Question

Zoysia University must purchase mowers for its landscape department. The university can buy six EVF mowers that cost $7,900 each and have annual, year-end maintenance costs of $1,775 per mower. The EVF mowers will be replaced at the end of Year 4 and have no value at that time. Alternatively, Zoysia can buy seven AEH mowers to accomplish the same work. The AEH mowers will be replaced after seven years. They each cost $6,900 and have annual, year-end maintenance costs of $2,225 per mower. Each AEH mower will have a resale value of $700 at the end of seven years. The university’s opportunity cost of funds for this type of investment is 7 percent. Because the university is a nonprofit institution, it does not pay taxes. It is anticipated that whichever manufacturer is chosen now will be the supplier of future mowers. What is the EAC of each type of mower?

Answer 1

for EAC for each mower we need to calculate first the present value of the costs for each of he mower.

amc = annual maintenance cost

r is the rate of interest

n is the no of years

Present value for the 7 year mower =initial cost + amc * [ 1 - 1/(1 + r)^n] /r - Salvage value / ( 1 + r)^n

Present value for the 7 year mower = 6900 + 2225 [ 1 - 1/1.07^7] / 0.07 - 700 / 1.07^7

= 6900 + 11991.40 - 435.92

= 18,455.48

Total present value of 7 mowers = 18455.48 * 7 =129,188.36

EAC can be calculated as below

129188.36 = EAC * [ 1 - 1/1.07^7] /0.07

129188.36 = EAC * 5.3892894   

EAC = $23,971.31

Present value for the 4 year mower =initial cost + amc * [ 1 - 1/(1 + r)^n] /r

Present value for the 4 year mower = 7900 + 1775 [ 1 - 1/1.07^4] / 0.07

= 7900 + 6012.30 = 13912.3

Total present value of 6 mowers = 13912.3 * 4 = 83473.8

EAC can be calculated as below

83473.8 = EAC * [ 1 - 1/1.07^4] /0.07

83473.8 = EAC * 3.387211257

EAC = $24,643.81