Question

A bicycle manufacturer currently produces 201,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $1.80 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct? in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $260,000 and would be obsolete after ten years. This investment could be depreciated to zero for tax purposes using a? ten-year straight-line depreciation schedule. The plant manager estimates that the operation would require $36,000 of inventory and other working capital upfront? (year 0), but argues that this sum can be ignored since it is recoverable at the end of the ten years. Expected proceeds from scrapping the machinery after ten years are $19,500. If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%?, what is the net present value of the decision to produce the chains? in-house instead of purchasing them from the? supplier?

Answer 1

After Tax Production Cost	1.5*201000(1-0.35)	195,975.00
Present Value of Production Costs	195975*PV($1,15%,10 years)
PV Annuity Factor=	(1-(1+r)^-n)/r
where
r=	discounting rate
n=	no of years
PV Annuity Factor=	(1-((1+0.15)^-10))/0.15	5.02
Present Value of Production Costs (A)	195975*5.02	983,794.50
Annual Depreciation	260000/10	26,000.00
Tax Savings from Depreciation	26000*35%	9,100.00
PV of Tax Savings from Depreciation (B)	-26000*5.02	-     130,520.00
Net Working Capital in Year 0	36000/1	36,000.00
PV of Recovery of Net Working Capital	36000/(1.15)^10	8,898.65
Total PV of Net Working Capital ('C)	36000-8898.65	27,101.35
Proceeds from scrapped machinery		19,500.00
PV of proceeds	-19500/1.15^10	-          4,820.10
PV of proceeds after tax(D)	-4820.10*(1-0.35)	-3133.065
Cost of Machinery ('E)		260000
Present value of cost of producing inhouse	(A+B+C+D+E)	1,137,242.79
After Tax value of purchase	201000*1.8*5.02*(1-0.35)	1,180,553.40
NPV of Producing in house	1180553.40-1137242.79	43310.61
Since NPV of producing in house is positive, it is cheaper to produce inhouse