Question

The current riskfree rate is 4% and the expected rate of return on the market portfolio is 10%. The Brandywine Corporation has two divisions of equal market value. The debt to equity ratio (D/E) is 3/7. The company’s debt can be assumed to present no risk of default. For the last few years, the Brandy division has been using a discount rate of 12% in capital budgeting decisions and the Wine division a discount rate of 10%. You have been asked by their managers to report on whether these discount rates are properly adjusted for the risk of the projects in the two divisions.

(i) What are the betas of typical projects implicit in the discount rates used by the two divisions?

(ii) You estimate that the equity beta of Brandywine is 1.6. Is this consistent with the equity beta implicit in the discount rates used by the two divisions?

(iii) You estimate that the stock beta of the Korbell Brandy Corp. is 1.8. This company is purely in the brandy business, its debt to equity ratio is 2/3 and its debt beta is 0.2. Based on this information (and on your estimate, from section (b), of Brandywine’s equity beta), what discount rate would you recommend for projects in the Brandy and in the Wine divisions of Brandywine?

Answer 1

As per CAPM equation

Required rate of return (Re) = rf+(Rm-rf)×equity beta

Where

rf = risk free rate=4%

Rm= market retuen=10%

Re for brandy devision= 12%

Therefore

12=4+(10-4)×equity beta

Equity beta of brandy = 1.333

Similarly equity beta of wine is

10=4+(10-4)×equity beta

Equity beta of wine= 1

Part b

Equity beta if brandywine = wieghted average of divisional equity betas

Since both have equal market value

Brandywine equity beta =.50×1.333+.50×1=1.166

So iur estimate 1.6 is not consistent with beta inherent in the discount rates.

Part c

Stock beta is the levered beta which js  basically the beta of common stock.

Now we need lever this beta for brandy using debt qeuity of 3/7

Levered beta or equity beta = unlevered beta ×(1+DER)

= 1.8×(1+3/7)=2.57

Brandy division should use this beta to set uts discount rate

Rate should be =4×(10-4)×2.57=19.42%

Let us calculate equity beta for wine division

We estimated overall equity beta for brandywine which was 1.6 this is a weighted average

Let say equity beta of whine is b

Therefore

2.57×.5+b×.5=1.6

b= .63

Hence discount rate for whine = 4+(10-4)×.63=7.78%