Give step-by-step solution with explanation and final answer:
Your company has just signed a three-year nonrenewable contract with the city of New Orleans for earthmoving work. You are investigating

Question

Give step-by-step solution with explanation and final answer:
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

​$209,000

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

​$78,000.

If the projected operating expense for the equipment is

​$62,000

per​ year, what is the​ after-tax equivalent uniform annual cost​ (EUAC) of owning and operating this​ equipment? The effective income tax rate is

28​%,

and the​ after-tax MARR is

11​%

per year.GDS Recovery Rates (ry)
Year 5-year Property Class
1 0.2000
2 0.3200
3 0.1920
4 0.1152
5 0.1152
6 0.0576

Discrete Compounding; i=11%
Single Payment Uniform Series
Compound Compound Sinking Capital
Amount Present Amount Present Fund Recovery
Factor Worth Factor Factor Worth Factor Factor Factor
To Find F To Find P To Find F To Find P To Find A To Find A
Given P Given F Given A Given A Given F Given P
N FIP PIF FIA PIA AIF AlP
1 1.1100 0.9009 1.0000 0.90

VIPSolutions · Accepted Answer

To calculate the after-tax equivalent uniform annual cost (EUAC) of owning and operating the equipment, follow these steps:

### Step 1: Calculate Annual Depreciation

Using the MACRS rates for a 5-year property class:

- Year 1: $ 209,000 \times .200 = 41,800 $
- Year 2: $ 209,000 \times .320 = 66,880 $
- Year 3: $ 209,000 \times .192 = 40,128 $

### Step 2: Calculate Tax Savings from Depreciation

Tax savings = Depreciation $\times$ Tax rate

- Year 1: $ 41,800 \times .28 = 11,704 $
- Year 2: $ 66,880 \times .28 = 18,726.40 $
- Year 3: $ 40,128 \times .28 = 11,236.84 $

### Step 3: Calculate After-Tax Operating Expenses

Operating expense per year = $ 62,000 $

After-tax operating expense = Operating expense $\times$ (1 - Tax rate)

- After-tax operating expense = $ 62,000 \times .72 = 44,640 $

### Step 4: Calculate After-Tax Salvage Value

Salvage value = $ 78,000 $

Tax on salvage value = (Salvage value - Book value at end of Year 3) $\times$ Tax rate

- Book value at end of Year 3 = Initial cost - Total depreciation
  - Total depreciation = $ 41,800 + 66,880 + 40,128 = 148,808 $
  - Book value = $ 209,000 - 148,808 = 60,192 $

Tax on salvage value = $ (78,000 - 60,192) \times .28 = 4,986.24 $

After-tax salvage value = Salvage value - Tax on salvage value
- After-tax salvage value = $ 78,000 - 4,986.24 = 73,013.76 $

### Step 5: Calculate Present Worth of Costs

Sum present worth of all costs using the factors from the table:

1. **Initial Cost:**

Present Worth = $ 209,000 $

2. **Operating Expenses (Years 1-3):**

Present Worth = After-tax operating expense $\times$ P/A factor

$ 44,640 \times 2.4437 = 109,086.77 $

3. **Tax Savings from Depreciation (Years 1-3):**

Present Worth of Tax Savings = 
   $$
   11,704 \times .9009 + 18,726.40 \times .8116 + 11,236.84 \times .7312 = 35,109.77
   $$

4. **After-Tax Salvage Value (End of Year 3):**

Present Worth = After-tax salvage value $\times$ P/F factor

$ 73,013.76 \times .7312 = 53,402.06 $

Total Present Worth of Costs:

$$ 
209,000 + 109,086.77 - 35,109.77 - 53,402.06 = 229,574.94 
$$

### Step 6: Calculate EUAC

Use the Capital Recovery Factor (A/P) for 3 years at 11%:

EUAC = Total Present Worth $\times$ A/P factor

$$ 
229,574.94 \times .4092 = 93,935.63 
$$

### Final Answer

The after-tax equivalent uniform annual cost (EUAC) of owning and operating the equipment is approximately **$93,935.63** per year.

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