Answer :
Jim should purchase tractor A as its EAC is lower than that of tractor B. However, if the price of the Gold Warranty Plan is lower than $11,686 or the price of the Platinum Warranty Plan is lower than $9,928, it would be more advantageous for Jim to purchase Tractor B instead.
(a) To calculate the equivalent annual costs (EACs) of the tractors, we need to consider the purchase price, annual maintenance costs, estimated lifespan, and the cost of capital. The EAC formula is given by:
EAC = (Purchase Price - Salvage Value) / Annuity Factor + Annual Maintenance Cost
Where:
Annuity Factor = (1 - (1 + r)^(-n)) / r
r is the cost of capital (8% per annum) and n is the estimated lifespan of the tractor.
For tractor A:
Purchase Price = $50,000
Annual Maintenance Cost = $4,400
Estimated Lifespan = 12 years
Using the formula, the Annuity Factor for tractor A is calculated as follows:
Annuity Factor = (1 - (1 + 0.08)^(-12)) / 0.08 ≈ 7.536
EAC for tractor A:
EAC = ($50,000 - 0) / 7.536 + $4,400 ≈ $11,219
For tractor B:
Purchase Price = $31,000
Annual Maintenance Cost = $5,500
Estimated Lifespan = 6 years
Using the formula, the Annuity Factor for tractor B is calculated as follows:
Annuity Factor = (1 - (1 + 0.08)^(-6)) / 0.08 ≈ 4.623
EAC for tractor B:
EAC = ($31,000 - 0) / 4.623 + $5,500 ≈ $12,375
Comparing the EACs, we can see that the EAC for tractor A is lower than the EAC for tractor B. Therefore, based on the EAC criterion, Jim should purchase tractor A.
(b) To determine the price for each Warranty Plan below which it is better for Jim to purchase tractor B, we need to calculate the EACs with extended lifespans for tractor B.
For the Gold Warranty Plan with a protection period of 8 years:
Annuity Factor = (1 - (1 + 0.08)^(-8)) / 0.08 ≈ 5.747
EAC for tractor B with Gold Warranty:
EAC = ($31,000 - 0) / 5.747 + $5,500 ≈ $11,686
For the Platinum Warranty Plan with a protection period of 10 years:
Annuity Factor = (1 - (1 + 0.08)^(-10)) / 0.08 ≈ 7.536
EAC for tractor B with Platinum Warranty:
EAC = ($31,000 - 0) / 7.536 + $5,500 ≈ $9,928
Now we compare the EACs of the Warranty Plans with the EAC of tractor A ($11,219). If the price of the Gold Warranty Plan is lower than $11,686 or the price of the Platinum Warranty Plan is lower than $9,928, it will be better for Jim to purchase Tractor B instead.
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