Question

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In mid-2009, Rite Aid had CCC-rated, 6-year bonds outstanding with a yield to maturity of 17.3%. At the time, similar maturity Treasuries had a yield of 3 %. Suppose the market risk premium is 5% and you believe Rite Aid's bonds have a beta of 0.31. The expected loss rate of these bonds in the event of default is 60%. a) What annual probability of default would be consistent with the yield to maturity of these bonds in mid-2009? b) In mid-2015, Rite-Aid's bonds had a yield of 7.1 %, while similar maturity Treasuries had a yield of 1.5%. What probability of default would you estimate now? c) From 2010 to 2014, the annual market returns were 10%, -5%, 10%, 7%, and 3%. During the same years Rite Aid's annual stock returns were 15%, -9%, 20%, 12%, and 2%. What is the equity beta and expected equity return of Rite Aid using these five years of data? In mid-2015 WholeFoods decides to expand their operations into the pharmacy sector. As a comparable company, the CEO of WholeFoods has identified Rite Aid, which currently has a Debt-to-Equity Ratio of 3. Whole Foods stock price is $20 per share, with 15 million shares outstanding. It also has $100 million in outstanding corporate debt, with an average credit rating of A- and a debt beta of 0.05 (Whole Foods plans to maintain the same capital structure going forward). Find the appropriate after-tax WACC for Whole Food's expansion project if the company will be subject to a 25% corporate tax rate.

Answer 1

a) The formula used to determine the Probability of default:

Probability of default as per market risk premium:

P= S * (1+r)/(1-RR) , where:
S = spread = 0.05*0.31 = 1.55%
R = risk-free rate = 3%
RR = expected recovery rate ad default = 40% (since expected loss rate is 40%)

P = 0.0155 * (1.03)/(0.6) = 2.660833%

Probability of default as per Yield to maturity of bond:

P= S * (1+r)/(1-RR) , where:
S = spread = 17.3% - 3% = 14.3%
R = risk-free rate = 3%
RR = expected recovery rate ad default = 40% (since expected loss rate is 40%)

P = 0.143 * (1.03)/(0.6) = 24.54833%

b) The formula used to determine the Probability of default:

P= S * (1+r)/(1-RR) , where:
S = spread = 7.1% - 1.5% = 5.6%
R = risk-free rate = 3%
RR = expected recovery rate ad default = 40% (since expected loss rate is 40%)

P = 0.056 * (1.03)/(0.6) = 9.6133%

c) Beta = Covariance of Market returns with Stock Returns / Variance of Market returns. The following table computes Beta:

	2010	2011	2012	2013	2014
Market Returns	10%	-5%	10%	7%	3%
Stock Returns	15%	-9%	20%	12%	2%
Premium	5%	-4%	10%	5%	-1%

Covariance	0.0057
Variance	0.00316
Beta	1.80379747

Average market returns

5%

Expected Equity return = risk-free rate + market portfolio premium * Equity Beta

Here,
the risk-free rate has to be assumed. Let us say it is 3%

Market portfolio premium = Average market return - risk-free rate = 5%-3% = 2%

Expected equity return = 3% + 2% * 1.80379747 = 6.6075949%

d) WACC = (VE/V ​× Re)+((VD/V))×Rd×(1−Tc))
where,
VE=Market value of the firm’s equity= $300m
VD=Market value of the firm’s debt = $100m
V=VE+VD = $400m
Re=Cost of equity = 6.6075949%, as given in part c of question
Rd=Cost of debt = 7.1%, as given in Part b
Tc=Corporate tax rate​ = 25%

WACC = (0.75 ​× 6.6075949%)+((0.25))×7.1%×(0.75)) = 6.2869462%