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.

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Required:
a. What is the yield-to-maturity of the debt?
b. What is its expected return?

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Question Completion:

Suppose the Gladstone has zero-coupon debt with a $100 million face value due next year.

Answer:

Gladstone Corporation

a) The yield-to-maturity of the debt is:

9.5%

b) Its expected return is:

$5.474 million

Explanation:

Data and Calcualtions:

Zero-coupon debt = $100,000

Risk-free interest rate = 5%

Values from new product = one of $150 million, $135 million, $95 million, or $80 million outcomes equally likely = Total value = $460 million

Expected initial value without leverage = $460 million * 0.25 (1/4) = $115 million

Present value of expected initial value = expected initial value discounted by 5%

= $115 million * 0.952

= $109.48 million

Yield to maturity = (PV - Debt)/Debt = $9.48/$100 * 100 = 0.0948 = 9.5%

Expected return = $109.48 million * 5% = $5.474 million

Expected rate of return = $5.474/$100 * 100 = 5.5%

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