Question

Please provide the answers in clear way

A company is planning to install a new automated plastic-molding press. Four different presses are available. The initial capital investments and annual expenses for these four different alternatives are:

	Press
	P1	P2	P3	P4
Capital Investment	$24,000	$30,400	$49,600	$52,000
Annual expenses	$31,200	$29,100	$25,200	$22,900
Press life (years)	5	5	5	5

Assume each press has the same output capacity of 150,000 units per year, has no salvage value at the end of its useful life, and the minimum attractive rate of return is 10%. The selling price for each plastic molded unit is $0.425 per unit.

a) Which press should you purchase if 150,000 nondefective units per year are produced by each press and all units can be sold?

b) Which press should you purchase is each press still produces 150,000 units per year, but the estimated unit reject rate is 7.4% for P1, 1.3% for P2, 2.6% for P3, and 4.6% for P4, where all nondefective units are sold but the defective units have no market value?

Answer 1

Both cases can be solved by maximizing the profit.

Profit = Total units sold - Total costs incurred in operating the press

a) Let us say T = C + L*A.

where C = Capital investment, L = Life of a press, A = Annual Expense and T = Total cost incurred over the entire life of a press.

In this case we will try to buy a press which gives minimum T value because selling capacity and unit costs are same for all presses.

For P1, T = 24,000 + 5*31,200 = $180,000

For P2, T = 30,400 + 5*29,100= $175,900

For P3, T = 49,600 + 5*25,200 = $175,600

For P4, T = 52,000 + 5*22,900 = $166,500

T value for P4 is the least, therefore P4 should be chosen in this case.

b) Here,total units sold becomes a decision factor due to different rejection rates.

S = L*P*U*A.

S = Total value of units sold over the entire life of a press

P = Price per unit

U = Units produced per year

A = Acceptance percent = 1 - Rejection precent

Profit = S - T.

For P1, Profit = 5*0.425*150,000*(1-0.074) - 180,000 = $ 115,162.5

For P2, Profit = 5*0.425*150,000*(1-0.013) - 175,900 = $ 138,706.25

For P3, Profit = 5*0.425*150,000*(1-0.026) - 175,600 = $ 134,862.5

For P4, Profit = 5*0.425*150,000*(1-0.046) - 166,500 = $ 137,587.5

Here, we see that P2 gives the maximum profit under similar conditions. Therefore P2 should be chosen in this case.