Question

Use X = 66

Q4. For this question, X is the first two digits (from the right) of your student ID. Two machines are under consideration for a new production line. Machine A costs $50,000 and is expected to have a salvage value of $6,500 at the end of its 5 years useful life. It will have a fixed cost of $16,000 per year and a variable cost of $55 per unit. On the other hand, machine B costs $55,000 and is expected to have a salvage value of $7,000 at the end of its 7 years useful life. It will have a fixed cost of $14,500 per year and a variable cost of $(X+56) per unit. Determine the quantity that must be produced and sold every year for the two machines to break even at an interest rate of 3%. List any assumptions needed to solve the problem.

Answer 1

Machine A:

Initial cost = 50,000

salvage value = 6,500

useful life = 5 years

Fixed cost = 16,000

Variable cost = 55 per unit

Machine B:

Initial cost = 55,000

Salvage value = 7,000

useful life = 7 years,

Fixed cost = 14,500

Variable cost = X + 56 = 66 + 56 = 122 per unit

Interest rate = 3%

So, for break even point, the equivalent uniform annual worth of expenditure has to be equal to the uniform annual worth of revenue. Let Q_A be the number of units that need to be sold and produced each year for machine A and Q_B be the same for machine B. We also need to assume that the selling price of each of the unit of output = 200. So, that the annual revenue brought in by machine A and machine B are 200Q_A and 200Q_B respectively.

Machine A:

AW of cost = 50,000(A/P, 3%,5) + 16,000 + 55Q_A

= 50,000 * 0.2184 + 16,000 + 55Q_A

AW of cost= 26,920 + 55Q_A

AW of revenue = 6,500(A/F, 3%,5)

= 6500 * 0.1884 = 1224.6 + 200Q_A

So, AW of cost = AW of revenue,

26,920 + 55Q_A = 1224.6 + 200Q_A

26,920 - 1224.6 = 200Q_A - 55 Q_A

25,695.4 = 145Q_A

Q_A = 177

This is the quantity that needs to be produced and sold each year for machine A to breakeven.

Machine B:

AW of cost = 55,000(A/P,3%,7) + 14,500 + 122Q_B

= 55,000* 0.1605 + 14,500 + 122Q_B

= 23,327.5 + 122 Q_B

AW of revenue = 7,000(A/F,3%,7) + 200Q_B

= 7000 *0.1305 + 200Q_B

= 913.5 + 200Q_B

So, AW of cost = AW of revenue

23,327.5 + 122 Q_B = 913.5 + 200Q_B

23,327.5-913.5 = 200Q_B - 122Q_B

22,414 = 78Q_B

Q_B = 287

This is the quantity that needs to be produced and sold for machine B to break even.

So, we see for the same selling price = 200, the machine B needs to produce a much higher output = 287 >177 as compared to the amount of output that machine A needs to produce to break even. This is mainly because the variable cost of machine B is much higher than machine A, so a greater quantty is needed to recover that.