Question

We are examining a new project. We expect to sell 6,400 units per year at $58 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be $58 × 6,400 = $371,200. The relevant discount rate is 12 percent, and the initial investment required is $1,750,000. After the first year, the project can be dismantled and sold for $1,620,000. Suppose you think it is likely that expected sales will be revised upward to 9,400 units if the first year is a success and revised downward to 5,000 units if the first year is not a success.

a. If success and failure are equally likely, what is the NPV of the project? Consider the possibility of abandonment in answering.

b. What is the value of the option to abandon?

Answer 1

a. Calculating the NPV of the Project

Cash Flow for Year 1 = $371,200

If the first year is a success, expected sales will be revised upwards to 9,400 units.
Therefore, Present Value of Estimated Cash Flows from the project after the first year if the first year is a success
= (9,400 * 58) * cdf @12% for 9 years ...(cdf = cumulative discounting factor)
= $545,200 * 5.328...
= $2,904,961.79

Abandonment Value after 1 year = $1,620,000
Total = $2,904,961.79 + $1,620,000 = $4,524,961.79

Success and failure are equally likely. Therefore, Probability of success and failure in first years is 0.5 each

Therefore, PV of future Cash flows after first year
= $4,524,961.79 * 0.5
= $2,262,480.90
Add : Year 1 Cash Flows = $371,200

Therefore, Projected Cash Inflows from the Project at Year 1 = $2,262,480.90 + $371,200
= $2,633,680.90
Less: Initial Investment $1,750,000

Therefore, NPV = $2,633,680.90 - $1,750,000 = $883,680.90

Therefore, the NPV of the project is $883,680.90

Note: We have considered the Abandonment Value instead of Cash flows from reduced sales units of $5,000 in case of failure as Abandonment option is more profitable than continuing with 5,000 units in case the first year is a failure.

b. Calculating the Value of the Option to Abandon

Abandon Value after 1 year = $1,620,000

Present Value of Estimated Cash Flows from the project after the first year if the first year is a failure
= (5,000 * 58) * cdf @12% for 9 years
= $290,000 * 5.328...
= $1,545,192.44

Therefore, Gain from Abandonment = $1,620,000 - $1,545,192.44
= $74,807.56
Probability of Failure in the first year = 0.5

Therefore, Actual Gain from Abandonment at Year 1 = $74,807.56 * 0.5
= $37,403.78

Therefore, Gain from Abandonment at Year 0 = $37,403.78 * PVF @12% for 1 year
= $37,403.78 * (1/1.12)
= $33,396.23

Therefore, the value of the option to abandon is $33,396.23


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