Question

You were appointed the CFO of a firm with 2 divisions:
Div. 1 -- produces regular telephones
Div. 2 -- produces specialty micro-chips which are used in cell phones

Given Information:
Market value of your firm’s debt = $100 million
Market value of your firm’s equity = $100 million
Overall/total value of firm = $200 million.
Beta of firms’ equity = 2
Firm’s debt = riskless.
Expected excess return on the market over the riskless rate = 8% percent
Risk-free rate = 2%

Assume that the CAPM holds.

Suppose that you cannot identify a firm that is comparable in systematic risk to your cell phone division (Division 2), but do manage to identify a single-segment telephone firm, firm X, whose underlying business has systematic risk (asset beta) identical to that of your telephone business (Division 1). This firm has an equity beta of 1.0, a debt beta of 0.1, and a debt-to-equity ratio of 0.5. Furthermore, you expect total cash flow (to the asset) from Division 1 to be $10 million per year indefinitely (from t=1 onward).

Question 1: What is the value of Division 1?

Question 2: What is the value of Division 2?
(Hint: Start by working out the asset beta of Division 1)

Answer 1

1). Asset beta for Division 1:

Asset beta bu = equity beta*(E/V) + debt beta*(D/V)

where E/V = equity to total value ratio and D/V = debt to total value ratio

D/E = 0.5 so E/V = 1/(1+0.5) = 0.67 and D/V = 1-0.67 = 0.33

Asset beta = (1*0.67) + (0.1*0.33) = 0.70

Unlevered cost of capital = riskfree rate + (asset beta*market risk premium)

= 2% + (0.70*8%) = 7.60%

Value of Division 1 = cash flow to the asset/unlevered cost of capital = 10/7.60% = 131.58 million

2). Firm value = 200 million

So, value of Division 2 = Firm value - Division 1 value = 200 - 131.58 = 68.42 million