Question 4. Unlevering and Relevering Beta Jane is working on a valuation deal t

Question

Question 4. Unlevering and Relevering Beta Jane is working on a valuation deal to acquire a private company, DLT Inc.. She carefully selected three comparable companies and pulled the data for comparables, as shown in the table below Additional information about the target company DTL plans to keep a target capital structure of 20% debt financing, DV-2090 The average interest coverage ratio over past 3 years is 15 Additional market data and information The 3-month Treasury bill yield is 1%: The 10-year Treasury note yield is 3% The market risk premium is estimated to be 6%. The corporate tax rate is 21% Comparable Company Target Capital Structure D/V Credit Rating Equity Beta Tax Rate COMP1 Yes 40% COMP2 NO 10% COMP3 NO 30% 2.5 21% 1.2 21% 21% Identify and apply the appropriate formula to unlever beta for all three comparables Use the MEDIAN unlevered beta as a proxy for the target company, DLT. Calculate DLT's unlevered cost of capital Identify and apply the appropriate formula to relever beta and apply the CAPM model to estimate DLT's cost of equity Define investment grade bond Which comparable company's bond is considered investment grade? - D (DIV) E 1-(DIV) Tip: Here is a formula to calculate There are multiples routes to get to D/E. You may come up with your way to calculate DE

Explanation / Answer

First we unlever the beta of all 3 companies, formula for doing so is -

Unlevered beta = Levered beta/ 1 + D/E (1 - tax rate)

For using the above formula, let us find D/E of all 3 companies

D/E = (D/V) / 1 - (D/V)

COMP1 D/E = 0.4 / 1-0.4 = 0.4/0.6 = 0.6667

COMP2 D/E = 0.1 / 1-0.1 = 0.1111

COMP3 D/E = 0.3/1-0.3 = 0.4286

NOW USING Unlevered beta = Levered beta/ 1 + D/E (1 - tax rate)

COMP1 UNLEVERED BETA = 2.5 / 0.6667 ( 1 - 21%) = 4.75

COMP2 UNLEVERED BETA = 1.2 / 0.1111 ( 1 - 21%) = 13.67

COMP3 UNLEVERED BETA = 2 / 0.4286 (1 - 21%) = 5.91

MEDIAN UNLEVERED BETA (i.e. when we arrange betas in ascending order, middle value is median beta) = 5.91

DLT's equity beta = unlevered beta * 1 + D/E (1 - TAX)

DLT's equity beta = 5.91 * ( 1 + 0.25 (1 - 21%)) = 7.08%

DLT's Unlevered cost of capital (Ko) = weight of debt * post tax debt rate + weight of equity * equity beta of DLT

DLT's Unlevered cost of capital (Ko) = (0.2 * 0.03) + (0.8*0.0708) = 6.264%

CAPM = Risk free return + beta (risk premium)

CAPM return = 3 + 7.08 (6) = 45.48%

Investment Grade Bond - There are essentially 2 grades of bonds, the investment grade and the speculative grade. Companies with good fundamentals and growth prospects considering its risk-return expectations are grouped under investment grade. Credit rating agencies rate the bonds as AAA, AA, A, BBB etc - the bonds with rating BBB and above are classified as investment grade. While those with lower rating are classified as speculative grade. They are also called junk bonds.

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