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# 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.

Asked 10 months ago
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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.

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% ##### Dr. Tina Weimann IV
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