Excerpt

## Introduction

Options are a financial instrument with which one can reduce risk. Financial options are used by companies for this purpose and come in many forms, for example commodity, currency or interest rate options.

Options are also embedded in real investment decisions, for example in the form that a company gains the possibility (or option) to make a very profitable future investment (B), but only under the condition that the original investment (A) is made. This possibility increases uncertainty about the future, and has a value to the purchaser of the asset (A) at the time of purchase. Option pricing attempts to value this. This offers an alternative form of investment appraisal to the traditional Discounted Cash Flow (DCF) methods such as Net Present Value (NPV), that do not and can not account for and place a value on this uncertainty.

There are two major methods of valuing options. One is the binomial method and the other is the Black & Scholes Formula. The options valued here all use the Binomial Model assuming European Options.

## Calculating a Development Option (Call)

To value the land in question the binomial option pricing method is used to determine the value of having the option to develop the land after purchase. The specific method used in this case is the Hedging Method.

Abbildung in dieser Leseprobe nicht enthalten

So is 95.000 because this is the net effect of taking the current asking price at 175.000 minus the current achievable resale value of 80.000.i.e. the current net actual value of the land. Su is 300.000 because this is the expected value of the land as a building plot and as such depicts the best possible outcome for Moore (best case scenario).

Sd, 80.000, is the expected value of the land after purchase should it not become a building plot and remain agricultural (worst case scenario).

ExPr of 90.000 is the amount that must be paid at t1 (equal to the exercise date - ExDt), one year after the initial outlay of So at to, to be in the position to develop the land and gain the 300.000 (Su). Rf is given. Cu is the value gained if Su becomes true.

Oppositely Cd occurs if Sd becomes true and is therefore 0. The 80.000 that will be received on sale is not shown here because it has been accounted for under So.

After defining the above parameters it is required to calc ulate the option delta or hedging Ratio as follows:

Abbildung in dieser Leseprobe nicht enthalten

This tells us that to produce a risk free position it is necessary to sell 1,047619 options for each security held.

Therefore the risk free outcome is:

Abbildung in dieser Leseprobe nicht enthalten

The most you would pay for this future value today would not be 80.000 as suggested, but the value discounted at the risk free rate:

Abbildung in dieser Leseprobe nicht enthalten

This is then deducted from the price of the asset: 95.000 - 76.190,48 = 18.809,5

To find the value of both one call on the asset and the maximum acceptable value for the development option:

Abbildung in dieser Leseprobe nicht enthalten

The value of purchasing the land is therefore the value of the development option or call (17.955) plus the value of the agricultural land (80.000):

Abbildung in dieser Leseprobe nicht enthalten

Considering that the present value of the land is 95.000 it appears that this investment is worthwhile and should be undertaken, as the predicted value including the option is higher than the current value.

## Land Acquisition Strategy

An acquisition strategy can be formulated for Moore through manipulation of the Put-Call-Parity fo rmula.

The formula is as fo llows:

Value of Call + Present Value of Exercise Price = Value of Put + Share(Asset) Value The pay off from one side of the above equation is identical to the pay off from the other side of the equation. This relationship is important, because if we know 3 of the items involved we can use the formula to value the missing one.

We have already calculated the call value for the acquisition above, using the hedg- ing method of binomial option pricing. If we substitute the value of the call into the above formula and twist the formula around we will be able to calculate the value of the put.

17.955 + Present Value of Exercise Price - Share(Asset) Value = Value of Put The Present Value of Exercise Price can be calculated by discounting the exercise price, that we also know, at the risk free rate as follows:

Abbildung in dieser Leseprobe nicht enthalten

Knowing this we only need to subtract the asset value to arrive at the Value of the put.

The asset has a present value of 95.000, because this is the net effect between what the farmer is demanding and what the market is offering at present.

To conclude the value of the put must therefore be:

Abbildung in dieser Leseprobe nicht enthalten

By again rearranging the now completed Put-Call-Parity formula we can formulate an investment strategy for Moore

Abbildung in dieser Leseprobe nicht enthalten

**[...]**

- Quote paper
- Andrew Brabner (Author), 2002, Corporate Finance - Assignment Two, Munich, GRIN Verlag, https://www.grin.com/document/7644

Publish now - it's free

Comments