Question

4.

Macbeth Spot Removers is entirely equity financed with values as shown below:

Data
Number of shares		1,800
Price per share	$	18
Market value of shares	$	32,400

Although it expects to have an income of $2,300 a year in perpetuity, this income is not certain. This table shows the return to stockholders under different assumptions about operating income. We assume no taxes.

	Outcomes
Operating income ($)	1,300	1,800	2,300	2,800

Suppose that Macbeth Spot Removers issues only $3,780 of debt and uses the proceeds to repurchase 210 shares. The interest rate on the debt is 10%.

a. Calculate the equity earnings, earnings per share, and return on shares for each operating income assumption. (Input all values as a positive number. Round your "Earnings per share" answers to 2 decimal places. Enter your "Return on shares" answers as a percent rounded to 2 decimal places. Round the other answers to the nearest whole number.)

	Outcomes
Operating income ($)
Interest
Equity earnings ($)
Earnings per share ($)
Return on shares (%)

b. If the beta of Macbeth's assets is .96 and its debt is risk-free, what would be the beta of the equity after the debt issue? (Round your answers to 2 decimal places.)

All-equity beta
Debt beta
D/E ratio
Equity beta

Answer 1

a) Initial Market value of equity = 32400, Debt issued = 3780

Market value of equity after debt is issued = 32400 - 3780 = 28620

No of shares outstanding after debt is issued = Initial shares - shares repurchased = 1800 - 210 = 1590

Interest on debt = Interest rate x debt issued = 10% x 3780 = 378

We know that

Equity Earnings = (Operating income - interest)(1-tax rate)

As taxes are ignored therefore Equity Earnings = (Operating income - interest)

Earnings per share = Equity earnings / No of shares outstanding after debt is issued

Return on shares = Equity Earnings / Market value of equity after debt is issued

We will calculate for each of the outcomes using above formula

If operating income = 1300, then Equity earnings = 1300 - 378 = 922, Earnings per share = 922 / 1590 = 0.5798 = 0.58 , Return on shares = 922 / 28620 = 3.2215% = 3.22%

If operating income = 1800, then Equity earnings = 1800 - 378 = 1422, Earnings per share = 1422 / 1590 = 0.8943 = 0.89 , Return on shares = 1422 / 28620 = 4.9685% = 4.97%

If operating income = 2300, then Equity earnings = 2300 - 378 = 1922, Earnings per share = 1922 / 1590 = 1.2088 = 1.21 , Return on shares = 1922 / 28620 = 0.0671= 6.7155% = 6.72%

If operating income = 2800, then Equity earnings = 2800 - 378 = 2422, Earnings per share = 2422 / 1590 = 1.5232 = 1.52 Return on shares = 2422 / 28620 = 8.4626% = 8.46%

	Outcomes
Operating income ($)	1300	1800	2300	2800
Interest	378	378	378	378
Equity earnings ($)	922	1422	1922	2422
Earnings per share ($)	0.58	0.89	1.21	1.52
Return on shares (%)	3.22%	4.97%	6.72%	8.46%

b) We know that according capital asset pricing model

Required Return on Asset = Risk free rate + Beta of Asset x market risk premium

Similarly Cost of debt = Risk free rate x Beta of debt x market risk premium

Beta of debt = (Cost of debt - Risk free rate) / Market risk premium

As debt is risk free therefore , Cost of debt = risk free rate

Beta of debt = (Risk free rate - Risk free rate) / Market risk premium = 0 / market risk premium = 0

Hence if debt is risk free , then beta of debt = 0

We know that All equity beta is the beta of firm without any leverage. Asset beta represents risk to firm because of its business risk and after removing affects of leverage. Hence, Asset beta is unlevered beta or beta of all equity firm

Hence All equity beta = Asset beta = 0.96

Debt / Equity = D/E = 3780/28620 = 0.1320 = 0.13

If Beta of debt = 0, then Equity beta = Asset Beta [1 + (D/E)(1-tax rate)] = 0.96[1 + (3780/28620)(1-0%)] = 0.96 x [1 + 0.1320] = 0.96 x 1.1320 = 1.0867 = 1.09

All-equity beta	0.96
Debt beta	0.00
D/E ratio	0.13
Equity beta	1.09