Question

Your company has just signed a​ three-year nonrenewable contract with the city of New Orleans for earthmoving work. You are investigating the purchase of heavy construction equipment for this job. The equipment costs ​$196,000 and qualifies for​ five-year MACRS depreciation. At the end of the​ three-year contract, you expect to be able to sell the equipment for ​$77,000. If the projected operating expense for the equipment is ​$61,000 per​ year, what is the​ after-tax equivalent uniform annual cost​ (EUAC) of owning and operating this​ equipment? The effective income tax rate is 25​%, and the​ after-tax MARR is 10​% per year.

GDS Recovery Rates (r) Year 5-year Property Class 0.2000 0.3200 0.1920 0.1152 0.1152 0.0576 O UNAWN

Answer 1

Solution :-

Initial cost of $1946,000

Annual cost of $61,000

We deducted the tax rate, since we will have a tax deduction for incurring annual expenses, so, on net basis , our net cost would be = annual cost x (1-tax rate)

So, our annual after tax cost would be = $61,000 x (1- 0.25)

                                                = 61000 x 0.75

                                                = $45750

Along with this, we will also be receiving the benefit of depreciation tax shield, i.e. tax benefit upon depreciation, which is calculated as below -

Depreciation for 1st year = 0.20 x 196000 = $39200

Depreciation for 2nd year = 0.32 x 196000 = $62720

Depreciation for 3rd year = 0.192 x 196000 = $37632

SO,

Depreciation tax shield are as under-

Depreciation tax shield for 1st year = 0.25 x 39200 = $9800

Depreciation tax shield for 2nd year = 0.25 x 62720 = $15680

Depreciation tax shield for 3rd year = 0.25 x 37632 = $9408

So, our net annual cash expenses = Annual Exps after tax Saving - Depreciation tax shield

Hence, for 1st year = 45750 - 9800 = $35950

            for 2nd year = 45750 - 15680 = $30070

            for 3rd year = 45750 - 9408 = $36342

The Book value of machinery after 3 years would be -

=Cost of equipment - [(GDS recovery rate for total of 3years) x cost of equipment]

=196000 - (0.2 + 0.32 + 0.192)x196000

=196000 - 139552

= $56448

But the equipment is expected to sell after 3 years at $77,000

Hence, capital gain = 77000 - 56448

                                    = $20552

There net inflow after 3 years on selling of the equipment -

= Selling price - (tax rate x capital gain)

= 77000 - 0.25 x 20552

= 77000 - 5138

= $71862

Computation of EUAC-

EUAC = PV of all the expenses and income / PVAF(10% , 3)

where,

PVAF(10% , 3) = annuity factor of 10% for 3 years

Therefore, PV of all the expenses

= 196000 + 35950 / (1.10)¹ + 30070 / (1.10)² + 36342 / (1.10)³ - 71862 / (1.10)³

= $226846.4

PVAF(10%,3) = 2.487

Therefore,

EUAC = $226846.4 / 2.487

            = $91218.28

If there is any doubt please ask in comments

Hence, our Equivalent uniform annual cost = $85,512.53