A software company is considering translating its program into French. Each unit of the program sells for $50 and incurs a variable cost of $10 to produce. Currently, the size of the market for the product is 300,000 units per year, and the English version of the software has a 30% share of the market. The company estimates that the market size will grow by 10% a year for the next five years, and at 5% per year after that. It will cost the company $6 million to create a French version of the program. The translation will increase its market share to 40%. Given a 10-year planning horizon, for what discount rates is it profitable to create the French version of the software?
You are thinking of starting Peaco which will produce Peakbabies, a product that competes with Ty’s Beanie Babies. In year 0 (right now), you will incur costs of $4 million to build a plant. In year 1, you expect to sell 80,000 Peakbabies for a unit price of $25. The price of $25 will remain unchanged through years 1 to 5. Unit sales are expected to grow by the same percentage (g) each year. During years 1 to 5, Peaco incurs two types of costs: variable costs and SG&A (selling, general, and administrative) costs. Each year, variable costs equal half of revenue. During year 1, SG&A costs equal 40% of revenue. This percentage is assumed to drop 2% per year, so during year 2, SG&A costs will equal 38% of revenue, and so on. Peaco’s goal is to have profits for years 0 to 5 sum to 0 (ignoring the time value of money). This will ensure that the $4 million investment in year 0 is paid back by the end of year 5. What annual percentage growth rate g does Peaco require to pay back the plant cost by the end of year 5?
The file P02_43.xlsx contains a template for a car loan. Specifically, once values are entered in the blue cells, you need to enter formulas in the gray cells to calculate the amount financed, the monthly payment (assuming that monthly payments stay the same throughout the term of the loan), the total interest paid, and an amortization schedule. For the latter, fill in the entire gray area with formulas, but use IF functions so that blanks appear past the term of the loan.
A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, $20; year 2, $82; year 3, $60; year 4, $2. (Note: It can be shown that if the cash flow of a project changes sign only once, the project is guaranteed to have a unique IRR.)