5. The analysis period is infinite at the annual interest rate of 10%. Initial m

Question

5. The analysis period is infinite at the annual interest rate of 10%. Initial machine cost $400,000 Annual maintenance costs 20,000 Annual benefits 150,000 Life 20 years It is assumed to replace the machine every 20 years at $400,000 for an infinite period. The annual maintenance costs and benefits will be changed as follows: Annual maintenance costs increase $1,000 every year after the first year for the useful o Annual benefits decrease $5,000 every year after the first year for the useful life period Calculate the equivalent uniform annual benefit (EUAB) and equivalent uniform annual cost life period (EUAC). (15 points)

Explanation / Answer

Since the analysis period is infinite but the useful life is finite, EUAB and EUAC will be the EUAB/ EUAC of the finite period which is 20 years.

EUAB= 150000- 5000*A/G(10%, 20)

EUAB = 150000- 5000*6.508

= $117,460

EUAC = EUAC of capital costs + EUAC of maintenance costs

EUAC of capital costs= (Initial value + Replacement cost*(P/F, 10%,20))* (A/P,10%,20)

=( 400000+400000*0.1486 )* 0.1175

= 53984.2

EUAC of maintenance costs = 20000+1000*(A/G,10%,20)

= 20000+ 1000*6.508

=26,508

Total EUAC = 53984.2 +26,508 = $80,492.20

NOTE: Refer to Annual Compound Interest tables http://global.oup.com/us/companion.websites/9780199778126/pdf/Appendix_C_CITables.pdf

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