###### Study Notes for CFA® Level II – Qua ...

Reading 0: Introduction to Linear Regression (Now Part of Level I) -a. Describe... **Read More**

Options are financial derivatives that give buyers the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price and date. Likewise, real options are capital budgeting options that allow managers the right, but not the obligation, to undertake certain business initiatives in the future, such as deferring, abandoning, or expanding a project. Fundamentally, these can alter the value of the investment decisions made today.

The following are types of real options:

**Timing options:**A company delays investing now with the hopes that improved information in the future could help improve the NPV of the project.**Sizing options:**Anallows the company to abandon the project when results are discouraging and can be exercised when the cash flow of abandoning a project exceed the present value of continuing the project. On the other hand, a**abandonment option**allows the company to make additional investments when future financial results are strong.**growth option****Flexibility options:**permits the company to increase its prices to take advantage of the excess demand which it cannot meet by increasing its production due to low capacity. The company can also use**Price setting option**to profit from having additional shifts and working overtime to meet the additional demand.**production-flexibility options****Fundamental options:**Payoffs from a project such as the mining of minerals increase or decrease the value of an investment depending on whether they will find the said mineral. Many research and development projects are examples of fundamental options.

There are four common approaches to evaluating capital projects with real options:

- Using the NPV without considering options. If the NPV is positive, the firm goes ahead with the investment.
- Using the formula: \(\text{Project’s NPV = NPV (based on discount cash flows alone) – Cost of options + Value of options }\)
- Using decision trees.
- Using option pricing models.

McGill Automotive estimates the NPV of a new assembly plant to be -$600,000. The firm is evaluating an additional investment of $700,000 (present value) to enable management to pay overtime wages to workers in the new assembly plant in the event the new product crosses over to global markets. The option has an estimated present value of $2 million.

Whatis the value of the new assembly plant, including the real option?

$$\begin{align*}\text{Project’s NPV}&=\text{NPV}(\text{based on DCF alone})-\text{Cost of options}+\text{Value of options}\\&=-600,000- 700,000 + 2,000,000\\&=$700,000\end{align*}$$

## Question

Gatsby Solutions is considering a capital project with the following information:

- The initial outlay is $190,000.
- The annual after-tax operating cash flows have a 40% probability of being $20,000 for 5 years and a 60% probability of being $70,000 for the same 5 years.
- The project’s life is 5 years.
- The salvage value at project end is 0.
- The required rate of return (RRR) is 12%.
- In one year, the company has an abandonment option out of which Gatsby Solutions would receive the salvage value of $100,000.
The NPV of the project, assuming the optimal abandonment strategy, is

closest to:

- -$9,761.
- $4,257.
- $62,334.
## Solution

The correct answer is B.If higher cash flows occur and Gatsby does not abandon the project, the NPV is:

$$\text{NPV}=-190,000+\sum_{t=1}^{5}\frac{70,000}{(1.12)^{t}}=$62,334$$

If Gatsby abandons when the lower cash flows occur, Gatsby receives the first-year cash flow and the abandonment value:

$$\text{NPV}=-190,000+\frac{20,000+100,000}{1.12}=-$82,857$$

The expected NPV is:

$$\text{NPV} = 0.4(˗ 82,857) + (0.6)(62,334) = $4,257$$

Reading 19: Capital Budgeting

*LOS 19 (e) Describe types of real options relevant to a capital project.*