SmartOptions, Inc. (SO) currently has no debt. Its assets will be worth $800 mil
ID: 2802947 • Letter: S
Question
SmartOptions, Inc. (SO) currently has no debt. Its assets will be worth $800 million in one year if the economy is strong, but only $300 million in one year if the economy is weak. Both events are equally likely. Assume its cost of capital is determined to be 10%. 1. Find the market value (i.e. the price today) of SO’s assets. 2. Now assume SO recapitalizes by issuing debt. First, a senior bond for $300 million dollars with a promised rate of 10%. Second, a junior bond for $100 million which promises a 20% rate of return. Find SO’s (levered) equity cost of capital under the recapitalized capital structure.
1. Find the market value (i.e. the price today) of SO’s assets.
2. Now assume SO recapitalizes by issuing debt. First, a senior bond for $300 million dollars with a promised rate of 10%. Second, a junior bond for $100 million which promises a 20% rate of return. Find SO’s (levered) equity cost of capital under the recapitalized capital structure.
Explanation / Answer
Probability of strong economy = 0.5
Probability of weak economy = 0.5
Net worth with strong economy = $800 Mn
Net worth with weak economy = $300 Mn
Net worth next year = Probability of strong economy*Net worth with strong economy + Probability of weak economy* Net worth with weak economy
= 0.5 * $800 Mn + 0.5 * $300 Mn = $550 Mn
Net worth now = Net worth next year / (1+10%) = $550 Mn/ 1.1 = $500 Mn
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Senior Bond payout = $300 Mn * (1+ 10%) = $330 Mn
Junior Bond payout = $100 Mn * ( 1+ 20%) = $120 Mn
Firm's Future Equity value when net worth is $800 Mn = $800 Mn - $330 Mn - $120 Mn = $350 Mn
Firm's Future Equity value when net worth is $300 Mn = $300 Mn - $330 Mn - $120 Mn = $0 Mn
Firm's Future Equity value = 0.5 * $350 Mn + 0.5 * $0 = $175 Mn
Equity value today = $500 - $300 - $100 = $100 Mn
Levered cost of capita = (Firm's Future Equity value/Equity value today) - 1 = $175/$100 - 1 = 75%
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