Question

A manufacturing company is planning to purchase a conveyor belt. They would like you to compare two following conveyor belt options and let them know which conveyor belt company should purchase at MARR is 12%. Justify your answer using PW analysis.

Convey belt 1: initial cost 30,000 and annual maintence cost is 5,000 decreased by 800 each year until the end of its life. the annual savings is 20,000 and salvage is 10,000. The useful life is 3 years.

convey belt 2: Initial cost is 30,000 and annual maintenance cost is 10,000 decreased by 12% each year until the end of its life. annual savings is 15,000 increased by 22%. The salvage value is 20,000 and the useful life is 4 years

Answer 1

Analysis period will be 12 yrs (LCM of 3 & 4)

NPW of convey belt 1 = -30000 + (20000 - 5000)*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3) + (P/F,12%,3)*(-30000 + (20000 - 5000)*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3)) + (P/F,12%,6) * (-30000 + (20000 - 5000)*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3)) + (P/F,12%,9) *(-30000 + (20000 - 5000)*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3))

= -30000 + 15000*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3) + (P/F,12%,3)*(-30000 + 15000*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3)) + (P/F,12%,6) * (-30000 + 15000*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3)) + (P/F,12%,9) *(-30000 + 15000*(P/A,12%,3) + 800 * (P/G,12%,3) + 10000 * (P/F,12%,3))

= -30000 + 15000*2.401831 + 800 *2.220754 + 10000 *0.711780 + 0.711780*(-30000 + 15000*2.401831 + 800 *2.220754 + 10000 *0.711780) + 0.506631 * (-30000 + 15000*2.401831 + 800 *2.220754 + 10000 *0.711780) + 0.360610 *(-30000 + 15000*2.401831 + 800 *2.220754 + 10000 *0.711780)

= 38483.81

For Convey Belt 2

Present value of geometric series = A * [1 - (1+g)^n / (1+i)^n] / (i - g)

Present value of one cycle of maint cost = 10000 * [1 - (1-0.12)^4 / (1+0.12)^4] / (0.12 + 0.12)

= 10000 * [1 - (0.88)^4 / (1.12)^4] / (0.24)

= 10000 * 2.578678

= 25786.78

Present value of one cycle of annual savings = 15000 * [1 - (1+0.22)^4 / (1+0.12)^4] / (0.12 - 0.22)

= 15000 * [1 - (1.22)^4 / (1.12)^4] / (-0.1)

= 15000 * 4.0788516

= 61182.77

NPW of convey 2 for 12 year study period = -30000 + 61182.77 - 25786.78 + 20000 * (P/F,12%,4) + (P/F,12%,4)*(-30000 + 61182.77 - 25786.78 + 20000 * (P/F,12%,4)) + (P/F,12%,8) * (-30000 + 61182.77 - 25786.78 + 20000 * (P/F,12%,4))

= -30000 + 35395.99 + 20000 *0.635518 + 0.635518*(-30000 + 35395.99 + 20000 *0.635518) + 0.403883* (-30000 + 35395.99 + 20000 * 0.635518)

= 36926.11

As NPW of convey 1 is higher, it should be selected