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Finding minimum sales to make investment desirable

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You work for an automobile company that is considering developing a new car. The product development cost for this new car will be $500 million per year for 3 years. During the third year of product development, the company will incur $1 billion for manufacturing set up costs. Three years after the start of product development, the company will begin making and selling cars. Production and sales will last 7 years, and each car sold will generate incremental profit of $2,500. After 7 years, the salvage value associated with the manufacturing facilities will be $200 million. The company's cost of capital is 12%. Assume all cash flows occur at the end of the year.

a. What is the minimum number of cars the company must sell during each of the 7 years of the product's life to make this investment desirable under the net present value criterion?

b. What will the minimum number of vehicles be if the company's cost of capital is 15%?

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Solution describes the steps to find out minimum number of car sales to make investment desirable with NPV criteria.

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Please refer attached file for better understanding of formulas.

Solution:

a. What is the minimum number of cars the company must sell during each of the 7 years of the
product's life to make this investment desirable under the net present value criterion?

We know PV=FV/(1+r/100)^n
PV = Present Value of cash flow
FV = Future value of cash flow
r = discount rate per period
n = number of period
r=0.12
Figure in millions
Year End Development cost Manufacturing Costs Total outflows PV at 12%
1 500 500 446.4285714
2 500 500 398.5969388
3 500 1000 1500 1067.670372

Present Value of Cash outflows= 1912.695882 ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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