Question

We are examining a new project. We expect to sell 6,000 units per year at $74 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $74 × 6,000 = $444,000. The relevant discount rate is 18 percent, and the initial investment required is $1,710,000. After the first year, the project can be dismantled and sold for $1,540,000. Suppose you think it is likely that expected sales will be revised upward to 9,000 units if the first year is a success and revised downward to 4,600 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. (Do not round intermediate calculations and round your answer to 2 decimal places. e.g., 32.16.)
b.	What is the value of the option to abandon? (Do not round intermediate calculations and round your answer to 2 decimal places. e.g., 32.16.)

Answer 1

a). NPV = -Initial Investment + [0.5 x PV of Cash Inflows success] + [0.5 x PV of Cash Inflows failure]

= -$1,710,000 + [0.5 x $74 x 9,000 x {(1 - 1.18^-10) / 0.18}] + [0.5 x $74 x 4,600 x {(1 - 1.18^-10) / 0.18}]

= -$1,710,000 + [$333,000 x 4.4941] + [$170,200 x 4.4941]

= -$1,710,000 + $1,496,530.74 + $764,893.49 = $551,424.22

b). If the project can be abandoned and is abandoned,

NPV = -Initial Investment + [0.5 x PV of Cash Inflows success] + [0.5 x {TV / (1+r)}]

= -$1,710,000 + [0.5 x $74 x 9,000 x {(1 - 1.18^-10) / 0.18}] + [0.5 x {$1,540,000/1.18}]

= -$1,710,000 + [$333,000 x 4.4941] + [0.5 x $1,305,084.75]

= -$1,710,000 + $1,496,530.74 + $652,542.37 = $439,073.11

Since the value of the project when abandoned is less than the value of the project when not abandoned, the project will not be abandoned. This is true even if sales do not turn out to be a Success. Therefore, given the set of assumptions, the abandonment option has no value.