We are examining a new project. We expect to sell 5,600 units per year at $70 ne
ID: 2736440 • Letter: W
Question
We are examining a new project. We expect to sell 5,600 units per year at $70 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $70 × 5,600 = $392,000. The relevant discount rate is 18 percent, and the initial investment required is $1,550,000. After the first year, the project can be dismantled and sold for $1,270,000. Suppose you think it is likely that expected sales will be revised upward to 8,600 units if the first year is a success and revised downward to 4,200 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 only be desirable if the project were a success. This implies that if the project is a success, projected sales after expansion will be 17,200. Note that abandonment is an option if the project is a failure. If success and failure are equally likely, what is the NPV of the project? What is the value of the option to expand? (Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).)
Explanation / Answer
Answer: Base case NPV=-1550000+$392000*PVIFA(18%,10)
=211687.2
Sucess PV=$602000*PVIFA(18%,10)=$2705448.2
Failure PV=$294000*PVIFA(18%,10)=$1321265.4
PV=2705448.2*0.5+1321265.4*0.5=2013356.8
NPV=2013356.8-1550000
=463356.8
Answer:The gain from the option to expand is the present value of the cash flows from the additional units sold, so:
Gain from option to expand = $70(8,600)(PVIFA18%, 9) = $2590406
We need to find the value of the option to expand times the likelihood of expansion. We also need to find the value of the option to expand today, so:
Option value = (0.50)($2590406)/1.18 = $1,097630
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