# hw5 - Introduction to derivatives Fall 2011 BUSI 588...

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Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Homework 5 Homework 5 Due at the beginning of class, October 12th, 2011. 1. (*) A firm want to raise \$30m to invest in a project. After the \$30m investment, the firm will have a total asset value of \$100. The risk-free rate is 10%, and the volatility of the return on assets is 20%. (a) If the firm wants to issue 10-year debt (zero-coupon), what face value do they need to set? (b) Now imagine that the bond has been issued (with a face value that you found in the previous part), but that the stockholders can choose an action that changes the nature of the cash flows. Namely, the shareholders can: (1) do nothing, (2) take an action that will immediately reduce the value of the assets from \$100 to \$99m and at the same time raise the volatility to 30%. Will the shareholders take this action? (c) If the bondholders anticipated this possibility when they were offered to invest in the company, what do you expect they would have demanded as a face value? (d) Would the shareholders have an incentive to include a covenant prohibiting the action in part (b) above? 2. (**) Consider a firm with current asset value of \$200m. The firm has debt outstanding, which they issued 5 years ago, with zero-coupon and face value F = 250, which matures in 1 year. T-bonds are currently yielding 8%, and the firm’s assets have a 25% volatility. (a) What would you expect the firm’s debt to trade at? What is its current credit spread? (b) The firm can invest \$12m in order to get future cash flows which, in PV terms, are worth \$20m. Management is considering issuing some equity in order to finance this project, since the firm would have a hard time tapping bond markets. In particular, management will go to the current shareholders and ask them to put down the \$12m in order to...
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hw5 - Introduction to derivatives Fall 2011 BUSI 588...

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