Question

We are examining a new project. We expect to sell 7,100 units per year at $56 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $56 × 7,100 = $397,600. The relevant discount rate is 14 percent, and the initial investment required is $1,800,000. After the first year, the project can be dismantled and sold for $1,200,000. Suppose you think it is likely that expected sales will be revised upward to 10,800 units if the first year is a success and revised downward to 3,900 units if the first year is not a success. Suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would be desirable only if the project is a success. This implies that if the project is a success, projected sales after expansion will be 21,600. Note that abandonment is still an option if the project is a failure.

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.)
a. NPV
b. Option value

Answer 1

a. If success and failure are equally likely, what is the NPV of the project?

$584,710.17

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

NPV = -$398,596.49

option value = $1,200,000 at the end of year 1

Step-by-step explanation:

option to abandon:

initial investment = -$1,800,000

net cash flow year 1 = $397,600 + $1,200,000 = $1,597,600

NPV = -$1,800,000 + $1,597,600/1.14 = -$398,596.49

if first year is a success:

initial investment = -$1,800,000

net cash flow year 1 = $397,600

net cash flow year 2 to 10 = 18,00 x $56 = $604,800

NPV = -$1,800,000 + $397,600/1.14 + [$604,800 x 4.9464 (PV annuity factor, 14%, 9 periods)] = -$1,800,000 + $348,771.93 + $2,991,582.72 = $1,540,354.65

if first year is a failure:

initial investment = -$1,800,000

net cash flow year 1 = $397,600

net cash flow year 2 to 10 = 3,900 x $56 = $218,400

NPV = -$1,800,000 + $397,600/1.14 + [$218,400 x 4.9464 (PV annuity factor, 14%, 9 periods)] = -$1,800,000 + $348,771.93 + $1,080,293.76 = -$370,934.31

since the possibility of success or failure is equally possible, then we should average net cash flows for years 2 to 10:

initial investment = -$1,800,000

net cash flow year 1 = $397,600

net cash flow year 2 to 10 = ($604,800 + $218,400) / 2 = $411,600

NPV = -$1,800,000 + $397,600/1.14 + [$411,600 x 4.9464 (PV annuity factor, 14%, 9 periods)] = -$1,800,000 + $348,771.93 + $2,035,938.24 = $584,710.17