Semester 2, 2018/19
Dr. Stefan Petry
FOUNDATIONS OF FINANCE
PROBLEM SET 3: Capital structure I - SOLUTIONS
Question 1: Recapitalizing to capture the tax shield
Assume that Midco Industries wants to boost its stock price. The company currently has 20
million shares outstanding with a market price of $15 per share and no debt. Midco has had
consistently stable earnings, and pays a 35% tax rate. Management plans to borrow $100 million
on a permanent basis and they will use the borrowed funds to repurchase outstanding shares.
a) What is Midco’s value without leverage?
b) What will the total value of the levered firm be and what will be the value of equity?
c) Assume Midco repurchases its shares at the current price of $15/share. What will the new
share price be?
d) What is the total gain to shareholders?
e) In an efficient market, what would happen at the repurchase announcement?
Answer:
a) What is Midco’s value without leverage?
Without leverage
VU = (20 million shares) × ($15/share) = $300 million
b) What will the total value of the levered firm be and what will be the value of equity?
If Midco borrows $100 million using permanent debt, the present value of the firm’s future tax
savings is
PV(interest tax shield) = τcD = 35% × $100 million = $35 million
Thus the total value of the levered firm will be
VL = VU + τ cD = $300 million + $35 million = $335 million
Because the value of the debt is $100 million, the value of the equity is
E = VL − D = $335 million − $100 million = $235 million
1
Dr. Stefan Petry
FOUNDATIONS OF FINANCE
PROBLEM SET 3: Capital structure I - SOLUTIONS
Question 1: Recapitalizing to capture the tax shield
Assume that Midco Industries wants to boost its stock price. The company currently has 20
million shares outstanding with a market price of $15 per share and no debt. Midco has had
consistently stable earnings, and pays a 35% tax rate. Management plans to borrow $100 million
on a permanent basis and they will use the borrowed funds to repurchase outstanding shares.
a) What is Midco’s value without leverage?
b) What will the total value of the levered firm be and what will be the value of equity?
c) Assume Midco repurchases its shares at the current price of $15/share. What will the new
share price be?
d) What is the total gain to shareholders?
e) In an efficient market, what would happen at the repurchase announcement?
Answer:
a) What is Midco’s value without leverage?
Without leverage
VU = (20 million shares) × ($15/share) = $300 million
b) What will the total value of the levered firm be and what will be the value of equity?
If Midco borrows $100 million using permanent debt, the present value of the firm’s future tax
savings is
PV(interest tax shield) = τcD = 35% × $100 million = $35 million
Thus the total value of the levered firm will be
VL = VU + τ cD = $300 million + $35 million = $335 million
Because the value of the debt is $100 million, the value of the equity is
E = VL − D = $335 million − $100 million = $235 million
1
