Question

Potable water is in short supply in many developing countries. To address this​ need, two mutually exclusive water purification systems are being considered for implementation in a developing country. Doing nothing is not an option. The MARR is

66​%

per year.

Answer the following​ questions:

a. Calculate the net AW of each system over the service life.

b.Calculate the modified​ B/C ratio for each of the two systems.

c. Use the​ B/C ratio method to determine which system is more economical.

System 1        

Initial Capital      ​$140,000 

Annual Revenues   ​$56,000 

Annual Costs ​$20,000  

Service life (years) 10

Salvage value $16,800

IRR 22.8%

System 2

Initial capital ​$260,000

Annual Revenues  ​$83,000

Annual Costs ​$42,000

Service life​ (years) 10   

Salvage value      ​$57,200

IRR                   11.1​%

       

Answer 1

(a)

AW, System 1 ($) = -140,000 x A/P(66%, 10) + (56,000 - 20,000) + 16,800 x P/F(66%, 10) x A/P(66%, 10)

= -140,000 x 0.6642** + 36,000 + 16,800 x 0.0063** x 0.6642**

= -92,988 + 36,000 + 70.30

= -56,917.7

AW, System 2 ($) = -260,000 x A/P(66%, 10) + (83,000 - 42,000) + 57,200 x P/F(66%, 10) x A/P(66%, 10)

= -260,000 x 0.6642** + 41,000 + 57,200 x 0.0063** x 0.6642**

= -172,692 + 41,000 + 239.35

= -131,452.65

(b)

Modified B/C ratio = (PW of benefits - PW of Annual costs) / (Initial cost - PW of Salvage value)

System 1 = [(56,000 - 20,000) x P/A(66%, 10)] / [140,000 - 16,800 x P/F(66%, 10)]

= (36,000 x 1.5056) / [140,000 - (16,800 x 0.0063)]

= 54,201.6 / (140,000 - 105.84)

= 54,201.6 / 139,894.16

= 0.3874

System 2 = [(83,000 - 42,000) x P/A(66%, 10)] / [260,000 - 57,200 x P/F(66%, 10)]

= (41,000 x 1.5056) / [260,000 - (57,200 x 0.0063)]

= 61,729.6 / (260,000 - 360.36)

= 61,729.6 / 259,639.64

= 0.2378

(c)

Conventional B/C ratio = PW of Benefits / (Initial cost - PW of Salvage value + PW of Annual cost)

System 1 = [56,000 x P/A(66%, 10)] / [140,000 - 16,800 x P/F(66%, 10) + 20,000 x P/A(66%, 10)]

= (56,000 x 1.5056) / [140,000 - (16,800 x 0.0063) + 20,000 x 1.5056]

= 84,313.6 / (140,000 - 105.84 + 30,112)

= 84,313.6 / 170,006.16

= 0.4959

System 2 = [83,000 x P/A(66%, 10)] / [260,000 - 57,200 x P/F(66%, 10) + 42,000 x P/A(66%, 10)]

= (83,000 x 1.5056) / [260,000 - (57,200 x 0.0063) + 42,000 x 1.5056]

= 124,964.8 / (260,000 - 360.36 + 63,235.2)

= 124,964.8 / 322,874.84

= 0.3870

Both systems have a Conventional B/C ratio less than 1 which is not an acceptance criterion. But since one must be chosen, System 1 should be selected since it has higher Conventional B/C Ratio.