Jim is considering buying one of the following tractors for use in his farm: Tractor Estimated lifespan (years) Purchase price Annual maintenance cost A B 12 6 $50,000 $31,000 $4,400 $5,500 Maintenance costs are assumed to be paid at the end of each year within the tractor's estimated lifespan. The cost of capital is 8% per annum. (a) Calculate the equivalent annual costs (EACs) of the two tractors, and show that Jim should purchase tractor A based on this criterion.

(b) It is known that buyers of tractor B can optionally purchase one of the following protection plans (at the time of tractor purchase): • Gold Warranty Plan: Provides protection of the tractor for at most 8 years from the date of purchase. • Platinum Warranty Plan: Provides protection of the tractor for at most 10 years from the date of purchase. Should a Warranty Plan be purchased, it is assumed that the estimated lifespan of tractor B will lengthen to the respective protection period, and maintenance costs will be payable until the end of the protection period. Based on the EAC criterion, calculate the price for each of the two Warranty Plans, below which it will be better for Jim to purchase tractor B instead.

Question

03-04-2024
Business

High School

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Jim is considering buying one of the following tractors for use in his farm: Tractor Estimated lifespan (years) Purchase price Annual maintenance cost A B 12 6 $50,000 $31,000 $4,400 $5,500 Maintenance costs are assumed to be paid at the end of each year within the tractor's estimated lifespan. The cost of capital is 8% per annum. (a) Calculate the equivalent annual costs (EACs) of the two tractors, and show that Jim should purchase tractor A based on this criterion.

(b) It is known that buyers of tractor B can optionally purchase one of the following protection plans (at the time of tractor purchase): • Gold Warranty Plan: Provides protection of the tractor for at most 8 years from the date of purchase. • Platinum Warranty Plan: Provides protection of the tractor for at most 10 years from the date of purchase. Should a Warranty Plan be purchased, it is assumed that the estimated lifespan of tractor B will lengthen to the respective protection period, and maintenance costs will be payable until the end of the protection period. Based on the EAC criterion, calculate the price for each of the two Warranty Plans, below which it will be better for Jim to purchase tractor B instead.

Answer :

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jaychudasama1311 jaychudasama1311 · Answer 1 · 2024-10-02T10:05:16-04:00

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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