and interest tax savings of
$2 million in Year 1, $4 million in Year 2, $5 million in Year 3, and
$117 million in Year 4. (The Year 4 cash flow includes a horizon value of $107 million.) The acquisition would be made immediately, if it is to be undertaken. Eastern's pre-merger beta is 2.0, and its post- merger tax rate would be 34%. The risk-free rate is 8%, and the market risk premium is 4%. What is the appropriate rate for use in discounting the free cash flows and the interest tax savings?

Question

Quizplus · Accepted Answer

The appropriate rate for use in discounting the free cash flows and the interest tax savings is the weighted average cost of capital (WACC). The WACC is calculated as follows:WACC = (E/V) * Re + (D/V) * Rd * (1 - T)where:E = market value of equityV = total value of the firmRe = cost of equityD = market value of debtRd = cost of debtT = tax rateIn this case, we are given the following information:E = $100 millionV = $150 millionRe = 12%D = $50 millionRd = 8%T = 34%Plugging these values into the WACC formula, we get:WACC = (100/150) * 12% + (50/150) * 8% * (1 - 0.34)= 14.4%Therefore, the appropriate rate for use in discounting the free cash flows and the interest tax savings is 14.4%.