Question

Gladstone Corporation is about to launch a new product. Depending on the success of the new​ product, Gladstone may have one of four values next​ year: $146 ​million, $138 ​million, $92 ​million, and $81 million. These outcomes are all equally​ likely, and this risk is diversifiable. Suppose the​ risk-free interest rate is 5% and​ that, in the event of​ default, 28% of the value of​ Gladstone's assets will be lost to bankruptcy costs.​ (Ignore all other market​ imperfections, such as​ taxes.)

a. What is the initial value of​ Gladstone's equity without​ leverage? Now suppose Gladstone has​ zero-coupon debt with a $100 million face value due next year.

b. What is the initial value of​ Gladstone's debt?

c. What is the​ yield-to-maturity of the​ debt? What is its expected​ return?

d. What is the initial value of​ Gladstone's equity? What is​ Gladstone's total value with​ leverage?

Suppose Gladstone has 10 million shares outstanding and no debt at the start of the year.

e. If Gladstone does not issue​ debt, what is its share​ price?

f. If Gladstone issues debt of $100 million due next year and uses the proceeds to repurchase​ shares, what will its share price​ be? Why does your answer differ from that in part ​(e​)?

Answer 1

a). Initial value of equity without leverage = average of all possible equity values discounted at 5% for 1 year

= [(146 + 138 + 92 + 81)/4]*(1/(1+5%)) = 114.25/1.05 = 108.81 million (value of equity without leverage)

b). If the company has zero-coupon debt with a face value (FV) of $100 million due next year then debt holders will have first claim from the company. In case the company has a value of $146 or $138 million, FV of the debt will be paid. If firm value is $92 or $81 million then complete amount will go towards debt payment, with 28% bankruptcy costs.

Value of debt = 25%*(100 + 100 + (100%-28%)*92 + (100%-28%)*81)/(1+5%) = 81.14/1.05 = 77.28 million (initial value of debt)

c). YTM of the debt is (FV/current value)-1 = (100/77.28) -1 = 29.41%

Expected return is the risk-free return of 5%

d). With the $100 million debt, equity-holders will get the residual amount after debt-holders have been paid.

Value of equity = 25%*[(146-100) + (138-100) + 0 + 0]/(1+5%) = 21/1.05 = 20.00 million

Total firm value with leverage = debt value + equity value = 77.28 + 20.00 = 97.28 million

e). If the company has no leverage then total firm value is the equity value which is 108.81 million

Share price = total equity value/shares outstanding = 108.81/10 = $10.881 per share

f). Is debt is issued and shares are repurchased then the new share price will be

97.28/10 = $9.73 per share (This share price will be lower due to bankruptcy costs.)