Question

The expected annual maintenance expense for a new piece of equipment is $10,000.

This is Alternative A. Alternatively, it is possible to perform the maintenance every fifth

year at a cost of $50,000 (Alternative B). In either case, maintenance will be performed in

the fifth year so that the equipment can be sold for $100,000 at that time. If the MARR is

15% per year (before income taxes), which alternative should be recommended in each of

these situations?

a) Before income taxes are considered.

b) After income taxes are considered when t = 25%.

c) Is there a different selection before and after income taxes are considered?

Answer 1

(a)
In either case, Equipment can be sold at $100,000. So it is irrelevant for selection.
MARR (before tax) =				15%
We shall determine present value of maintenance cost in each alternative.
Alternative A
Annual Maintenance cost				10000
Cumulative P.V.F. @15% for 5 Years				3.352155
(1-(1/(1.15)^5))/0.15
Present value of Annual maintenance cost					$ 33,521.55
Alternative B
Maintenance in 5th Year				50000
Regular Maintenance provided				10000
Total				60000
P.V.F. @15% for 5th Year				0.497177
(1/(1.15)^5)					29830.6041
Cost is less in Alternative B. So Alternative B should be choosen in case of Before income tax.
(b)
MARR before tax				15%
Tax rate				25%
MARR After tax = 0.15 * (1-0.25) =				0.1125	or 11.25%
Alternative A
Annual Maintenance cost				10000
Cumulative P.V.F. @11.25% for 5 Years				3.672771
(1-(1/(1.1125)^5))/0.1125
Present value of Annual maintenance cost					$ 36,727.71
Alternative B
Maintenance in 5th Year				50000
Regular Maintenance provided				10000
Total				60000
P.V.F. @11.25% for 5th Year				0.586813
(1/(1.1125)^5)					35208.7942
Cost is less in Alternative B. So Alternative B should be chosen in case of After income tax.
c)
In both cases cost is less in Alternative B. So there is no difference selection before and after taxes.