# Equity as a call option example

The stock and bond price variance are first annualized: Payoff on a Natural Resource Investment Obtaining the inputs for valuing natural resource options. Input Estimation Process 1. Time to Expiration Relinqushment Period: Time to exhaust inventory - based upon inventory and capacity output. Variance in value of underlying asset based upon variability of the price of the resources and variability of available reserves. Development Lag Calculate present value of reserve based upon the lag.

It will take twenty years to empty the mine, and the firm owns the rights for twenty years. Every year of delay implies a loss of one year of production. The additional value accrues directly from the mine's option characteristics. Given this information, the inputs to the Black-Scholes can be estimated as follows: The estimated opportunity cost of this delay is the lost production revenue over the delay period.

Extending the option pricing approach to value natural resource firms. Input to model Corresponding input for valuing natural resource firm Value of underlying asset Value of cumulated estimated reserves of the resource owned by the firm, discounted back at the dividend yield for the development lag.

Exercise Price Estimated cumulated cost of developing estimated reserves Time to expiration on option Average relinquishment period across all reserves owned by firm if known or estimate of when reserves will be exhausted, given current production rates. Riskless rate Riskless rate corresponding to life of the option Variance in value of asset Variance in the price of the natural resource Dividend yield Estimated annual net production revenue as percentage of value of the reserve.

Valuing an oil company - Gulf Oil in Variance in value of underlying asset Variance in cash flows of similar assets or firms Variance in present value from capital budgeting simulation. Exercise Price on Option Option is exercised when investment is made. Cost of making investment on the project; assumed to be constant in present value dollars.

Expiration of the Option Life of the patent 5. Dividend Yield Cost of delay Each year of delay translates into one less year of value-creating cashflows Illustration Moreover, the dependence of the option value to price, volatility and time is not linear — which makes the analysis even more complex.

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