Question $1$

$($a$)$ You have the following information for Alpha plc:

Equity: $500,000$ shares. The company just paid a dividend of $2$ and the dividends are expected to grow by $3\%$ per year indefinitely. The current share price is $20.$ The return of Alpha's equity has a standard deviation of $24\%$ per annum and a correlation with the market of $0\mathrm{.}9.$

Debt: $10,000$ bonds outstanding, with $20$ years to maturity, a coupon rate of $7\%$ and a face value of $1,000.$ The price of the bonds is $901\mathrm{.}036$ and they pay coupons semiannually.

The market risk premium is $6\%$ and the standard deviation of the returns of the market is $15\%.$ Treasury bills are yielding $4\%$ and the corporate tax rate is $20\%.$

REQUIRED

i$)$ Calculate the cost of equity using the dividend growth model.

$(3$ marks$)$

ii$)$ Calculate the cost of equity using the security market line $($SML$)$ method.

$(6$ marks$)$

iii$)$ What is Alpha's weighted average cost of capital $($WACC$)?$

$(8$ marks$)$

iv$)$ Now assume that you are financial manager of Alpha plc$,$ and you have been asked by one of your large shareholders the following questions, $"$If debt can reduce the weighted average cost of capital, why does it then increase the risk of a company? Is it possible for financial manager to diversify bankruptcy risk away like other risks?" What are your answers to these questions? Explain.

$(6$ marks$)$

AND

$($b$)$ Delta plc announced this morning that its profit from last quarter has dropped $15\%$ compared to the previous quarter. The closing price of the company at the end of the day is up $5\%$ from yesterday. Is this evidence against market efficiency? Explain.

$(7$ marks$)$

$($continued overleaf$)$

$2$

AND

$($c$)$ Beta plc is an all$-$equity firm with $500,000$ shares of equity outstanding. The current price per share is $20.$ Beta is planning to announce that it will issue $5$ million of perpetual bonds and use the proceeds to repurchase equity. The required return on the bonds is $6\%.$ After the sale of the bonds, Beta will maintain the same capital structure indefinitely. The company currently generates annual pre$-$tax earnings of $1$ million. This level of earnings is expected to remain constant in perpetuity. The company is subject to $20\%$ corporate tax rate. Assume that there are no transaction costs or financial distress costs.

REQUIRED

i$)$ What is the expected return on Beta's equity before the announcement of the debt issue?

$(4$ marks$)$

ii$)$ How many shares will the company repurchase as a result of the debt issue?

$(5$ marks$)$

iii$)$ What is the required return on Beta's equity after the restructuring?

$(5$ marks$)$

iv$)$ Now assume that there is cost of financial distress that depends on the level of debt $($B$).$ Specifically, the expected cost of financial distress $($CFD$)$ for Beta plc is given by CFD $=(\frac{1}{9},000,000)B^2.$ What is the level of debt and equity that maximises the value of Beta?

$(6$ marks$)$