# EOC Reading 23-Calculate project NPV with expansion option

Hi all, the question comes from exercises 18 from the reading 23, which it asks about the NPV with an expansion option

• The original project:
• An outlay of C\$190 million at time zero.
• Cash flows of C\$40 million per year for Years 1–10 if demand is “high.”
• Cash flows of C\$20 million per year for Years 1–10 if demand is “low.”
• Additional cash flows with the optional expansion project:
• An outlay of C\$190 million at time one.
• Cash flows of C\$40 million per year for Years 2–10 if demand is “high.”
• Cash flows of C\$20 million per year for Years 2–10 if demand is “low.”
• Whether demand is “high” or “low” in Years 1–10 will be revealed during the first year. The probability of “high” demand is 0.50, and the probability of “low” demand is 0.50.
• The option to make the expansion investment depends on making the initial investment. If the initial investment is not made, the option to expand does not exist.
• The required rate of return is 10 percent.

What is the NPV (C\$ millions) of the optimal set of investment decisions for Society Services including the expansion option?

1. 6.34.
2. 12.68.
3. 31.03.

How the answer calculated the answer is following 1. calculate the binominal price of the project without option 2. calculate the NPV of high scenario, times 0.5, and add this value to the no option project value

Why is it calculated like this? what I would do is calculate high and low scenario and add the weighted sum, and this question itself is confusing me, whats the use of the option here?

Thanks

“How the answer calculated the answer is following 1. calculate the binominal price of the project without option 2. calculate the NPV of high scenario, times 0.5, and add this value to the no option project value”

You know whether the demand is high or low before you have a take a decision regarding the option.

If demand is low (50% probability), you just don’t exercise it, so nothing happens.

If demand is high (50% probability), you do exercise the option. Just calculate its NPV under this scenario, and add (Option value*probability) to the initial NPV.

Hope it helps

so the option exercise is not in conflict or exclusive with the original high scenario? I was thinking if you exercise the high scenario, the original high sceanrio doesnt exist anymore, but it seems it is just an add on here?

I’m not sure what you mean by “exercise the high scenario” here.

You exercise the option to expand. It may very well be that you’ll exercise it only when demand is high.

Yes it is just an add-on. The initial investment will stay regardless of whether the option is exercised or not