AAA Pest Control uses the following: before-tax MARR = 14% per year, after-tax MARR = 7% per year, and Te = 50%. Two new spray machine options have the following estimates and will generate the same GI each year.

Question

Select A or B under the following conditions using the method described or as instructed:



(a) Before-tax PW analysis using spreadsheet functions.

(b) After-tax PW analysis using classical SL depreciation over the 10-year life using hand solution.

(c) After-tax PW analysis using MACRS depreciation with a 5-year recovery period using a spreadsheet. Assume the machines will be retained for 10 years, then sold at the estimated salvage values.

Answer 1

(a) Function for PWA: = -PV(14%,10,-3000,3000) – 15000 displays PWA = $-29,839



Function for PWB: = -PV(14%,10,-1500,5000) – 22000 displays PWA = $-28,475



Select B with a slightly higher PW value.

(b) All AOC estimates generate tax savings; GI estimates are equal.



Machine A

Annual depreciation = (15,000 - 3,000)/10 = $1200

Tax savings = (AOC + D)(0.5) = 4200(0.5) = $2100

CFAT = -3000 + 2100 = $-900



PWA = -15,000 - 900(P/A,7%,10) + 3000(P/F,7%,10)

= -15,000 - 900(7.0236) + 3000(0.5083)

= $-19,796



Machine B

Annual depreciation = (22,000 – 5000)/10 = $1700

Tax savings = (1500 + 1700)(0.50) = $1600

CFAT = –1500 + 1600 = $100



PWB = –22,000 + 100(P/A,7%,10) + 5000(P/F,7%,10)

= –22,000 + 100(7.0236) + 5000(0.5083)

= $–18,756

Again, select B with a slightly higher PW value.

(c) Again, select machine B. All methods give the same conclusion



By hand, if needed:



MACRS with n = 5 and a DR in year 10, which is a tax, not a tax savings.

Tax savings = (AOC + D)(0.5), years 1-6

CFAT = -AOC + tax savings, years 1-10.