Question

As of September​ 2012, Google​ (GOOG) had no debt. Suppose the​ firm's managers are considering issuing​ zero-coupon debt due in 16 months with a face value of

$ 165.7

​billion, and using the proceeds to pay a special dividend. Google currently has a market value of

$ 231.3

billion and the​ risk-free rate is

0.28 %

Using an implied volatility

σ=38.60%​,

answer the​ following:

a. If​ Google's current equity beta is 1.16​,

estimate​ Google's equity beta after the debt is issued.

b. Estimate the beta of the new debt.

​(​Note: Make sure to round all intermediate calculations to at least five decimal places.​)

Answer 1

All financials are in $ billion.

Part (a)

After debt is issued:

We need to calculate the market value of debt and equity of Google. Equity can be seen as a call option on the assets of the firm with strike price equal to the face value of the debt of the firm. We therefore need to value Equity as a call option using Black Scholes Model.

The Black Scholes Formula is presented below.

We will now resort to excel. Please see the snapshot below.

Hence, market value of Equity after debt is issued = E = 77.35

Market value of debt = D = S - E = 231.30 - 77.35 =  153.95

Part (a)

Beta of equity after debt is issued = Equity unlevered beta x (1 + D / E) = 1.16 x (1 + 153.95 / 77.35) =  2.30881 (Please round it off as per your requirement)

Part (b)

Unlevered equity beta =1.16 = Proportion of debt in capital structure x Beta of debt + Proportion of equity in capital structure x Equity beta after debt is issued = D / S x Beta of debt + E / S x Beta of equity after debt is issued = 153.95 / 231.30 x Beta of debt + 77.35 / 231.30 x 2.30881 = 0.66559097 x Beta of debt +  0.772086

Hence, Beta of debt = (1.16 - 0.772086) / 0.66559097 =  0.582812 (Please round it off as per your requirement)