Show work We are examining a new project. We expect to sell 6,100 units per year

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We are examining a new project. We expect to sell 6,100 units per year at $75 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be $75 x 6,100 = $457,500 The relevant discount rate is 18 percent, and the initial investment required is $1,720,000. After the first year, the project can be dismantled and sold for $1,550,000. Suppose you think it is likely that expected sales will be revised upward to 9,100 units if the first year is a success and revised downward to 4,700 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.) NPV b. What is the value of the option to abandon? (Do not round intermediate calculations and round your answer to 2 decimal pl aces, e.g., 32.16.) Option value $14,061.36

Explanation / Answer

Units per year if successful 9100
Units per year if unsuccessful 4,700
Net cash flow per unit$ 75
Initial operating cash flow$ 457500
Initial investment$ 1720000
Life time 10
Discount rate 18%
Abandonment value $ 1550,000

a) If the project is a success, present value of the future cash flows will be:

PV future CFs = $75 x 9100 x PVIFA (18%, 10yrs) = 75 x 9100 x 4.49 = 30, 64,425

Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so:
Expected value of project at Year 1 = [($30, 64,425+$1550, 000)/2] +$457,500 = 2764713

The NPV is the present value of the expected value in one year plus the cost of the equipment, so: NPV = -$1720000+ (2764713)/1.18 = $622977.1

We need to find the sale quantity where the success and failure are equal
so: 1550,000 = ($75)*Q(PVIFA18%,10)
Q = 1550, 000/ [75*(4.49)]
Q = 4602.82 = 4603
Since the quantity sold 4,700 which is greater than 4603 units, we should not abandon the project.

b) Since we couldn’t abandon the project, the present value of the future cash flows when the quantity is 4,700 will be: PV future CFs = $75 x 4,700 x PVIFA(18%, 10yrs) = $1582725

The gain from the option to abandon is the abandonment value minus the present value of the cash flows if we cannot abandon the project,
so: Gain from option to abandon = $1550,000- 1582725 = -32725
We need to find the value of the option to abandon times the likelihood of abandonment. So, the value of the option to abandon today is: Option value = (.50)(-32725)/1.18= -13866.5

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