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

Hey guys did u solved this ? Bouchard Industries is a Canadian company that manufactures gutters for residential houses. Its management believes it has developed a new process that produces a superior product. The company must make an initial investment of CAD190 million to begin production. If demand is high, cash flows are expected to be CAD40 million per year. If demand is low, cash flows will be only CAD20 million per year. Management believes there is an equal chance that demand will be high or low. The investment, which has an investment horizon of ten years, also gives the company a production-flexibility option allowing the company to add shifts at the end of the first year if demand turns out to be high. If the company exercises this option, net cash flows would increase by an additional CAD5 million in Years 2–10. Bouchard’s opportunity cost of funds is 10%.

The internal auditor for Bouchard Industries has made two suggestions for improving capital allocation processes at the company. The internal auditor’s suggestions are as follows:

Suggestion 1: “In order to treat all capital allocation proposals in a fair manner, the investments should all use the risk-free rate for the required rate of return.”

Suggestion 2: “When rationing capital, it is better to choose the portfolio of investments that maximizes the company NPV than the portfolio that maximizes the company IRR.”

Question
What is the NPV (CAD millions) of the optimal set of investment decisions for Bouchard Industries including the production-flexibility option?

B is correct. The additional NPV of adding shifts if demand is “high” is

NPV=∑10t=251.10t=C\$26.18 million.NPV=∑�=21051.10�=C\$26.18 million.

If demand is “low,” the production-flexibility option will not be exercised. The optimal decision is to add shifts only if demand is high.

Because the production-flexibility option is exercised only when demand is high, which happens 50% of the time, the expected present value of adding shifts is

NPV = 0.50(26.18) = CAD3.09 million.

The total NPV of the initial project and the production-flexibility option is

NPV = –CAD5.66 million + CAD13.09 million = CAD7.43 million.

The option to add shifts, handled optimally, adds sufficient value to make this a positive-NPV project.
i still dont know how it gets npv = 26.18

well in the end i solved it , dont really know how the book did it , but here is how i did it:

1. Calculate the expected cash flows for each scenario:
• High demand scenario: Cash flows are CAD40 million per year for 10 years, plus an additional CAD5 million in years 2-10 if the production-flexibility option is exercised. So, the cash flows for this scenario are:

CF0 = -190 CF1 = 40 CF2 = 45 CF3 = 45 CF4 = 45 CF5 = 45 CF6 = 45 CF7 = 45 CF8 = 45 CF9 = 45 CF10 = 45

• Low demand scenario: Cash flows are CAD20 million per year for 10 years, with no production-flexibility option. So, the cash flows for this scenario are:

CF0 = -190 CF1 = 20 CF2 = 20 CF3 = 20 CF4 = 20 CF5 = 20 CF6 = 20 CF7 = 20 CF8 = 20 CF9 = 20 CF10 = 20

after that just NPV 1 X 0.5 +NPV 2 X 0.5
so then u get the answer (b) CAD7.43 million.
i still got no clue on how the book got the 26.18.