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Investment Opportunities as Real Options: Getting Started on the Numbers
By Timothy A. Luehrman July-August 1998 Issue
The article talks of how Option Pricing explains in a more interactive and better manner about corporate investments than the Discounted Cash Flow (DCF) and Net Present Value (NPV) methods. The writer compares the DCF method with the Option Pricing method to evaluate a project not only finding the difference between the two but also to look at the commonalities to understand the framework more lucidly.
As per the article a corporate investment opportunity is more like a call option as it has a right and not an obligation to acquire the operating assets of a company. A European option is used to map an investment decision of a Corporate where the Value of the
acquiring project’s
operating assets is comparable to a stock price. Similarly, expenditure required to acquire a project
s’
assets is compared to the exercise price, time to decision to the time to expiration, time value of money to the risk-free rate and riskiness of the project to the variance of returns on a stock. Also,
Option Value = S-X = NPV
, so that when NPV is negative, the firm will not invest in the project.
NPV and Option pricing
is similar in investment decisions and making the payments as well. The deferral to making a payment is beneficial in both cases. In NPV, we earn the time value of money and in case of option pricing, if the price of the asset increases, we shall exercise the earlier option available to us and if in case the prices of the assets plunge, we may choose not to invest and save ourselves from making a bad investment. NPV misses the decision of not paying for the assets thereby making option pricing method more lucrative. The article furthers the NPV to a
Modified NPV = S - PV(X)
;
PV(X) = X/(1+r
f
) ^t
thereby involving four of the five Option Pricing model variables in the equation. The author then converts the difference of the variable into a ratio and naming the equation as NPVq to make it mathematical and easier to interpret. The negative NPV now takes a value between 0 and 1, the positive NPV takes a value above 1 and an NPV = 0 now becomes NPVq = 1. Similarly, the article also quantifies for the cumulative volatility of the investment in the project. It first identifies a logical method of measuring the uncertainty and then expresses the same into a mathematical form that would be easier to interpret and use for practical purpose.
Variance is the ideal measure of uncertainty (
σ
2
)
but in this case, we need to incorporate the importance of time as well thus making the measurement as
σ
2
t. To further make the calculations legible the author uses the
cumulative volatility as
σ
(t)^0.5
. This way all the five variables of Options are put into use while determining the value of a project using the
Black Scholes Model
. The metrics so formed is linked to the Black Scholes Model for which the author generates a table. The Option value can also be located on a two-dimensional graph wherein the X-axis represents the NPVq and the Y-axis represents the volatility represented by
σ
(t)^0.5.
The article further goes on to postulate its theory on a company called Franklin chemicals that undergoes two investments over its phased expansion of manufacturing facility.
Valuing an Oil Company takeover: Essar Oil
Essar Oil was the target of a takeover in early 2016 at $70 per share (It had 165.30 million shares outstanding, and total debt of $9.9 billion).
ã It had estimated reserves of 3038 million barrels of oil and the average cost of
developing these reserves was estimated to be $10 a barrel in present value dollars.
ã The average relinquishment life of the reserves is 12 years.
ã The price of oil was $22.38 per barrel, and the production cost, taxes and royalties
were estimated at $7 per barrel.
ã The bond rate at t
he time of the analysis was 9.00%.
ã
Essar was expected to have net production revenues each year of approximately 5% of the value of the developed reserves. The variance in oil prices is 0.03.
Inputs for valuing undeveloped reserves
Value of underlying asset = Value of estimated reserves discounted back for period of development lag = 3038 * ($ 22.38 - $7) / 1.052 =
$42,380.44
Exercise price = Estimated development cost of reserves = 3038 * $10 =
$30,380 million
Time to expiration = Average length of relinquishment option =
12 years
Variance in value of asset = Variance in oil prices =
0.03
Riskless interest rate =
9%
Dividend yield = Net production revenue/ Value of developed reserves =
5% Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = 1.6548 N(d1) = 0.9510 d2 = 1.0548 N(d2) = 0.8542 Call Value = 42,380.44 exp(-0.05)(12) (0.9510) -30,380 (exp(-0.09)(12) (0.8542) =
$ 13,306 million
Submitted by
–
Arjun Bhargava (2016PGP015) Harshit Pandey (2016PGP023) Sayantan Sarkar (2016PGP050) Vivek Singh (2016PGP060) Girraj Goyal (2016PGP080) Jatin Bedi (2016PGP082)

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