Question

Problem 5: CAPM and Cost of Capital

Columbia Gas Company (CGC) is a publicly listed company with a current share price of

$25 per share. CGC has 33 million shares outstanding and $100 million in long-term debt. CGC’s long-term debt consists of bonds issued with a face value of $100 million with 10 years to maturity with annual coupon rate of 11% (APR). The long-term bonds are currently trading at par value.

Columbia Gas Company (CGC) has a standard deviation of 36% and a correlation with the market of 0.85. Assume the risk-free rate is 4% and the market portfolio has an expected return of 13% and a standard deviation of 22%. The corporate tax rate is 30%.

A. What are the three main assumptions of capital asset pricing model (CAPM)? Are these assumptions realistic in the real world? Explain.

B. Calculate CGC’s beta with the market?

C. Calculate CGC’s cost of equity?

D. Calculate CGC’s after-tax cost of debt?

E. Calculate CGC’s weighted average cost of capital (WACC)?

Answer 1

Assumptions of CAPM Model

1. There is risk-free asset on which there is no restriction on borrowing and lending at the risk free rate
2. There are no taxes and transaction costs on borrowing and lending of securitites
3. Investors have Similar expectations of risk and return

These assumptions are not truly realistic in the real world as every invstor has different risk reward preferences and has different time horizon of investments.

Risk free assets are not unlimited in supply and there can be fluctuations in the risk free rates.

Taxes and transaction costs are applicable in real world trading activities

beta = correlation x ( std dev of CGC / std dev of market portfolio)

beta = 0.85 x ( 36% / 22% )

beta = 1.39

Cost of equity = risk free rate + beta x ( return of market portfolio - risk free rate)

Cost of equity = 4% + 1.39 x ( 13% - 4%)

Cost of equity = 4% + 12.51%

Cost of equity = 16.51%

After tax cost of debt = coupon rate x ( 1 - tax rate)

After tax cost of debt = 11% x ( 1 - 30%)

After tax cost of debt = 7.7%

WACC = (cost of equity x market value of equity + cost of debt x market value of debt )/ (market value of equity + market value of debt)

market value of equity = no of shares x price of share = 25 x 33 million = 82.5 million

market value of debt = 100 million (given)

WACC = (16.51% x 82.5 + 7.7% x 100) / 100 + 82.5

WACC = 21.32/182.5

WACC = 11.68%

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