Cathy has one year left before she completes her degree in industrial engineerin

ID: 1204806 • Letter: C

Question

Cathy has one year left before she completes her degree in industrial engineering. She is spending this summer working for her family's firm, MMM (Molehill & Mountain Movers). MMM runs a fleet of heavy construction equipment and sells gravel for roadwork from its pit. They are opening a new section of the pit, and they must choose between conveyor and front-end loader systems for loading the trucks. In the past they have used front-end loaders. The firm's CPA has asked Cathy to analyze the after-tax cost of the two choices. Her task is complicated by uncertainty over the depreciation portion of the tax code. It is up for revision once again (the prolonged business boom has raised the pressure for increasing business taxes). Thus the system may be depreciated under (a) straight line, (b) sum-of-the-year's digits (SOYD), (c) double declining balance, or (d) modified accelerated cost-recovery system (MACRS). The current tax system does not have a special rate for capital gains, but it may be reinstituted at a rate of 66.67%. The other complicating factor is the effect of inflation, which the CPA said can be assumed to affect all numbers equallyexcept for tax calculations based on book values. At least the CPA simplified the task by defining the after-tax rate of return as 6%, and the tax rate as 40%. The CPA asked for a recommended decision based on Table 26-1. Table 26-1 Cost Summary for Conveyor and Front-End Loader Front End Conveyor Loader First cost $250,000 $110,000 Salvage value $80,000 $30,000 Life 15 years 15 years Operation cost $32,000 $45,000

Explanation / Answer

Tax advantage because of depreciation=D*T

Total cost= Initial cost + P.V of (Operation cost -T*Dep)-P.V of salvage value

Conveyer

Front end loader

Initial cost

250000

110000

Salvage value

80000

30000

Operation cost

32000

45000

Life

Discount rate

Tax

40%

For straight line Dep

Depreciation of conveyer=(250000-80000)/15=11333.33

Total cost of Conveyer=250000+(32000-11333.33*0.4)*Annuity factor(15 years@6%)-80000/(1.15^15)

Total cost of Conveyer=250000+(32000-11333.33*0.4)*9.712-80000/(1.15^15)=$506,924.7

Depreciation of Front end loader=(110000-45000)/15=4333.33

Total cost of Front end loader =110000+(45000-4333.33*0.4)*Annuity factor(15 years@6%)-45000/(1.15^15)

Total cost of Front end loader =110000+(45000-4333.33*0.4)*9.712 -45000/(1.15^15)=$524,675.6

Thus for straight line depreciation Conveyer is cheaper than front end load as Total cost of conveyer is less. Thus Cathy should recommend Conveyer over front end load

For sum-of-the-year's digits (SOYD) Depreciation

Total cost of Conveyer=250000+260852-80000/(1.15^15)= 501020.4412

Total cost of Front end loader =110000+417956-(45000/(1.15^15)=522425.7482

Conveyer is cheaper than front end load as Total cost of conveyer is less. Thus Cathy should recommend Conveyer over front end load

For Double Declining Balance method

Depreciation %=(2/15)*(1-cummulative depreciation )

Total cost of Conveyer=250000+266182-80000/(1.15^15)= 506350.4412

Total cost of Front end loader =110000+419994-(45000/(1.15^15)= 524463.7482