Question

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

Data
Number of shares		2,700
Price per share	$	27
Market value of shares	$	72,900

Although it expects to have an income of $3,200 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 ($)	2,200	2,700	3,200	3,700

Suppose that Macbeth Spot Removers issues only $7,830 of debt and uses the proceeds to repurchase 290 shares. The interest rate on the debt is 9%.

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.)

	Outcome	outcome	outcome	outcome
Operating Income
Interest
Equity earnings
Earnings per share
Return on Shares

b. If the beta of Macbeth's assets is 0.65 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

Part a)

The completed table is provided as below:

______

Notes:

The calculations are given as below:

Interest = Value of Debt Issued*Interest Rate = 7,830*9% = $704.70 or $705

_____

Earnings Per Share = Equity Earnings/(Number of Shares - Shares Repurchased)

Earnings Per Share (When Operating Income is 2,200) = 1,495/(2,700-290) = $0.62

Earnings Per Share (When Operating Income is 2,700) = 1,995/(2,700-290) = $0.83

Earnings Per Share (When Operating Income is 3,200) = 2,495/(2,700-290) = $1.04

Earnings Per Share (When Operating Income is 3,700) = 2,995/(2,700-290) = $1.24

_____

Return on Shares = Earnings Per Share/Price Per Share*100

Return on Shares (When Operating Income is 2,200) = 0.62/27*100 = 2.30%

Return on Shares (When Operating Income is 2,700) = 0.83/27*100 = 3.07%

Return on Shares (When Operating Income is 3,200) = 1.04/27*100 = 3.83%

Return on Shares (When Operating Income is 3,700) = 1.24/27*100 = 4.60%

______

Part b)

The completed table is given as follows:

______

Notes:

The calculations are provided as below:

All Equity Beta = Beta of Macbeth's Assets = 0.65

____

Debt Beta = 0 (as it is risk free)

____

Debt/Equity Ratio = Total Debt/Total Equity = 7,830/(72,900-7,830) = 0.12

____

Beta of Assets = Debt Beta*Total Debt/Total Value + Equity Beta*Total Equity/Total Value

Substituting values in the above formula, we get,

0.65 = 0*7,830/72,900 + Equity Beta*(72,900-7,830)/72,900

Rearranging Values, we get,

Beta of Equity = (0.65*72,900)/(72,900-7,830) = 0.73