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: $150 million, $135 million, $95 million, or $80 million. These outcomes are all equally likely, and this risk is diversifiable. Gladstone will not make any payouts to investors during the year. Suppose the risk-free interest rate is 5% and assume perfect capital markets.

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

Answer: SEE EXPLANATION

Step-by-step explanation:

Given the following ;

Values depending on Success

$150M, $135M, $95M, $80M

Risk free rate = 5% = 0.05

Pervebtage to be lost in case of bankruptcy = 25% = 0.25

A.) 0.25 × [( 150 + 135 + 95 + 80) ÷ 1.05] = $109.52 million

Assume a zero-coupon debt with a $100million face value

B.) 0.25 × [( 100 + 100 + (95×0.75) + (80×0.75)) ÷ 1.05] = $78.87 million

C.) Yield to maturity (YTM)

(100M÷78.87M) - 1

1.2679 - 1 = 0.2679 = 26.79%

Expected return = 5%

D.) Equity value

0.25 × [( 150 + 135 + (95×0.75) + (80×0.75)) ÷ 1.05] = $99.11 million

E.) share if no debt is issued

109.52 ÷ 10 = 10.95 per share

F.) Share price if debt of $100M is issued

99.11 ÷ 10 = 9.91 per share

The price differs because bankruptcy cost will Lower the share price.