Kenny owns a very profitable ice cream stand. Based on the results of a marketin
ID: 2707920 • Letter: K
Question
Kenny owns a very profitable ice cream stand. Based on the results of a marketing research project that cost $8,000, Kenny is now considering adding a line of frozen yogurt to his product mix.
Kenny expects that the machine necessary to produce the yogurt will cost $250,000, last for five years and have a salvage value of $20,000 at the end of the fifth year. For tax purposes, Kenny will depreciate the yogurt machine over the five years to a zero salvage value using the straight-line method.
Kenny will incur extra annual fixed costs of $3,000 per year if he acquires this machine, while his variable costs (the cone/cup, yogurt, wrapping paper, spoons, etc.) will be $1.00 per serving. He expects to sell 200 servings a day (365 days in a year) at a price per serving to be determined. The annual rent on his stand under the existing no cancelable lease (with seven years remaining) is $18,000 per year, with built-in annual increases to cover inflation (expected to be 3% annually).
The relevant income tax rate for Kenny
Explanation / Answer
We should ignore the annual rent as it will be incurred irrespective of whether Kenny adds the frozen yogurt line.
Yearly depreciation = 250,000/5 = 50,000
Let price per serving be X
So pre-tax profit per year = (X-1)*200*365 - 3,000 - 50,000 = 73,000*X - 126,000
Post tax profit = (73,000*X - 126,000)*(1-40%) = 43,800*X - 75,600
Annual cash flow = post tax profit+depreciation = 43,800*X - 75,600 + 50,000 = 43,800*X - 25,600
Let this annual cashflow be Y.
So NPV = -250,000 + Y/1.18^1 + Y/1.18^2 + Y/1.18^3 + Y/1.18^4 + Y/1.18^5 + 20,000*(1-40%)/1.18^5 = 3.127171*Y - 244,755
When this is equal to zero, Y = 78,267.1
So Y = 43,800*X - 25,600 = 78,267.1
Solving, we get X = $ 2.37
So the minimum price that should be charged by Kenny is $2.37
Hope this helped ! Let me know in case of any queries.
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