Marston Marble Corporation is considering a merger with the Conroy Concrete Comp

Question

Marston Marble Corporation is considering a merger with the Conroy Concrete Company. Conroy is a publicly traded company, and its beta is 1.30. Conroy has been barely profitable, so it has paid an average of only 20% in taxes during the last several years. In addition, it uses little debt; its target ratio is just 25%, with the cost of debt 9%. If the acquisition were made, Marston would operate Conroy as a separate, wholly owned subsidiary. Marston would pay taxes on a consolidated basis, and the tax rate would therefore increase to 35%. Marston also would increase the debt capitalization in the Conroy subsidiary to wd = 40%, for a total of $22.27 million in debt by the end of Year 4, and pay 9.5% on the debt. Marston's acquisition department estimates that Conroy, if acquired, would generate the following free cash flows and interest expenses (in millions of dollars) in Years 1-5:

Year Free Cash Flows Interest Expense

1 $1.30 $1.2

2 1.50 1.7

3 1.75 2.8

4 2.00 2.1

5 2.12 ?

In Year 5, Conroy's interest expense would be based on its beginning-of-year (that is, the end-of-Year-4) debt, and in subsequent years both interest expense and free cash flows are projected to grow at a rate of 6%. These cash flows include all acquisition effects. Marston's cost of equity is 10.5%, its beta is 1.0, and its cost of debt is 9.5%. The risk-free rate is 6%, and the market risk premium is 4.5%.

a. What is the value (in dollars) of Conroy's unlevered operations, and what is the value of Conroy's tax shields under the proposed merger and financing arrangements?

b. What is the dollar value of Conroy's operations? If Conroy has $10 million in debt outstanding, how much would Marston be willing to pay for Conroy?

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Part A:

Cost of Equity = Risk Free Rate + Beta*(Market Risk Premium) = = 6% + 1.3(4.5%) = 11.85%

Unlevered Cost of Equity = 25%*9% + 75%*11.85% = 11.14%

Unlevered Value of Horizon = Free Cash Flow in Year 5*(1+Growth Rate)/(Unlevered Cost of Equity - Growth Rate) = 2.12*(1+.06)/(.1114-.06) = 43.72 million

Unlevered Value of Operations (Vop Unlevered) = 1.3/(1+.1114)^1 + 1.5/(1+.1114)^2 + 1.75/(1+.1114)^3 + 2/(1+.1114)^4 + (2.12+43.74)/(1+.1114)^5 = $32.02 million

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Interest in Year 5 = Value of Debt in Year 4*(9.5%) = 22.27*9.5% = 2.116

Tax Shield in Year 5 = Interest in Year 5*(Tax Rate) = 2.116*(.35%) = .7405 (post merger tax rate is to be used)

For other years, the tax shield will be calculated by multiplying the interest amount with the tax rate.

Tax Shield in Year 1 = 1.2*.35 = .42

Tax Shield in Year 2 = 1.7*.35 = .595

Tax Shield in Year 3 = 2.8*.35 = .98

Tax Shield in Year 4 = 2.1*.35 = .735

Horizon Value Tax Shield in Year 5 = Tax Shield in Year 6/(Unlevered Cost of Equity - Growth Rate) = .7405*(1.06)/(.1114 - .06) = 15.28 million

Value of Tax Shields (Vtax shields) = .42/(1+.1114)^1 + .595/(1+.1114)^2 + .980/(1+.1114)^3 + .735/(1+.1114)^4 + (.741+15.28)/(1+.1114)^5 = $11.50 million

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Part B:

New Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt)*(D/S) = 11.14% + (11.14%-9.50%)*(.40/.60) = 12.23%

WACC = .40*9.5%*(1-.35) + .20*(12.23%) = 9.81%

Horizon Value = Free Cash Flow in Year 4*(1+Growth Rate)/(WACC

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