You are trying to estimate the cost of capital for Polo Ralph Lauren (PRL), an upscale specialty retailer. The firm is in only one business, specialty retailing; comparable firms have an average published beta of 1.20, an average debt ratio of 30% and an average tax rate of 35%. The firm has provided you with the following information:

The regression beta is 0.75 with a standard error of 0.5.

The firm’s bonds are rated A, and the default spread for A rated bond is 1%. The company plans to maintain its current debt ratio of 25%.

The Treasury bond rate is 2.5% and the market risk premium is 6.5%.

The tax rate for PRL is 40%.

a) Estimate PRL’s beta based upon the comparable firms (i.e. Bottom up beta)

b) Estimate the range for the regression beta at a 95% confidence interval

c) Which beta estimate (regression or bottom-up) do you use and why?

d) Estimate the cost of equity for the firm

e) Estimate the cost of debt for the firm   

f) Estimate the cost of capital (WACC) for the firm

a. For calculation of bottom up levered beta of the company, then we need to calculate the asset beta of the beta which is known as unlevered beta. This unlevered beta is calculated from the beta of the comparable firms.

Asset beta = beta of the comparable firms / { 1 + [( 1 - tax rate) * debt to equity ratio]}

Comparable firm beta = 1.2

debt ratio = 30%

If the debt of the comparable firm is 30%, then equity is 1 - debt = 1 - 0.3 = 0.7 = 70%

So, debt to equity ratio = 0.3/0.7 = 0.42857 = 0.43

tax rate = 35%

So, asset beta = 1.2 / { 1 + [( 1 - 0.35) * 0.43]}

= 1.2 / { 1 + [ 0.0.65 * 0.43 ] }

= 1.2 / { 1 + 0.2795}

= 1.2 / 1.2795

= 0.93787

= 0.94

Then, project beta or levered bottom up beta = Asset beta * [ 1 + {( 1 - tax rate) * debt to equity ratio }]

Debt ratio of the company = 25%

equity = 1 - debt

= 1 - 0.25

= 0.75 = 75%

So, debt to equity ratio of the company = 0.25/0.75 = 0.33

Tax rate of the PRL company = 40%

So, Levered bottom up beta = 0.94 * [ 1 + {( 1 - 0.4)} * 0.33]

= 0.94 * [ 1 + {0.6*0.33}]

= 0.94 * [ 1 + 0.198]

= 0.94 * 1.198

= 1.12612 = 1.13 ( answer)

b. Regression beta = 0.75

Standard error = 0.5

95 % confidence interval has a z critical value of 1.96 ( as given in the z table)

So, Range of the regression beta = Regression beta  z value * standard error.

Confidence interval is the range of the values in which true value lies in. So, above formula is the calculation for confidence interval.

So, Upper range = 0.75 + 1.96 * 0.5

= 0.75 + 0.98 = 1.73

Lower range = 0.75 - 1.96 * 0.5

= 0.75 - 0.98 = -0.23

The regression beta lies between -0.23 to 1.73 (answer)

c. we use the bottom up beta estimate for further calculation. Beta measures the risk of the business. It is very sensitive to market conditions. It measures both the company's business nad financial risk. That is why we use that beta for WACC calculation as WACC is measured for the company and it should consist of all the risk that the compay bears so that the company may not be overvalued. The regression beta is used in multiple regression models when we need to create models and estimate teh errors in the model and how sensitive is the error to the current market conditions.

So, we should always use bottom up beta for company's calculation as it measures the riskiness of the company in both business and financial area.

d. Market premium = 6.5%

Bottom up beta = 1.13

risk free rate = 2.5%

So, according to CAPM,

Cost of equity = Risk free rate + ( Market rate - risk free rate ) * beta

= risk free rate + market risk premium * beta

= 2.5 + 6.5 * 1.13

= 2.5 + 7.345

= 9.845% (answer)

e. Cost of the debt of firm = Risk free rate + default spread of the bond.

Default spread is the extra percentage charged if the bond defaults. It acts as the default risk premium. The borrower has to pay this extra premium to the lender. The borrower has to pay this premium above the risk free rate. So we add the risk free rae to default spread.

Risk free rate = 2.5%

Default spread = 1%

Therefore, Cost of debt of the firm = 2.5 + 1 = 3.5% (answer)

f. WACC of the firm = weight of the debt * Cost of debt ( 1 - tax rate) + weight of equity * cost of equity

Tax rate = 40%

weight of debt = debt ratio of the company = 25%

Weight of equity = 1 - weight of debt

= 1 - 0.25 = 0.75 = 75%

Cost of debt = 3.5% (calculated above)

Cost of equity = 9.845% ( calculated above)

Therefore, WACC of the firm = 0.25 * ( 1 - 0.4) * 3.5 + 0.75 * 9.845

= 0.25*0.6*3.5 + 0.75*9.845

= 0.525 + 7.38375

= 7.90875% = 7.91% ( answer)