# solution

Carlson Co. is a manufacturing firm. Carlson Co.Ă˘â‚¬â„˘s current value of operations, including debt and equity, is estimated to be \$15 million. Carlson Co. has \$6 million face-value zero coupon debt that is due in five years. The risk-free rate is 5%, and the volatility of companies similar to Carlson Co. is 50%. Carlson Co.Ă˘â‚¬â„˘s performance has not been very good as compared to previous years. Because the company has debt, it will repay its loan, but the company has the option of not paying equity holders. The ability to make the decision of whether to pay or not looks very much like an option.

Based on your understanding of the Black-Scholes option pricing model (OPM), calculate the following values and complete the table. (Note: Use 2.7183 as the approximate value of e in your calculations. Also, do not round intermediate calculations. Round your answers to two decimal places.)

Carlson Co. Value (Millions of dollars)

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Equity value
Debt value
Debt yield

Carlson Co.Ă˘â‚¬â„˘s management is implementing a risk management strategy to reduce its volatility. Complete the following table, assuming that the goal is to reduce Carlson Co.Ă˘â‚¬â„˘s volatility to 30%.

Carlson Co. Goal (Millions of dollars)

Equity value at 30% volatility
Debt value at 30% volatility
Debt yield at 30% volatility

Complete the following sentence, assuming that Carlson Co.Ă˘â‚¬â„˘s risk management strategy is successful:

If its risk management strategy is successful and Carlson Co. can reduce its volatility, the value of Carlson Co.Ă˘â‚¬â„˘s debt will [increase/decrease], and the value of its stock will [increase/decrease] .