### Syllabus B2b)

Evaluate embedded real options within a project, classifying them into one of the real option archetypes.

### NPV presumes decisions are now or never..

NPV doesn't accept that decisions are flexible and managers have a choice of actions

The **Real options method **estimates a value for this choice

#### Real options build on NPV where there's uncertainty and..

when the decision isn't now or never

when a decision can be changed

when there are opportunities depending on an initial project being undertaken

So NPV tries to put risks into the cost of capital

Real options puts a value on this uncertainty - sees it as an opportunity

#### Ok - so how do you value these Real Options??

Well you need to estimate of the value attributable to three types of real options:

The option to delay a decision (a type of call option)

The option to abandon a project once started (which is a type of put option), and

The option to exploit follow-on opportunities (which is a type of call option).

#### Real options value will use BSOP and put-call parity and has 5 variables...

The underlying asset value (Pa), (the PV of future project cash flows)

The exercise price (Pe), (the amount paid / RECEIVED when the call/ PUT option is exercised)

The risk-free (r), which is normally given or taken from the return offered by a short-dated government bill

The volatility (s), which is the project risk (measured by the standard deviation)

The time (t), in years, left before the opportunity to exercise ends.

### Example 1: Delaying the decision

A company is considering bidding for the exclusive rights to undertake a project, which will initially cost $35m.

Year | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Cashflows | 20 | 15 | 10 | 5 |

The relevant cost of capital for this project is 11% and the risk free rate is 4.5%. The likely volatility (standard deviation) of the cash flows is estimated to be 50%.

### Solution to Example 1

NPV without any option to delay the decision:

Year | Today | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

Cashflows | -35 | 20 | 15 | 10 | 5 |

Discounted at 11% | -35 | 18 | 12.2 | 7.3 | 3.3 |

**NPV = $5.8m**

Now let's suppose the company doesn't have to make the decision right now but can wait for two years...

Year | 3 | 4 | 5 | 6 |
---|---|---|---|---|

Cashflows | 20 | 15 | 10 | 5 |

Discounted at 11% | 14.6 | 9.9 | 5.9 | 2.7 |

Variables to be used in the BSOP model

Asset value (Pa) = $14.6m + $9.9m + $5.9m + $2.7m = $33.1m

Exercise price (Pe) = $35m

Exercise date (t) = Two years

Risk free rate (r) = 4.5%

Volatility (s) = 50%

Using the BSOP model:

d1 = 0.401899

d2 =-0.30521

N(d1) =0.656121

N(d2) =0.380103

Call value =$9.6m

So the company can delay its decision by two years and can bid as much as $9.6m instead of $5.8m for the exclusive rights to undertake the project.

The increase in value reflects the time before the decision has to be made and the volatility of the cash flows

### Example 2: Exploiting a follow-on project

A company is considering a project with a small positive **NPV of $3m** but there is a possibility of further expansion using the technologies developed for the initial project.

The expansion would involve a second project in four years’ time.

Currently, the present values of the cash flows of the second project are estimated to be $90m and its estimated cost in four years is expected to be $140m.

The standard deviation of the project’s cash flows is likely to be 40% and the risk free rate of return is currently 5%

### Solution to Example 2

The variables to be used in the BSOP model for the second (follow-on) project are as follows:

Asset Value (Pa) = $90m

Exercise price (Pe) = $140m

Exercise date (t) = Four years

Risk free rate (r) = 5%

Volatility (s) = 40%

Using the BSOP model

d1 = 0.097709

d2 = -0.70229

N(d1 )= 0.538918

N(d2 )= 0.241249

**Call value =$20.85m**

The overall value to the company is $23.85m, when both the projects are considered together.

At present the cost of $140m seems substantial compared to the present value of the cash flows arising from the second project.

Conventional NPV would probably return a negative NPV for the second project and therefore the company would most likely not undertake the first project either. However, there are four years to go before a decision on whether or not to undertake the second project needs to be made.

A lot could happen to the cash flows given the high volatility rate, in that time. The company can use the value of $23.85m to decide whether or not to invest in the first project or whether it should invest its funds in other activities. It could even consider the possibility that it may be able to sell the combined rights to both projects for $23.85m.

### Example 3: The option to abandon a project

Duck Co is considering a five-year project with an initial cost of $37,500,000 and has estimated the present values of the project’s cash flows as follows:

Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Cashflows | 1,496.9 | 4,938.8 | 9,946.5 | 7,064.2 | 13,602.9 |

Swan Co has approached Duck Co and offered to buy the entire project for $28m at the start of year three.

The risk free rate of return is 4%.

Duck Co’s finance director is of the opinion that there are many uncertainties surrounding the project and has assessed that the cash flows can vary by a standard deviation of as much as 35% because of these uncertainties.

### Solution to example 3

Since it is an offer to sell the project as an abandonment option, a put option value is calculated based on the finance director’s assessment of the standard deviation and using the Black-Scholes option pricing (BSOP) model, together with the put-call parity formula.

Although Duck Co will not actually obtain any immediate cash flow from Swan Co’s offer, the real option computation below, indicates that the project is worth pursuing because the volatility may result in increases in future cash flows.

**Without the real option:**

Present value of cash flows approx. = $37,049,300

Cost of initial investment = $37,500,000

NPV of project = $37,049,300 – $37,500,000 = $(450,700)

**With the real option**

The asset value of the real option is the sum of the PV of cash flows foregone in years three, four and five, if the option is exercised ($9.9m + $7.1m + $13.6m = $30.6m)

Asset value (Pa) $30.6m

Exercise Price (Pe) $28m

Risk-free rate (r) 4%

Time to exercise (t) - Two years

Volatility (s) 35%

d1 = 0.588506

d2 = 0.093531

N(d1) = 0.721904

N(d2) = 0.537259

Call Value = 8.20

Put Value = $3.45m

Net present value of the project with the put option is approximately $3m ($3.45m – $0.45m).

If Swan Co’s offer is not considered, then the project gives a marginal negative net present value, although the results of any sensitivity analysis need to be considered as well. It could be recommended that, if only these results are taken into consideration, the company should not proceed with the project. However, after taking account of Swan Co’s offer and the finance director’s assessment, the net present value of the project is positive. This would suggest that Duck Co should undertake the project.