For simplicity, we shall assume zero-coupon debt with a maturity value, MWe shall define D and the value ofrisky debt and Drf as the value of riskfree debt
The difference between these valuesis the value of the Put Option, PD,that the Debt holders have sold theEquity holdersThis put option allows the Equityholders to sell the firm to the Debtholders for M if VN < M
If at the maturity date of the debt, N,the value of the firm is less than thedebt’s maturity value, VN < M, thenthe Equity holders will not pay thedebt, and let the Debt holders takeover the firm
We want to preempt the competitionfrom entering the PLTD market whichwe believe will be highly profitable inthe long runThe Lev-I might teach us things thatwill be useful for developing the nextgeneration Lev-II
This may look a bit different:No rfT term in the d1 and d2 calculationXe-rt, not X, in the denominator of thelogarithmThe result is the same, but a bit moreelegant
S Today's PV of the cash flows 1,248.43X Cost (Investment) of the Project 3,000.00rf Risk free rate 10% T Term of the option (Years) 4σ Standard Deviation (assumed) 50%
How Can It Be So Valuable?How Can It Be So Valuable?
The option valuation only considersthose outcomes that will result inpositive NPVs for the Lev-IIIf we get to 2008 and find theexpected cash flows are better thanwe anticipated, we will proceed withthe Lev-IIOtherwise, we do not proceed
Option theory can be used to justifyvery optimistic valuationsWhat happens is all of the firm’sprojects are accepted based on thevalue of options and none of theoptions expire in the money?
You have a claim that will allow yourfirm to obtain a 100% interest in anoil well by simply investing the $10million needed to develop the wellIf development has not begun by nextyear, the claim will expire and revertback to the government
Currently, you forecast annualperpetual cash flows of $1.1 millionThe discount rate is 10%NPV = 1.1MM/10% - $10MM = $1MMThis is positive, so you could proceedimmediately
Suppose that the price of oil is volatileIf the price of oil next year falls, theexpected perpetual annual cash flowswould be $0.8MM, resulting in aproject NPV of ($2MM)If the price rises, these cash flows willrise to $1.4MM, resulting in a projectNPV of $4MM
The passage of time resolvesuncertaintyIf a year from now, the conditionsdeteriorate, we can decide not toinvest in a bad projectWe are cutting of some of the left tailof the distribution
We can invest $12MM in a projectthat will generate gross margin of$1.7MM annually. This margin isexpected to grow at 9% annuallyFixed costs are $0.7MM annually andwill not grow.
Ignored in the previous example isthe fact that there are many possibleoutcomes or paths where it may bebetter to stop the project and collectthe project salvage values.Suppose that $10MM of the $12MMproject cost is for fixed assets thathave a salvage value that declines at10% annually.
