# a publically traded company with an infinite life span

1.      Consider Macbeth Spot Removers, a publically traded company with an infinite life span, which faces a range of annual operating incomes as depicted in the table below.  The rate of return on Treasury bonds is 10%.

 Data Number of shares 700 Price per share \$12 Market value of equity \$8400 Outcomes Operating income \$500 \$1,000 \$1,500 \$2,000 Earnings per share \$0.71 \$1.43 \$2.14 \$2.86 Return on equity 5.95% 11.90% 17.86% 23.81%

a.      Calculate the earnings per share and return on equity in the table above.

i.      Shown In Table Above

Macbeth Spot Removers issues \$2,400 of risk-free debt and uses the proceeds to repurchase 200 shares.

b.      Rework the table above to show how earning per share and equity returns now vary with operating income. Shown In Table Below

 Data Number of shares 500 Price per share \$12 Market value of equity \$6000 Outcomes Operating income \$500 \$1,000 \$1,500 \$2,000 Interest Net Income Earnings per share \$240 \$260 \$0.52 \$240 \$760 \$1.52 \$240 \$1260 \$2.52 \$240 \$1760 \$3.52 Return on equity 4.33% 12.66% 21% 29.33%

c.       If the beta of Macbeth’s unlevered assets is 0.8 and its debt is risk-free, what would be the beta of the equity after the debt issue?

i.      0.966 or 1.12

Ms. Macbeth’s investment bankers have just informed her that the new issue of debt is risky.  Debtholders will demand a return of 12.5%, which is 2.5% above the risk-free interest rate.

d.      How does this affect return on assets and return on equity?  Calculate these values. Shown In Table Below

 Data Number of shares 500 Price per share \$12 Market value of equity \$6000 Outcomes Operating income \$500 \$1,000 \$1,500 \$2,000 Return on Assets 5.95% 11.9% 17.86% 23.81% Return on equity 3.33% 11.67% 20% 28.33%

e.       Suppose that the β of unlevered equity was 0.6.  What will βA, βE, and βD be after the change to the capital structure?

i.      βA = 0.6 or 0.84 βE = 0.74 and βD  = 0.25