The Los Angeles, California, city engineer is analyzing a for-profit public works project at the port authority using an after-tax replacement analysis of the system installed 5 years ago (defender) and a challenger as detailed below. All values are in $1000 units. The effective state tax rate of 6% is applicable, but no federal taxes are imposed. The municipal after-tax return of 6% per year is required. Assume salvages in the future occur at the estimated amounts and use classical SL depreciation.

Question

(a) Perform the AW analysis by hand.

(b) Perform the evaluation using a spreadsheet.

(c) Would the decision be different if a before-tax replacement analysis were performed at i = 12% per year? Also, write the spreadsheet functions to display the AW values.

Answer 1

(a) By hand: Lives are set at 5 (remaining) for the defender and 8 years for the challenger.



Defender



Annual depreciation = 28,000 – 2000 = $2600

10

Annual tax savings = (2600 + 1200)(0.06) = $228

AWD = -15,000(A/P,6%,5) + 2000(A/F,6%,5) – 1200 + 228

= -15,000(0.2374) + 2000(0.1774) – 1200 + 228

= $– 4178

Challenger



DR from sale of D = Market value – BV5

= 15,000 – [28,000 – 5(2600)] = 0



Challenger annual depreciation = 15,000 – 3000 = $1500

Annual tax saving = (1,500 + 1,500)(0.06) = $180



Challenger DR, year 8 = 3000 – 3000 = 0



AWC = –15,000(A/P,6%,8) + 3000(A/F,6%,8) – 1500 + 180

= –15,000(0.16104) + 3000(0.10104) – 1320

= $–3432



Select the challenger

(b) Spreadsheet:

With n = 5, AWD = $-4178; with n = 8, AWC = $-3432.

Select the challenger



(c) AWD = –15,000(A/P,12%,5) + 2000(A/F,12%,5) – 1200

= –15,000(0.27741) + 2000(0.15741) – 1200

= $–5046



AWC = –15,000(A/P,12%,8) + 3000(A/F,12%,8) – 1500

= –15,000(0.2013) + 3000(0.0813) – 1500

= $–4276



Select the challenger. The before-tax and after-tax decisions are the same.

Functions: AWD: = -PMT(12%,5,-15000,2000) – 1200 displays $-5046 per year

AWC: = -PMT(12%,8,-15000,3000) – 1500 displays $-4276 per year