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You are an analyst for a pipe manufacturing corporation that is considering a new project which...

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Finance

You are an analyst for a pipe manufacturing corporation that isconsidering a new project which involves fabricating some custompipe for a single customer. The project will take advantage ofexcess capacity in an existing plant. The plant has the capacity toproduce 50,000 units of 18-inch pipe, but only 25,000 are beingproduced currently. Sales of 18-inch pipe are expected to increaseby 10% a year. You want to use some of the remaining capacity tomanufacture 20,000 units of custom 19.5-inch pipe for the next tenyears (which will use up 40% of the total capacity), your customerwill purchase this amount for the next ten years (no growth). Anaverage 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 is10%. Is there an opportunity cost involved for producing the custompipe? If so, how much is it?

Answer & Explanation Solved by verified expert
4.1 Ratings (865 Votes)

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

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