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.

Engineers in Division 2 now discover an opportunity to invest in a new production technology which would enable it to produce better micro-chips. The required investment would be $15 million today (t=0), but the investment would increase expected Division 2 sales revenues by $4 million per year (each year, indefinitely, starting at t=1). You should assume that the systematic risk (the asset beta) of Division 2 will be unaffected by the switch to the new production technology.

Question 1: What is the asset beta for Division 2?

Question 2: Would you recommend that your firm invests in the new production technology?

Question 3: Suppose your firm announces at t=0 that it will invest in the new production technology and issues $15 million worth of debt to finance the upfront investment.
If there are 10 million shares outstanding, what will the price per share be right after this has been done (i.e. right after t=0)?

Answer 1

1). Asset beta for the company = (equity beta*E/V) + (debt beta*D/V)

where E/V = equity to total value ratio = 0.5 and D/V = debt to total value = 0.5

Asset beta = (2*0.5) + (0*0.5) = 1

Asset beta for the company = Asset beta Division 1*(value of Division 1/total company value) + Asset beta Division 2*(value of Division 2/total company value)

From last question, we know that company value = 200 million; Division1 value = 131.58/200 = 0.66; Division2 value = 1-0.66 = 0.34 and asset beta for Division 1 = 0.70

1 = (0.70*0.66) + (B*0.34)

B = 1.58

Asset beta for Division 2 = 1.58

2). Unlevered cost of capital for Division 2 = riskfree rate + (asset beta(market risk premium)

= 2% + (1.58*8%) = 14.62%

Initial investment in the new technology = 15 million

PV of future cash flows = cash flow per year/unlevered cost of capital

= 4/14.62% = 27.37 million

NPV for the proposed technology = 27.37 -15 = 12.37 million so the company should invest in the technology.

3). After the debt issue, the equity value of the company is not changed so the share price will remain the same as before.