Problem 1 Assume the following about a 6-year project: Mean Std Dev Sales Growth 4% 3% COGS/Sales
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Question:
Problem 1
Assume the following about a 6-year project:
Mean Std Dev
Sales Growth 4% 3%
COGS/Sales 60% 10%
Fixed Cost $1,500
NWC as % of Sales 10%
Tax Rate 25%
Cost of Capital 12%
- Sales for the first year will be $10,500, but the sales in subsequent years are uncertain. Estimated sales growth is assumed to be normally distributed with a mean of 4% and a standard deviation of 3%. Costs of goods Sold (COGS) each year are uncertain as well but are assumed to be a percentage of sales. COGS as a percentage of sales is assumed to be distributed normally with a mean of 60% and a standard deviation of 10%.
- Fixed costs will be $1,500 per year.
- The project will require an initial investment in net working capital of $500. Beginning at year 1, NWC is 10% of sales. The entire NWC investment (across all years) will be recovered at the end of the project.
- To operate the project, a new piece of equipment must be purchased at a cost of $12,000. The equipment will be depreciated using the straight-line approach (depreciate over 6 years, no salvage value).
- The equipment will have 0 salvage value by the end of the project.
- The cost of capital facing the firm is 12%.
Tasks:
a) Calculate the NPV of the project while capturing the uncertainty in sales and costs of goods sold.
b) Simulate the NPV 500 times using a data table.
c) Graph the frequency distribution of the NPV estimates; calculate the mean NPV and standard deviation.
d) What is the probability that the NPV is positive? What is your recommendation for the project? Why?
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