Studdy AI Logo
Math

QuestionCalculate yearly depreciation for a van purchased for \$55,000 with a residual value of \$5,000 over 4 years using: a. straight-line, b. units-of-production, c. double-declining-balance methods.

Studdy Solution

STEP 1

Assumptions1. The cost of the van is 55,000.Theresidualvalueofthevanis55,000. The residual value of the van is 5,0003. The van is expected to be in service for4 years or100,000 miles4. The van traveled30,000 miles in the first year,25,000 miles in the second year, and22,500 miles in the third and fourth years

STEP 2

First, we need to calculate the depreciable base of the van. This is the cost of the van minus its residual value.
Depreciable Base=Cost of the van−Residual valueDepreciable\, Base = Cost\, of\, the\, van - Residual\, value

STEP 3

Now, plug in the given values for the cost of the van and its residual value to calculate the depreciable base.
Depreciable Base=$55,000−$5,000Depreciable\, Base = \$55,000 - \$5,000

STEP 4

Calculate the depreciable base of the van.
Depreciable Base=$55,000−$,000=$50,000Depreciable\, Base = \$55,000 - \$,000 = \$50,000

STEP 5

a. Straight-line methodThe annual depreciation expense using the straight-line method is the depreciable base divided by the useful life of the van.
Annual Depreciation Expense=Depreciable Base/Useful LifeAnnual\, Depreciation\, Expense = Depreciable\, Base / Useful\, Life

STEP 6

Plug in the values for the depreciable base and the useful life to calculate the annual depreciation expense.
Annual Depreciation Expense=$50,000/4 yearsAnnual\, Depreciation\, Expense = \$50,000 /4\, years

STEP 7

Calculate the annual depreciation expense using the straight-line method.
Annual Depreciation Expense=$50,000/4=$12,500 per yearAnnual\, Depreciation\, Expense = \$50,000 /4 = \$12,500\, per\, year

STEP 8

b. Units-of-production methodThe depreciation expense using the units-of-production method is calculated by dividing the depreciable base by the total expected units (miles in this case), and then multiplying by the actual units used each year.
Depreciation Expense=(Depreciable Base/Total Expected Units)timesActual UnitsDepreciation\, Expense = (Depreciable\, Base / Total\, Expected\, Units) \\times Actual\, Units

STEP 9

Plug in the values for the depreciable base, total expected units, and actual units for each year to calculate the depreciation expense.
For the first yearDepreciation Expense=($50,000/100,000 miles)times30,000 milesDepreciation\, Expense = (\$50,000 /100,000\, miles) \\times30,000\, milesFor the second yearDepreciation Expense=($50,000/100,000 miles)times25,000 milesDepreciation\, Expense = (\$50,000 /100,000\, miles) \\times25,000\, milesFor the third and fourth yearsDepreciation Expense=($50,000/100,000 miles)times22,500 milesDepreciation\, Expense = (\$50,000 /100,000\, miles) \\times22,500\, miles

STEP 10

Calculate the depreciation expense for each year using the units-of-production method.
For the first yearDepreciation Expense=$15,000Depreciation\, Expense = \$15,000For the second yearDepreciation Expense=$12,500Depreciation\, Expense = \$12,500For the third and fourth yearsDepreciation Expense=$,250Depreciation\, Expense = \$,250

STEP 11

c. Double-declining-balance methodThe depreciation expense using the double-declining-balance method is calculated by multiplying the book value at the beginning of each year by twice the straight-line rate. The straight-line rate is divided by the useful life.
Depreciation Expense=Book ValuetimestimesStraight Line RateDepreciation\, Expense = Book\, Value \\times \\times Straight\, Line\, RateThe book value at the beginning of each year is the cost of the van minus the accumulated depreciation.

STEP 12

Calculate the straight-line rate.
Straight Line Rate=/4=0.25Straight\, Line\, Rate = /4 =0.25

STEP 13

Calculate the depreciation expense for each year using the double-declining-balance method.
For the first yearDepreciation Expense=$55,000times2times0.25=$27,500Depreciation\, Expense = \$55,000 \\times2 \\times0.25 = \$27,500For the second yearDepreciation Expense=($55,000−$27,500)times2times0.25=$13,750Depreciation\, Expense = (\$55,000 - \$27,500) \\times2 \\times0.25 = \$13,750For the third yearDepreciation Expense=($55,000−$27,500−$13,750)times2times0.25=$6,875Depreciation\, Expense = (\$55,000 - \$27,500 - \$13,750) \\times2 \\times0.25 = \$6,875For the fourth yearDepreciation Expense=($55,000−$27,500−$13,750−$6,875)times2times0.25=$3,437.50Depreciation\, Expense = (\$55,000 - \$27,500 - \$13,750 - \$6,875) \\times2 \\times0.25 = \$3,437.50However, the depreciation expense for the fourth year should not reduce the book value below the residual value. So, the depreciation expense for the fourth year should be adjusted to \$3,437.50 - (\$3,437.50 + \$27,500 + \$13,750 + \$6,875 - \$5,000) = \$2,562.50.
The depreciation schedule is as follows| Year | Straight-Line | Units-of-Production | Double-Declining-Balance | |------|---------------|---------------------|--------------------------| | | \$12,500 | \$15,000 | \$27,500 | |2 | \$12,500 | \$12,500 | \$13,750 | |3 | \$12,500 | \$11,250 | \$6,875 | | | \$12,500 | \$11,250 | \$2,562.50 |

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord