Question

Consider the 2 cash flow options below at an interest rate of 10%

	A	B
Initial Cost	100,000	120,000
Year Cost 1	1000	1500
Year Cost 2	1400	1800
Year Cost 3	1800	2100
Year Cost 4	2200	2400
Year Cost 5	2600	2700
Year Cost 6	3000	3000
Year Cost 7	3400	3300
Year Cost 8	3800	3600
Year Cost 9	4200	3900
Year Cost 10	4600	4200
Year Cost 11	5000	4500
Year Cost 12	5400	4800
Year Cost 13	5800	5100
Year Cost 14	6200	5400
Year Cost 15	6600	5700

Option A stops at 15 years, while option B goes until year 30. The final year of option B is equal to 10200.

Yearly savings for option A is 10000 and for option B is 20000.

The salvage value for option A is 5000 and for option B is 12000.

Which option is better?

Answer 1

Option A:

Given, P = 100,000 , A1 = 1000 , G = 400 , n = 15 , Annual savings = 10000 , salvage value = 5000 , i =10%

Annual worth of option A = -100,000(A/P, 10%, 15) -[1000 + 400(A/G, 10%, 15)] + 10,000 + 5,000(A/F, 10%, 15)

                                        = -100,000(0.1315) -[1000 + 400(5.279)] + 10,000 + 5,000(0.0315)

                                        = -13,150 - 3,111.6 + 10,000 + 157.5

                                        = $-6,104.1

Option B:

Given, P = 120,000 , A1 = 1500 , G = 300 , n = 20 , Annual savings = 20000 , salvage value = 12000 , i =10%

Annual worth of option B = -120,000(A/P, 10%, 20) -[1500 + 300(A/G, 10%, 20)] + 20,000 + 12,000(A/F, 10%, 20)

                                        = -120,000(0.1175) -[1500 + 300(6.508)] + 20,000 + 12,000(0.0175)

                                        = -14,100 - 3,452.4 + 20,000 + 210

                                        = $2,657.6

Since the AW of option B is positive, therefore, option B is better.