The betafor the stockwillbe 2.00 for the next five years, anddropto 0.8 thereafter (as the leveragedecreases).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 thecapital structure during the period (1992‐1996) was 85%.Annualized variance in firm value = 0.152x 0.412+ 0.852x 0.172+ 2 x 0.15 x 0.85 x 0.5 x 0.41 x 0.17 =0.0335The 15‐year bond rate is6%. (the duration of this coupon bond is roughly 11 years to match the life of theoption)
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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 millionX, Exercise price: Face Value of outstanding debt= £8,865 milliont, Life of the option: Weighted average duration of debt= 10.93 years2, Variance in the value of the underlying asset= 0.0335r , Riskless rate: Treasury bond rate corresponding to option life= 6%Based upon these inputs,d1 =‐0.8582N(d1) = 0.1955d2 =‐1.4637N(d2) = 0.0717the 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 millionDebt Value= £2278m – £ 116 m= £2162 millionAppropriate 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 factthat the French and the British governments put pressure on the banks to roll over their debt makes the optioneven more.