Question

Flash back to June 20, 2010. Your firm, Horizon Communications, a diversified telecommunications firm, is thinking about selling its phone directories unit, Orange Book, to another firm, either Mustard Book or PLURAL. Either purchaser will maintain its current capital structure in financing the acquisition and in future operations. Orange Book has only one competitor, Mustard Book, whose sole business is phone directories. (PLURAL is a diversified firm.) In trying to value this division, Horizon is confronted with the information below. (Assume a debt beta of zero for each firm and that the beta of the tax shields will equal the beta of the unlevered firm. In other words, βD = 0 & βTax shield = βU.)

Mustard book Horizon PLURAL

βE 1.06 0.95 0.99

D/E 0.2 0.25 0.3

Tax rate 0.3 0.3 0.3

Before-tax cost of debt (rd) 0.1 0.09 0.08

Yields on U.S. Government Securities (on April 20, 2010)

Annualized Yield to Maturity

3-Month T-Bills 0.31%

1-Year Bonds 0.65%

5-Year Bonds 2.10%

10-Year Bonds 3.45%

20-Year Bonds 4.02%

30-Year Bonds 3.80%

Avg Annual Rets (1928-2008)

Average Annual Return

T-Bills 3.8%

Intermediate Bondsa 5.4%

Long-term Bondsb 5.5%

Large Company Stocksc 11.1%

Small Company Stocksd 14.5%

aPortfolio of U.S. Government bonds with maturity near 5 years.

bPortfolio of U.S. Government bonds with maturity near 10 years.

cStandard & Poor's 500 Stock Price Index.

dA subset of small cap stocks traded on the NYSE (1928-2008)

If Orange Book is to be purchased by Mustard Book, what is the appropriate βE (to use as an input into the WACC) for evaluating the value of the acquisition to Mustard Book?

If Orange Book is to be purchased by PLURAL, what is the appropriate βE (to use as an input into the WACC) for evaluating the value of the acquisition to PLURAL?

Calculate a cost of equity (RE) and WACC for the Orange Book acquisition, assuming that PLURAL purchases Orange Book.

How would your answer to part (c) change if PLURAL decided to lever up dramatically, to say a D/E = 1.0, and then planned on paying down debt in chunks? Please describe in words what would happen and how your analysis would (or would not) change.

Answer 1

	Mustard book	Horizon	PLURAL			US Govt Yeild			Avg Annual Rets (1928-2008)
βE	1.06	0.95	0.99			Annualized Yield to Maturity
D/E	0.2	0.25	0.3			3-Month T-Bills	0.3%		T-Bills	3.8%
Tax	0.3	0.3	0.3			1-Year Bonds	0.7%		Intermediate Bondsa	5.4%
Before tax cost of det	0.1	0.09	0.08			5-Year Bonds	2.1%		Long-term Bondsb	5.5%
						10-Year Bonds	3.5%		Large Company Stocksc	11.1%
						20-Year Bonds	4.0%		Small Company Stocksd	14.5%
						30-Year Bonds	3.8%
		Q1)	Horizon Levered Beta	0.95	<--Equity beta
			Unlvered beta	0.81	<--Levered beta/(1+(1-tax rate)*Debt/Equity), using D/E of Horizon
			Horizon levered beta	0.92	<--Unlevered beta*(1+(1-tax rate)*Debt/Equity), Using D/E of Mustard
		Q2)	Horizon Levered Beta	0.95	<--Equity beta
			Unlvered beta	0.81	<--Levered beta/(1+(1-tax rate)*Debt/Equity), using D/E of Horizon
			Horizon levered beta	0.98	<--Unlevered beta*(1+(1-tax rate)*Debt/Equity), Using D/E of Plural
		Q3)	Orange book cost of debt	9.0%	<--Horizon cost of debt
			CAPM cost of equity	10.3%	<--Rf+Beta levered*(Rm-Rf), where Rf=3-month T-bills, Rm=Large company stock returns, beta levered is levered beta calculated for horizon for Mustard
			D/E	0.3	<--D/E of plural
			E/Debt+Equity	76.9%	<--1/(1+D/E)
			D/Debt+Equity	23.1%	<--1-E/Debt+Equity
			WACC	9.34%	<--Cost of equity*Weight of equity+Cost of debt*weight of debt*(1-Tax rate)

The above table gives the case facts along with the answers to the Q1-3

Q4) If Plural decides to increase is D/E ratio by taking more debt, its cost of capital may incrase as the levered beta will increase, increasing the cost of equity but increasing the weight of debt in the WACC thus lowering the overall effect of cost of equity in WACC. Overall, the company becomes more risky by taking more risk as it maybe unable to payoff its debt in the future

Please reach out for any clarifications