Question

You are a small business owner considering two alternatives for your phone system.

	Plan A	Plan B
Initial cost ($)	50,000	120,000
Annual maintenance cost ($)	9,000	6,000
Salvage value ($)	10,000	20,000
Life	20 years	40 years

The discount rate is 8%. Which alternative would you pick?

Plan A or Plan B

Answer 1

Calculation of EAC of Plan A

n = 20 years

r = discount rate = 8%

P = annual maintenance cost = -$9,000

NPV of the Plan A = [P * [1 - (1+r)^-n] / r] + [Salvage Value / (1+r)^n] - Initial Cost

= [-$9,000 * [1 - (1+8%)^-20] / 8%] + [$10,000 / (1+8%)^20] - $50,000

= [-$9,000 * 0.785451793 / 0.08] + [$10,000 /4.66095714 ] - $50,000

= -$88,363.3268 + $2,145.48208 - $50,000

= -$136,217.845

EAC of Plan A = [r*NPV] / [1 - (1+r)^-n]

= [8% * -$136,217.845] / [1 - (1+8%)^-20]

= -$10,879.4276 / 0.785451793

= -$13,851.1716

= -$13,851.17

Calculation of EAC of Plan B

n = 40 years

r = discount rate = 8%

P = annual maintenance cost = -$6,000

NPV of the Plan B = [P * [1 - (1+r)^-n] / r] + [Salvage Value / (1+r)^n] - Initial Cost

= [-$6,000 * [1 - (1+8%)^-40] / 8%] + [$20,000 / (1+8%)^40] - $120,000

= [-$6,000 * 0.953969067/ 0.08] + [$20,000 /21.7245215] - $120,000

= -$71,547.68 + $920.618666 - $120,000

= -$191,527.061

EAC of Plan B = [r*NPV] / [1 - (1+r)^-n]

= [8% * -$191,527.061] / [1 - (1+8%)^-40]

= -$15,322.1649 / 0.953969067

= -$16,061.4903

= -$16,061.49

EAC of Plan B is higher than Plan A hence it is better to choose Plan A