You have run a regression of returns of Devonex, a machine tool manufacturer against the S&P500 index using monthly returns over the last years and arrived at the following regression equation:

ReturnDevonex = 0.3% +1.6* ReturnS&P500

a) The stock had a Jensen’s alpha of - 0.1% (on monthly basis) over this period.

1) Has the stock beaten the market? (1 mark)

2) Estimate the monthly Rf during the last 5 years. (2 marks)

b) If the standard error of the regression beta is 0.5. Estimate the range for the regression beta at a 67% confidence interval. (2 marks)

c) If the market risk premium is 5.5%, the tax rate is 40% and Devonex’s bonds are A rated, and the default spread for A rated bond is 1%

1) Estimate the cost of equity. (1 mark)

2) Estimate the cost of debt. (2 marks)

3) Estimate the WACC for Devonex if the debt ratio is 30%. (2 marks)

ANSWER:

a)

1. Jensen Alpha measures the excess return over the expected return as per CAPM model. If the excess return is positive i.e. stock has generated more return than what was expected from it then the stock has outperformed the market while if it is negative i.e. stock has generated less return than what was expected from it then it has underperformed the market.

The stock has underperformed the market over the past months as the Jensen Alpha is - 0.1% which shows that in the past months stock has underperformed by 0.1% per month than what was expected from it.

2. Jensen Alpha of Stock = - 0.1%

Regression Intercept = 0.3%

Beta of the stock = 1.6

Jensen Alpha = Regression Intercept - (1 - Beta of Stock) * Risk Free Rate

- 0.1% = 0.3% - (1 - 1.6) * Risk Free Rate

- 0.1% - 0.3% = 0.6 * Risk Free Rate

Risk Free Rate = - 0.4% / 0.6 = - 0.67%

Monthly Risk Free Rate would be - 0.67%

b) Beta of Stock = 1.6

Standard Error of Beta = 0.5

If the confidence interval is 67%, it is expected that Beta of stock would lie between +/- standard error as per normal distribution function. So,

Mean Beta of Stock - Standard Error of Beta < Beta < Mean Beta of Stock + Standard Error of Beta

1.6 - 0.5 < Beta < 1.6 + 0.5

1.1 < Beta < 2.1

So, beta of the stock would lie between 1.1 and 2.1 with a 67% probability.

c) Market Risk Premium = 5.5%

Tax Rate = 40%

Bond's Credit Rating = A

Default Premium on A rated bonds = 1%

Debt Ratio = 30%

Monthly Risk Free Rate = - 0.67%

Annualized Risk Free Rate = (1 + Monthly Risk Free Rate)¹² - 1

Annualized Risk Free Rate = (1 - 0.67%)¹² - 1 = - 7.71%

1) Cost of Equity:

As per CAPM Model,

Cost of Equity = Risk Free Rate + Market Risk Premium * Beta of Stock

Cost of Equity = - 7.71% + 5.5% * 1.6 = 1.09%

Cost of Equity of the company is 1.09%.

2) Cost of Debt:

After Tax Cost of Debt = (Risk Free Rate + Default Risk Premium) * (1 - Tax Rate)

After Tax Cost of Debt = (- 7.71% + 1%) * (1 - 40%) = - 4.03%

Cost of Debt of the company is - 4.03%.

3) WACC:

WACC = Debt Ratio * Cost of Debt + (1 - Debt Ratio) * Cost of Equity

WACC = 30% * - 4.03% + (1 - 30%) * 1.09% = - 0.45%

WACC for the company is - 0.45%.