Question

Sports Gear Ltd is a company that makes clothing. The company has a product line that pro- duces women’s tops of regular sizes. The same machine could be used to produce petite sizes as well. However, the remaining life of the machines will be reduced from 4 years to 2 years if the petite size production is added. The cost of identical machines with a life of 8 years is $1 300 000. Assume the opportunity cost of capital is 15 per cent. What is the opportunity cost of adding petite sizes?

Answer 1

If Machine is not used for Petite sizes, then machine will be replaced with identical machine after useful life is over means after 4 years

Cost paid after 4 years or future value = 1300000

interest rate (i) =15%

Present value of machine replaced = future value/(1+i)^n

=1300000/(1+15%)^4

=743279.2193

If Machine is used for Petite sizes, then machine will be replaced with identical machine after 2 years

Cost paid after 2 years or future value = 1300000

interest rate (i) =15%

Present value of machine replaced = future value/(1+i)^n

=1300000/(1+15%)^2

=982986.7675

Opportunity cost of adding Petitie sizes = Present value of machine replaced if petite is added - present value of machine replaced if petitie aizes is not added

=982986.7675-743279.2193

=239707.5482

So  the opportunity cost of adding petite sizes is $239707.55