L10 - Option to Expand and Abandon

# The beta for the stock will be 200 for the next five

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The beta for the stock will be 2.00 for the next five years, and drop to 0.8 thereafter (as the leverage decreases). Other Inputs: The stock has been traded on the LSE, and the annualized std deviation based upon ln (prices) is 41%. There are listed Eurotunnel bonds, the annualized std deviation in ln(price) for the bonds is 17%. The correlation between stock price and bond price changes has been 0.5. The proportion of debt in the capital structure during the period (1992 1996) was 85%. Annualized variance in firm value = 0.15 2 x 0.41 2 + 0.85 2 x 0.17 2 + 2 x 0.15 x 0.85 x 0.5 x 0.41 x 0.17 = 0.0335 The 15 year bond rate is 6% . (the duration of this coupon bond is roughly 11 years to match the life of the option)

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FINS3641 SAV Week 11: Valuation of the Option to Expand, the Option to Abandon, and Firms in Distress 15 Valuing Eurotunnel Equity and Debt in 1997 (Cont’d) Inputs to the BS Model: S, Value of the underlying asset: Value of the firm (note the error in the book) = £2,278 million X, Exercise price: Face Value of outstanding debt = £8,865 million t, Life of the option: Weighted average duration of debt = 10.93 years 2 , Variance in the value of the underlying asset = 0.0335 r , Riskless rate: Treasury bond rate corresponding to option life = 6% Based upon these inputs, d1 = 0.8582 N(d1) = 0.1955 d2 = 1.4637 N(d2) = 0.0717 the Black Scholes model implies the following values for equity and debt, bankruptcy prob. and default spread: Equity Value = Value of the call = £2278m x 0.1955 \$8,865m e ( 0.06 x10.93) (0.0717) = £116 million Debt Value = £2278m – £ 116 m = £2162 million Appropriate interest rate on debt = (\$8865m / \$2162m) (1/10.93) 1 = 13.7% Default spread = 13.7% 6% = 7.7% Probability of survival / Probability of bankruptcy = 7% / 93% Despite the high chance of bankruptcy, the equity still has a value because the debt is very long term. The fact that the French and the British governments put pressure on the banks to roll over their debt makes the option even more.