Willie Lohmann travels from city to city for business. Every other year he buys a used car for about $15,000. The dealer allows about $8000 as a tradein allowance, so Willie spends $7000 every other year for a car. Willie keeps accurate records of his expences, which total 32.3 per mile. Willie's employer has two plans to reimburse car expenses: Actual expenses: Willie will recieve all his operating expenses, and $3500 each year for the car's decline in value. Standard mileage rate: Willie will recieve 56.5 per mile but no operating expenses and no depreciation allowance. If Willie travels 18,000 miles per year, which method gives him the larger reimbursement? At what annual mileage do the two methods give the same reimbursement?

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25-11-2020
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Willie Lohmann travels from city to city for business. Every other year he buys a used car for about $15,000. The dealer allows about $8000 as a tradein allowance, so Willie spends $7000 every other year for a car. Willie keeps accurate records of his expences, which total 32.3 per mile. Willie's employer has two plans to reimburse car expenses: Actual expenses: Willie will recieve all his operating expenses, and $3500 each year for the car's decline in value. Standard mileage rate: Willie will recieve 56.5 per mile but no operating expenses and no depreciation allowance. If Willie travels 18,000 miles per year, which method gives him the larger reimbursement? At what annual mileage do the two methods give the same reimbursement?

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PiaDeveau PiaDeveau · Answer 1 · 2020-12-03T16:50:05+01:00

Answer:

Plan B is better.

Computation:

Total travel = 180,00 miles

Plan A:

Actual Expenses

Total Reimbursement = $3,500 + [18,000 x 32.3]

Total Reimbursement = $3,500 + $5,814

Total Reimbursement = $9,314

Plan B:

Standard Mileage

Total Reimbursement = 18000 x 56.5

Total Reimbursement = $10,170

So,

Plan B is better.

Difference in fixed reimbursement = $3500 Plan A

Difference in mileage rate = 56.5 - 32.3

Difference in mileage rate = 24.2 cents per mile

Difference in mileage rate = $0.242 per mile

Difference in fixed reimbursement = $3500 Plan A

anthougo anthougo · Answer 2 · 2021-11-30T16:17:19+01:00

a. The method that gives Willie Lohmann the larger reimbursement is Plan A.

b. The annual mileage where the two methods give the same reimbursement to Willie is 144.63 miles.

Data and Calculations:

Cost of used car = $15,000

Trade-in Allowance 8,000

Amount spent yearly = $7,000

Total expenses per mile = $32.3

Amount reimbursed with Plan A = $32.3 m + $3,500

Amount reimbursed with Plan B = $56.5 m

where m = per mile

Distance traveled per year = 18,000

Reimbursement from Plan A = $584,900 ($32.3 x 18,000 + $3,500)

Reimbursement from Plan B = $1,017,000 ($56.5 x 18,000)

For Plan A to equal Plan B, $56.5 m = $32.3 m + $3,500

From the equation, $56.5 m - $32.3 m = $3,500

Therefore, $24.2 m = $3,500

m = 144.63 ($3,500/$24.2)

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