Gladstone Corporation is about to launch a new product. Depending on the success

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,$95million, and $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 5.0% 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?

Explanation / Answer

a. Initial Equity Value without leverage = Unlevered Equity Value Probability/ (1 + risk-free rate)

Unlevered Equity Value Probability = Probablity * Equity for all four outcomes

= (0.25 * 150) + (0.25 * 135) + (0.25 * 95) + (0.25 * 80) = $ 115 million

Initial Equity Value without leverage = 115/(1 + 0.05) = $109.52 million

b.In this scenario, the value of debt will be $100 million when equity value is $150 million and $135 million. When the equity value is $95 million and $ 80 million because, in the last two cases, the company won't require the bond valued at face value ($100 million) as their investment requirement is less than $100 million.

Debt Value Probablity = Probablity * Debt for all four outcomes

= (0.25 * 100) + (0.25 * 100) + (0.25 * 95) + (0.25 * 80) = $ 93.75 million

Initial Debt Value = Debt Value Probability/ (1 + risk-free rate) = 93.75/(1+0.05) = $89.29 million

c.Yield to maturity = (Face Value/ Initial Value) - 1 = (100/89.29) - 1 = 0.1199 = 12%

Execpted return for the firm will be the risk free return = 5% because it has been mentioned that the risk is diversified.

d.Initial Equity Value with leverage = Levered Equity Value Probability/ (1 + risk-free rate)

Levered Equity Value Probability = Probablity * Equity after debt for all four outcomes

= (0.25 * 50) + (0.25 * 35) + (0.25 * 0) + (0.25 * 0) = $ 21.25 million

Initial Value of equity with leverage = 21.25/(1 + 0.05) = $20.24 million

Initial value of firm with leverage = Initial Value of equity with leverage + Initial Debt Value = 20.24 + 89.29 = $109.53 million

Outcome 1 Outcome 2 Outcome3 Outcome 4 Equity $150 million $135 million $95 million $80 million Probablility 0.25 0.25 0.25 0.25

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