Question

Two investments involving a virtual mold apparatus for producing dental crowns qualify for different property classes. Investment A has a cost of $52,500, lasts 9 years with no salvage value, and costs $150,000 per year in operating expenses. It is in the 3-year property class. Investment B has a cost of $79,000.00, lasts 9 years with no salvage value, and costs $125,000 per year. Investment B, however, is in the 7-year property class. The company marginal tax rate is 25%, and MARR is an after-tax 10%.

a. Based upon the use of MACRS-GDS depreciation, compare the AW of each alternative.Which should be selected? (Investment A; Investment B)

b. What must be Investment B's cost of operating expenses for these two investments to be equivalent?

Answer 1

1. Step 1 of 6

   (a)

   Two alternative projects are given, and one is required to be selected.

   Comment

2. Step 2 of 6

   Alternative 1 : The cost of the project is $58,500. The life of the project is 9 years. It is given that MACRS-GDS 3-year property class is applicable here for depreciation. The rates are 33.33%, 44.45%, 14.81%, and 7.41%. E.g. the depreciation for year 1 is $19,498.05 (which is 33.33% of $58,500.) Write the after-tax cash flows in a spreadsheet, as shown in Screenshot 1.

   

   Taxable income is calculated by summing up values in columns B and D. Tax is calculated by multiplying taxable income by 0.40. After-tax cash flow is calculated by subtracting tax from before-tax cash flow.

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3. Step 3 of 6

   Now calculate AW. To do that, click on any empty cell and type: =PMT(0.1,9,-NPV(0.1,G3:G11)-G2). And press Enter.

   

   As shown in the screenshot above, the annual worth Annual Worth of Alternative A is .

   Comment

4. Step 4 of 6

   Alternative 2 : The cost of the project is $87,500. The life of the project is 9 years. It is given that MACRS-GDS 9-year property class is applicable here for depreciation. The rates are 14.29%, 24.49%, 17.49%, 12.49%, 8.93%, 8.92%, 8.93%, and 4.46%. E.g. the depreciation for year 1 is $12,503.75 (which is 14.29% of $87,500.) Write the after-tax cash flows in a spreadsheet, as shown in Screenshot 3.

   

   Taxable income is calculated by summing up values in columns B and D. Tax is calculated by multiplying taxable income by 0.40. After-tax cash flow is calculated by subtracting tax from before-tax cash flow.

   Comment

5. Step 5 of 6

   Now calculate AW. To do that, click on any empty cell and type: =PMT(0.1,9,-NPV(0.1,G3:G11)-G2). And press Enter.

   

   As shown in the screenshot above, the annual worth Annual Worth of Alternative B is .

   Since the annual worth of alternative B is higher than the annual worth of alternative A (i.e. ), Alternative B should be selected.

   Comment

6. Step 6 of 6

   (b)

   Currently, Alternative B’s operating expenses are $125,000. The level of operating expenses that make the two alternatives equivalent is required to be calculated.

   To do this, “What if analysis” is required.

   Go to the spreadsheet as shown in screenshot 4. Now type “=B3” (without quotes) in cell B4 and press Enter. Do the same for cells B5, B6, B7, B8, B9, B10, and B11. That is, type “=B3” (without quotes) in each of these cells and press Enter. Doing this will help us in our “What if analysis,” although no change will be observed in the spreadsheet values as of now.

   Now press on “Data” tab and then press on “What if analysis” tab and select “Goal Seek.” A small goal seek window will come up. Fill up the required fields as follows:

   

   Press OK. The value in cell B3 has changed to as shown in Screenshot 5, and the annual worth of alternative B is now the same as that of alternative A.

   

   Hence, the two alternatives will be equivalent in value if the operating expenses of Alternative B were .