Modigliani Miller Theorem with Corporate Taxes

Consider an environment with corporate taxes similar to the example in slides $11-16,$

Lecture $10.$ Assume that corporate tax is $40\%$ and the required rate of returns on

Nodebt shares is $10\%.$

a$)$ Nodebt is an all$-$equity$-$financed company with total market value of

$$100M$ and $1M$ shares outstanding. Nodebt generates EBITs of $$5$M$,$

$$10M,$$$15M$ in a bad year, a normal year, and a good year respectively

$($with equal probabilities$).$ Calculate the rate of return on equity of Nodebt

in the three scenarios.

b$)$ Somedebt is an identical company except that management issue $$40M$

worth of corporate debt at $5\%$ interest rate and use the proceed to

repurchase some shares. Calculate the market value of Somedebt's equity

and the number of shares outstanding.

c$)$ Calculate the rate of return on equity of Somedebt in the three scenarios of

earnings.

d$)$ Use the formula in slide $19,$ Lecture $10$ to calculate the required rate of

return on the equity of Somedebt Corporation. Show that this is the same

as the average rate of return on Somedebt shares in part c$).$Modigliani$-$Miller Theorem

Cost of Equity Capital

$k_e=k+(k-r)\frac{D}{E}$

$k_e=k+(1-t)(k-r)\frac{D}{E}$