Question

King Ltd and Queen Ltd are both listed on the New York Stock Exchange having the same business risk. The expected return on the S&P 500 Index is 10% and the risk-free rate is 6%. These two firms are identical in all aspects except for their capital structure. Queen is an all-equity firm. King has both perpetual debts and common stocks. It has a debt to equity ratio of 1:4 and an equity beta which is equal to 1.25. Assume both firms can borrow at the risk-free rate. The EBIT of Queen Ltd is expected to be $100,000 per year in perpetuity. Assume there are no taxes, and all earnings of both firms are paid out as dividends.

(a) Calculate the cost of capital of each firm. (Show your calculations).

(b) Mr. Jackson, a shareholder of Queen Ltd, owns stocks that are worth $10,000. Calculate his annual cash flow from dividend under the current capital structure of Queen. (Show your calculations).

(c) Mr. Jackson believes that if he invests in King Ltd, it is impossible for him to have the same cash flows as he prefers from Queen Ltd. Critically evaluate whether he is true. Explain your justifications clearly with necessary calculations presented.

Answer 1

Solution:

Given:

Market Return, Rm 10%
Risk free, rf 6%

For Queen:

Debt   0; Equity   1 => D/E = 0

For King:

Debt 1; Equity 4 => D/E = 0.25

Firrms can borrow at risk free rate. So cost of debt ,Rd = rf = 6%.

No Taxes.

This follows MM Porposition I which states that value of the firm is independent of it capital structure and WACC remains constant and Cost of equity Re adjusts with increasing leverage.

A] Cost of Equity

For King:

Levered equity beta = 1.25

Levered cost of equity (Re) = rf + beta (rm - rf) = 6% + 1.25 *(10% - 6%) = 11%

Cost of capital for King = Re * E/(D+E) + Rd * (D/(D+E)) = 11%*4/5 + 6% * 1/5 = 10%

For Queen:

Unlevered Cost of Equity (Re) can be onbtained by using he following formula:

Levered Cost of equity rl = ru + D/E * (ru - rd)........... MM I - Proposition II

where,

rl --> levered cost of equity

ru --> unlevered cost of equity

rd --> cost of debt

Using Kings values as both the firms have same rick structure.

11% = ru + 0.25 *(ru - 6%) => 1.25 ru = 11% + 1.5% = 12.5% ==> ru = 10%

Cost of capital for Queen is 10%. ... (as only equity firm)

B] Dividend income

As Queen is total equity firm. The expected return from the firm is 10%. As all earnings are paid out as dividends, there are no taxes and EBIT is for perpetuity (growth is zero).

The expected return on equity should match the actual return on equity.

Therefore the actual return on equity is 10%.

Dividend income will be = Investment * return on equity = $10,000 * 10% = $1000.

C] Investment in Kings

Mr Jacksons cash flows will be more for same investment in the Kings.

Prima facie it looks like as EBIT is same and Kings has borrowed money so there will be some interest hence cash flow available to share holders will reduce, but that it not the case because with same investment (i.e $10,000) you get higher shareholding in Kings than in Queens.

Lets understand this.

As WACC is same at 10%, both the firm will have same market value i.e. 100,000/0.1 = 1000,000

Remember, Market Value of firm = Market Value of Equity + Market Value of Debt

In case of Queens, this market value is for entire equity so Market Value of Equity is 1000,000.

So for $10,000, Mr Jackson will get = $10,000/1000,000 = 1% of share holding in Queens.

In case of Kings, as DE ratios is 1:4, Market Value of Equity is 4 times market value of Debt;

So Market Value of Equity = 800,000 ....(200,000 will be debt for same market value of firm)

So for $10,000, Mr Jackson will get = $10,000/800,000 = 1.25% of share holding in Queens.

So his cash flows will be higher than investment in Queens.

Lets calculate his cash flows.

So Debt is 200,000 (it is perpetual) so interest is 200,000 *6% = 12,000

Cash Flow to equity = EBIT - Interest = 100,000 - 12,000 = 88,000

Cash Flow to Mr Jackson = 1.25% of 88,000 = 1,100 .....(he can get 1.25% shareholding with $10,000 and all earnings are distributed as dividends)

[Simple way to calculate his return is considering cost of equity = return on equity and then calculating dividend income as calculated in part by = $10,000 * 11% = $1100]

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