We are examining a new project. We expect to sell 5,100 units per year at $65 ne
ID: 2737828 • Letter: W
Question
We are examining a new project. We expect to sell 5,100 units per year at $65 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $65 × 5,100 = $331,500. The relevant discount rate is 15 percent, and the initial investment required is $1,500,000. After the first year, the project can be dismantled and sold for $1,220,000. Suppose you think it is likely that expected sales will be revised upward to 8,100 units if the first year is a success and revised downward to 3,700 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 16,200. 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? (Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).)
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).)
We are examining a new project. We expect to sell 5,100 units per year at $65 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $65 × 5,100 = $331,500. The relevant discount rate is 15 percent, and the initial investment required is $1,500,000. After the first year, the project can be dismantled and sold for $1,220,000. Suppose you think it is likely that expected sales will be revised upward to 8,100 units if the first year is a success and revised downward to 3,700 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 16,200. Note that abandonment is an option if the project is a failure.
Explanation / Answer
NPV if project is a success Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Initial Investment (1,500,000) Cash inflow @65 per units( 8100 1st yr & 16200 2nd yr onwards) 526,500 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 Net Cash Flow (1,500,000) 526,500 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 1,053,000 PV factor @15% 1 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 PV of Cash flows (1,500,000) 457,826 796,219 692,365 602,056 523,527 455,241 395,862 344,228 299,328 260,285 NPV = $ 3,326,937.3 NPV if project is a failure Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Initial Investment (1,500,000) Cash Flow Year 1 (3700 units) 240,500 Cash flow from dismantling 1,220,000 Net Cash Flows (1,500,000) 1,460,500 PV factor @15% 1 0.870 PV of Cash flows (1,500,000) 1,270,000 NPV = (230,000) Success Failure Total NPV $ 3,326,937 $ (230,000) Probability 50% 50% Expected NPV = 1,663,469 (115,000) $ 1,548,469 So NPV of the Project =$1,548,469 NPV of Project when expanded= $ 3,326,937.3 NPV of Project when discarded= $ (230,000.0) So Value of option to expand= $ 3,556,937.3
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