Question

A company is considering whether to replace
one of its construction equipment.
• The existing equipment has a current cost of $15,000,
which declines by 20% each year for three years. The
operating cost for this equipment is $20,000 for year 1,
$8,000 for year 2, and $12,000 for year 3.
• The proposed equipment will cost $50,000, last five
years, and has a market value that declines by 20%
each year. The operating cost for the proposed
equipment is $5,000 in year 1, increasing by $2,000
each year after that.
Use ESL analysis, with i= 10%, to determine what
the company should do. Solve by hand.

Answer 1

ESL analysis for existing equipment

Salvage value after 1 yr = 15000*(1-0.2) = 15000 * 0.8 = 12000

Salvage value after 2 yr = 12000*(1-0.2) = 12000 * 0.8 = 9600

Salvage value after 3 yr = 9600*(1-0.2) = 9600 * 0.8 = 7680

EUAC for 1 yr of use = 15000*(A/P,10%,1) + 20000 - 12000*(A/F,10%,1)

= 15000*1.1 + 20000 - 12000

= 24500

EUAC for 2 yr of use = 15000*(A/P,10%,2) + 8000 + (20000-8000)*(P/F,10%,1)*(A/P,10%,2) - 9600*(A/F,10%,2)

= 15000*0.576190 + 8000 + (20000-8000)* 0.909091*0.576190 - 9600*0.476190

= 18357.14

EUAC for 3 yr of use = 15000*(A/P,10%,3) + 8000 + (20000-8000)*(P/F,10%,1)*(A/P,10%,3) + 4000*(A/F,10%,3) - 7680*(A/F,10%,3)

= 15000*0.402115 + 8000 + (20000-8000)*0.909091*0.402115 + 4000*0.302115 - 7680*0.302115

= 17306.65

As minimum EUAC = 17306.65 in 3rd year, ESL = 3 yrs

ESL analysis for new equipment

Salvage value after 1 yr = 50000*(1-0.2) = 50000 * 0.8 = 40000

Salvage value after 2 yr = 40000*(1-0.2) = 40000 * 0.8 = 32000

Salvage value after 3 yr = 32000*(1-0.2) = 32000 * 0.8 = 25600

Salvage value after 4 yr = 25600*(1-0.2) = 25600 * 0.8 = 20480

Salvage value after 5 yr = 20480*(1-0.2) = 20480 * 0.8 = 16384

EUAC for 1 yr of use = 50000*(A/P,10%,1) + 5000 - 40000*(A/F,10%,1)

= 50000*1.1 + 5000 - 40000

= 20000

EUAC for 2 yr of use = 50000*(A/P,10%,2) + 5000 + 2000*(A/G,10%,2) - 32000*(A/F,10%,2)

= 50000*0.576190 + 5000 + 2000*0.476190 - 32000*0.476190

= 19523.81

EUAC for 3 yr of use = 50000*(A/P,10%,3) + 5000 + 2000*(A/G,10%,3) - 25600*(A/F,10%,3)

= 50000*0.402115 + 5000 + 2000*0.936556 - 25600*0.302115

= 19244.71

EUAC for 4 yr of use = 50000*(A/P,10%,4) + 5000 + 2000*(A/G,10%,4) - 20480*(A/F,10%,4)

= 50000*0.315471 + 5000 + 2000*1.381168 - 20480*0.215471

= 19123.03

EUAC for 5 yr of use = 50000*(A/P,10%,5) + 5000 + 2000*(A/G,10%,5) - 16384*(A/F,10%,5)

= 50000*0.263797 + 5000 + 2000*1.810126 - 16384*0.163797

= 19126.47

As minimum EUAC = 19123.03 in 4th year, ESL = 4 yrs

As Minimum EUAC of challenger is more than minimum EUAC of defender, existing machine should be kept for 3 yrs and then replaced