Question

Consider a growing firm that is expected to produce
earnings of $10 million next year. The firm’s earnings
growth rates are 15% per annum. The firm’s cost of capital
is 20%. Its tax rate is 0.
1. What is the market value of this firm?
2. What is the firm’s P/E ratio if it has no debt?
3. Now assume that the cost of capital for debt of $100
million is 8%, while the cost of capital for the remaining
levered equity is 32%. (Again, the weighted
average cost of capital is 50%·8%+50%·32% = 20%,
so the firm’s cost of capital has not changed.) Interest
on the $100 million debt is paid out. What is the
equity’s P/E ratio now?
4. Has the increase in debt increased or decreased the
firm’s P/E ratio?

Answer 1

1)

Market Value of Firm = $ 10,000,000 / ( 0.20 - 0.15)

= $ 10,000,000 / 0.05

= $ 200,000,000

2)

Since, the firm is all equity financed, the market value of firm will be market value of equity and EBIT will be earnings as all the earnings will be paid to stockholders.

P/E Ratio = $ 200,000,000 / $ 10,000,000

= 20

3) As per the question, weight of debt component and weight of equity component in capital structure is 50% each.

Value of Debt = $ 100,000,000

Value of Equity will be the same as Value of Debt = $ 100,000,000

Cost of Debt = 8%

Assuming, EBIT will be same as $ 10,000,000

Interest on Debt = 8 % of $ 100,000,000 = $ 8,000,000

Earnings for stockholders = EBIT - Interest Payments - Tax

= $ 10,000,000 - $ 8,000,000 - $ 0

= $ 2,000,000

= $ 100,000,0000 / $ 2,000,000

= 50

4) P/E ratio has increased as we see P/E ratio has increased from 20 to 50