Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,054,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $200,000 per year. Machine B costs $5,238,000 and will last for nine years. Variable costs for this machine are 30 percent and fixed costs are $135,000 per year. The sales for each machine will be $10.2 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. The company plans to replace the machine when it wears out on a perpetual basis.

Calculate the NPV for each machine. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

	NPV
Machine A	$
Machine B	$

Calculate the EAC for each machine. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

	EAC
Machine A	$
Machine B	$

Which machine should you choose?

Machine B Machine A

Answer 1

1.Calculation of Net present value (NPV) for both the machines :

Machine A  

Initial cash outflow = cost of the machine = 3,054,000

Life of the machine = 6 years

Depreciation on SLM basis = 3054000/6 = 509,000

Since depreciation is tax deductible expense, tax saving on depreciation = 509000*35% = 178,150

Cash inflows for each of the 6 years = [Sales*(1-variable cost ratio)-Fixed cost]*(1-Tax rate) + Tax saving on depreciation

= [10,200,000*(1-0.35)-200,000]*(1-0.35) + 178,150

= [10,200,000*65%-200,000]*65% + 178,150

= 4,357,650

NPV = Annual cash inflows * Present value annuity factor for 6 years @ 10% - Initial cash outflow

= 4,357,650 * 4.3553 - 3,054,000

= 15,924,873.05

Machine B

Initial cash outflow = cost of the machine = 5,238,000

Life of the machine = 9 years

Depreciation on SLM basis = 5,238,000/9 = 582,000

Since depreciation is tax deductible expense, tax saving on depreciation = 582000*35% = 203,700

Cash inflows for each of the 9 years = [Sales*(1-variable cost ratio)-Fixed cost]*(1-Tax rate) + Tax saving on depreciation

= [10,200,000*(1-0.30)-150,000]*(1-0.35) + 203,700

= [10,200,000*70%-150,000]*65% + 203,700

= 4,747,200

NPV = Annual cash inflows * Present value annuity factor for 9 years @ 10% - Initial cash outflow

= 4,747,200* 5.759 - 5,238,000

= 22,101,124.8

2.Calculation of Effective annual cost

Effective Annual cost for Machine = where n = period and r = required rate of return

Machine A = NPV/PVAF(6,10%) = 15924873.05/4.3553 = 3,656,435.39

Machine B = NPV/PVAF(9,10%) = 22101124.8/5.7590 = 3,837,667.09

3.Decision

When we have to choose between machines with unequal lives, EAC is the best tool to finally decide. Higher EAC indicates a better investment. Hence , Machine B is recommended.