Question

Alternatives A and B are being evaluated. The effective annual interest rate is 10%. What

alternative is economically superior?

	Alternative A	Alternative B
first cost	80,000	35,000
life	20 years	10 years
salvage value	7,000	0
annual costs
years 1-5	1000	3000
years 6-10	1500	4000
years 11 - 20	2000	0
additional cost
year 10	5000	0

Answer 1

We need to find Equivalent annual worth

Annual cost cash flow for A will be 1000 for yr 1 to 20 and extra 500 from yr 6 to 20 and extra 500 from yr 11 to 20

Annual cost cash flow for B will be 3000 from yr 1 to 10 and extra 1000 from yr 6 to 10

Present value of cash flow starting from other than year 1 will be calculated and then changed to annual series

Equivalent annual worth of option A

= -80000 *(A/P, 10%, 20) + 7000* (A/F, 10%,20)-1000-500 *(P/A, 10%, 15)*(P/F, 10%, 5) *(A/P, 10%, 20) -500 * (P/A, 10%, 10)*(P/F, 10%, 10) *(A/P, 10%, 20) - 5000 *(P/F, 10%, 10) *(A/P, 10%, 20)

= -80000 *0.1174596 + 7000*0.0174596 - 1000 - 500 *7.606079*0.620921323 *0.1174596 -500 *6.144567*0.3855432 *0.1174596 - 5000 *0.3855432 *0.1174596

= -10917.48

Equivalent annual of option B

= -35000 *(A/P, 10%, 10) -3000 -1000*(P/A, 10%, 5)*(P/F, 10%, 5) *(A/P, 10%, 10)

= -35000 *0.16274539 -3000 -1000*3.790786*0.620921323 *0.16274539

= -9079.155

Alternative B is economically superior as it has less annual cost