Question

You are an analyst for a pipe manufacturing corporation that is considering a new project which involves fabricating some custom pipe for a single customer. The project will take advantage of excess capacity in an existing plant. The plant has the capacity to produce 50,000 units of 18-inch pipe, but only 25,000 are being produced currently. Sales of 18-inch pipe are expected to increase by 10% a year. You want to use some of the remaining capacity to manufacture 20,000 units of custom 19.5-inch pipe for the next ten years (which will use up 40% of the total capacity), your customer will purchase this amount for the next ten years (no growth). An average unit of 18-inch pipe sells for $100 and costs $40 to make. The tax rate for the corporation is 40% and the discount rate is 10%. Is there an opportunity cost involved for producing the custom pipe? If so, how much is it?

Answer 1

		Present value of cash flow=(cash Flow/((1+i)^N)
		N=year of Cash Flow, i=discount rate =10%=0.1
		Production of 18 inch pipe in year 2	27500	(25000*1,1)
		Production of 18 inch pipe in year(N+1)=1.1*(Production in Year (N)
		Year	1	2	3	4	5	6	7	8	9	10
	A	Capacity	50000	50000	50000	50000	50000	50000	50000	50000	50000	50000
	B	Quantity of Custom 19.5 inch pipe	20000	20000	20000	20000	20000	20000	20000	20000	20000	20000
	C	Balance capacity available for 18-inh pipe	30000	30000	30000	30000	30000	30000	30000	30000	30000	30000
	D	Capacity required of 18 inch pipe	25000	27500	30250	33275	36602	40263	44289	48718	53590	58949
	E	Lost Production of 18 inch pipe			250	3275	6602	10263	14289	18718	20000	20000
	F=100-40	Contribution per unit of 18 inch pipe			$60	$60	$60	$60	$60	$60	$60	$60
	G=E*F	Before tax opportunity cost(Loss of Contribution)			$15,000	$196,500	$396,120	$615,780	$857,340	$1,123,080	$1,200,000	$1,200,000
	H=G*(1-0.4)	After tax Opportunity Cost			$9,000	$117,900	$237,672	$369,468	$514,404	$673,848	$720,000	$720,000	SUM
	PV=H/(1.1^N)	Present Value of Opportunity Cost (Lost Contribution)			$6,762	$80,527	$147,576	$208,555	$263,971	$314,355	$305,350	$277,591	$1,604,687
		Opportunity cost involved =Present Value of Lost Contribution	$1,604,687