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

The capital budgeting committee for Laroche Industries is meeting. Laroche is a North
American conglomerate that has several divisions. One of these divisions, Laroche Livery,
operates a large fleet of vans. Laroche’s management is evaluating whether it is optimal to
operate new vans for two, three, or four years before replacing them. The managers have
estimated the investment outlay, annual after-tax operating expenses, and after-tax salvage cash
flows for each of the service lives. Because revenues and some operating costs are unaffected
by the choice of service life, they were ignored in the analysis. Laroche Livery’s opportunity
cost of funds is 10 percent. The following table gives the cash flows in thousands of Canadian
dollars (C$).
20 Learning Outcomes, Summary Overview, and Problems
part-i-02 13 January 2012; 10:13:22
Service Life Investment Year 1 Year 2 Year 3 Year 4 Salvage
2 years 40,000 12,000 15,000 20,000
3 years 40,000 12,000 15,000 20,000 17,000
4 years 40,000 12,000 15,000 20,000 25,000 12,000
Schoeman Products, another division of Laroche, has evaluated several investment projects
and now must choose the subset of them that fits within its C$40 million capital budget.
The outlays and NPVs for the six projects are given below. Schoeman cannot buy fractional
projects, and must buy all or none of a project. The currency amounts are in millions of
Canadian dollars.
Project Outlay PV of Future Cash Flows NPV
1 31 44 13
2 15 21 6
3 12 16.5 4.5
4 10 13 3
5 8 11 3
66 8 2
Schoeman wants to determine which subset of the six projects is optimal.
A final proposal comes from the division Society Services, which has an investment
opportunity with a real option to invest further if conditions warrant. The crucial details are
as follows:

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 probably 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.
Society Services wants to evaluate its investment alternatives.
The internal auditor for Laroche Industries has made several suggestions for improving
capital budgeting processes at the company. The internal auditor’s suggestions are as follows:
Chapter 2 Capital Budgeting 21
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Suggestion 1. “In order to put all capital budgeting proposals on an equal footing, the
projects should all use the risk-free rate for the required rate of return.”
Suggestion 2. “Because you cannot exercise both of them, you should not permit a
given project to have both an abandonment option and an expansion/
growth option.”
Suggestion 3. “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.”
Suggestion 4. “Project betas should be used for establishing the required rate of return
whenever the project’s beta is different from the company’s beta.
A. 6.34.
B. 12.68.
C. 31.03.

Answer: B. 12.68.