Question

5.(20 pts) A special power tool for plastic products is classified $6,500, has a salvage value of $800 when sold at the end of 5 years, uniform annual end-of-ycar benefits (before tax) of $3,500 per year, and uniform annual operating and maintenance costs (before tax) of $1,200 per year. Compute the after-tax present worth (for an MARR of 10% ) , based on MACRS depreciation and a 34% corporate income tax rate. (MACRS percentages for a three-year property are 33.33%, 44.45 % , 14.81 %, and 7.41%, for years 1, 2, 3, and 4, respectivcly). as a MACRS 3-year property. It costs .34

Answer 1

Calculating depreciation

Initial cost = $6500

Depreciation for a year under MACRS = Rate of depreciation for a year x initial cost

For year 1, Rate of depreciation = 33.33% , Depreciation = 33.33% x 6500 =2166.45

Similarly we can find the depreciation for other years, we get the following values

Depreciation under 3 year MACRS class
Year	1	2	3	4
Depreciation rate	33.33%	44.45%	14.81%	7.41%
Depreciation	2166.45	2889.25	962.65	481.65

For year 5 depreciation = 0

Calculating after tax operating cash flow

After tax operating cash flow = EBIT(1-tax rate) + depreciation

After tax operating cash flow = (Annual operating benefits - Annual operating costs - depreciation)(1-tax rate) + depreciation

For year1, After tax operating cash flow = (3500 - 1200 - 2166.45)(1-34%) + 2166.45 = 133.55 x 66% + 2166.45 = 88.1430 + 2166.45 = 2254.5930

Similarly after tax operating cash flows can be calculated for other years, we get the following values

Calculating After tax Operating Cash flow
Year	1	2	3	4	5
Annual operating benefits	3500	3500	3500	3500	3500
Annual operating costs	1200	1200	1200	1200	1200
Depreciation	2166.4500	2889.2500	962.6500	481.6500	0.0000
EBIT	133.5500	-589.2500	1337.3500	1818.3500	2300.0000
EBIT(1-tax rate)	88.1430	-388.9050	882.6510	1200.1110	1518.0000
Plus: Depreciation	2166.4500	2889.2500	962.6500	481.6500	0.0000
After tax operating Cash Flow	2254.5930	2500.3450	1845.3010	1681.7610	1518.0000

Calculating after tax terminal cash flow

Book value at end of 5 years = Initial cost - (Sum of depreciation for 5 years) = 6500 - (2166.45 +2889.45 + 962.65 + 481.65 + 0) = 6500 - 6500 = 0

After tax Terminal cash flow at end of year 5 = Salvage value at end of 5 years - tax from sale of equipment at end of 5 years

After tax Terminal cash flow at end of year 5 = Salvage value at end of 5 years - tax rate (Salvage value at end of 5 years - Book valueat end of 5 years)

After tax Terminal cash flow at end of year 5 = 800 - 34%(800 - 0) = 800 - 272 = 528

Calculating present worth at MARR = 10%

After tax Present Worth = - Inital cost + Sum of present values of after tax operating cash flows discounted at MARR of 10% + Present value of After tax Terminal cash flow at MARR of 10%

After tax Present worth = -6500 + 2254.5930 / (1 + 10%) + 2500.3450 / (1 + 10%)² + 1845.3010 / (1 + 10%)³ + 1681.7610 / (1 + 10%)⁴ + 1518 / (1 + 10%)⁵ + 528 / (1 + 10%)⁵

After tax Present worth = -6500 + 2049.6300 + 2066.4008 + 1386.4019 + 1148.6653 + 942.5585 + + 327.8464 = 1421.5029 = 1421.50 (rounded to two decimal places)

Hence after tax present worth = $1421.50