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Use the following information for the next six questions: A firm has 2 million shares of...

Use the following information for the next six questions:

A firm has 2 million shares of common stock outstanding, currently selling at $60 per share.
It is expected to have EPS and dividends per share at the end of the current year in the amounts of $4 and $2.45, and a Return on Equity of 10%.
It also has $100 Million par value of debt on its books, which is currently selling at a 5% discount to par. The debt is 20-year debt with a 4% annual coupon rate.
The firm has ROE of 10% and a 25% marginal tax rate
The firm’s “regular” (non-adjusted) beta is 2.0, the current YTM on treasuries is 3%, and the market risk premium is 4%
The firm has a size beta of 0.20, a value beta of 0.50 and a liquidity beta of 0.15 -- historical returns on various subsets of firms are as follows:

Subset	Historical Average return
Small Firms	14%
Large Firm	10%
Value Firms	13%
Growth Firms	9.5%
Very Liquid firms	9%
Illiquid firms	13.5 %

What are the weights of debt and equity for the firm?
What is the cost of equity based on the Fama-French Model?
What is the cost of equity based on the Pastor-Stambaugh model?
What is the cost of equity based on the Gordon-Growth (i.e. constant growth) model?
What are the before and after-tax costs of debt?
What is the WACC for the firm using the Gordon-growth model’s cost of equity and the weights from question #22?

Expert Solution

a) Number of shares = 2,000,000

Market value per share = $60

Market value of equity = $60*2,000,000 = $120,000,000

Face value of Debt on books = $100,000,000

Market value of Debt = 5% below par = $95,000,000

Market Value of Debt + Equity = $215,000,000

Weight of Debt = ($95,000,000/$215,000,000) = 44.2%

Weight of Equity = ($120,000,000/$215,000,000) = 55.8%

b) Given:

Risk free rate = 3%, Regular Beta = 2, Market Risk Premium = 4%

Size beta =0.2, Value Beta = 0.5

Cost of equity = R_f + Beta_regular*Market risk Premium + Beta_size*(Small-Big) +Beta_value(Low-high)

=3% +2*4% + 0.2*(14%-10%) + 0.5*(13%-9.5%) = 3% +8% +0.8% + 2.25% = 14.05%

c)

Cost of equity = R_f + Beta_regular*Market risk Premium + Beta_size*(Small-Big) +Beta_value(Low-high) + Beta_liq*(illiquid - liquid)

=3% +2*4% + 0.2*(14%-10%) + 0.5*(13%-9.5%) +0.15*(13.5%-9%)

= 3% +8% +0.8% + 2.25% 0.675% = 14.725%

d) First of all we need to find the growth rate:

growth rate = ROE*(1-Payout ratio) = 10%* (1-2.45/4) = 3.875%

Cost of equity by gordon growth model = (DPS*(1+growth rate)/market price) + growth rate

= (2.45*(1+3.875%)/60)+ 3.875% = 8.12%

jeff jeffy answered 2 years ago

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