Question

Question 1 a. Kappa is an all-equity firm. It has 120,000 shares outstanding, currently worth £20 per share. The unlevered cost of equity is 20%. The firm has decided to issue £1,000,000 of 8% debt, and to use the proceeds to repurchase shares. Assume a 28% corporate tax rate.

i. According to Modigliani-Miller Proposition I with corporate taxes, what is the market value of the firm’s equity after the repurchase? (6 marks)

ii. What are the firm’s earnings before interest and taxes? (Assume that earnings are cash flows.) (6 marks)

iii. What is the return on equity after the change in the firm’s capital structure? (7 marks)

iv. What is the value of a share after the capital structure change? (10 marks)

AND b. Discuss the factors favoring a high-dividend policy. (12 marks)

AND c. Stock A has an expected return of 5% and a standard deviation of 10%. Stock B has an expected return of 10% and a standard deviation of 20%. The covariance between the returns of the two stocks is 0.001. Suppose an investor holds a portfolio consisting of only stock A and stock B. Find the portfolio weights, XA and XB, such that the variance of her portfolio is minimized. (9 marks)

Answer 1

(1)

(a) Number of Shares Outstanding = 120000, Current Stock Price =  £ 20, Tax Rate = 28 % and Proposed Perpetual Debt =  £ 1000000

As per Modgiliani-Miller Proposition, firm value post repurchase is Firm Value = All Equity Financed Value + Present Value of Interest Tax Shield = 120000 x 20 + 1000000 x 0.28 =  £ 2680000

(b) Let the firm's cash flow or Net Operating Profit After Tax (NOPAT) be £ K

Unlevered Cost of Equity = 20 %

Therefore, 2680000 = K / 0.2 + 1000000 x 0.28

2400000 = K / 0.2

K =  £ 480000

Therefore, Earnings Before Interest and Taxes (EBIT) = NOPAT / (1-Tax Rate) = 480000 / (1-0.28) =  £ 666666.67

(c) As soon as the firm announces the repurchase, the firm's share price and total value should increase owing to expectations of the benefits of the interest tax shield accruing to the firm.

Interest Tax Shield Value = 1000000 x 0.28 =   £ 280000

New Firm Value = 2400000 + 280000 =  £ 2680000

Price Per Share = 2680000 / 120000 =  £ 22.33

Debt Raised =  £ 1000000

Shares Repurchased = 1000000 / 22.33 ~ 44776.12

Shares Remaining = 120000 = 44776.12 ~ 75223.18

New Equity Value = E1 = 75223.88 x 22.33 ~  £ 1680000

Interest Rate on Debt = 8%

Interest Expense = 0.08 x 1000000 =  £ 80000

Net Income = EBIT - Interest Expense - Tax Expense = 666666.67 - 80000 - (666666.67 - 80000) x 0.28 =  £ 422400

Return on Equity = Net Income / E1 = 422400 / 1680000 ~ 0.25143 or 25.143 %

(d) Price per Share after repurchase (change in capital structure) =  £ 22.33 (as calculated in part(c))

NOTE: Please raise separate queries for solutions to the remaining sub-parts and/or unrelated questions.