Question

X=08

Q4. [20 marks] 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

Let n units are required for breakeven, then

EUAC of first machine = 50000*(A/P,3%,5) + 16000 + 55*n - 6500*(A/F,3%,5)

= 50000*0.218355 + 16000 + 55*n - 6500*0.188355

= 25693.44 + 55*n

EUAC of second machine = 55000*(A/P,3%,7) + 14500 + (08+56)*n - 7000*(A/F,3%,7)

= 55000*0.160506 + 14500 + (08+56)*n - 7000*0.130506

= 22414.29 + 64*n

for breakeven

25693.44 + 55*n = 22414.29 + 64*n

n = (25693.44 - 22414.29) / (64 - 55) = 364.35 ~ 365 (rounding up for breakeven)

Assumption:

Both alternatives will be available infinitely at same cost and same annual costs