To produce an item, equipment costing $250, 000 must be purchased. It will have

Question

To produce an item, equipment costing $250, 000 must be purchased. It will have a life of 4 years and an annual cost of $80, 000; each unit will cost $40 to manufacture. Buying the item externally will cost $100 per unit. Assume i-12% per year. Decision makers would like to determine the breakeven production number per year at which both methods are equivalent. Determine the PW equation for option 1 (Manufacture the item), Where X is the number of units per year PW1= 80, 000(P/A, 12%, 4)+40X(P/A, 12%, 4) PW1 80, 000(P/A, 12%.4)M0X PW1= 250, 000+ 80.000(P/A, 12%, 4)+40X(P/A.12%, 4) PW1= 250.000+ 80.000(P/A, 12%, 4)+40X

Explanation / Answer

1.

Let number of unit per annum = X

Variable cost = cost*units

= 40*X

Annual fixed cost to buy externally = -100Q --- (i)

Annual fixed cost to manufacture = -250,000(A/P, 12%, 4) – 80,000 – 40Q--- (ii)

Equating (i) and (ii)

-100X = -250,000(A/P, 12%, 4) – 80,000 – 40X

-100X + 40X= -250,000(A/P, 12%. 4) – 80,000

-60X= -250,000(A/P, 12%. 4) – 80,000

OR, pw1 = 250,000(A/P, 12%,4) +80,000 + 60X

Hence, correct option is d.

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