Question

he EPA is considering two water quality projects that offer the net benefit streams displayed in the table below

Benefits ($) in Year:

	1	2	3	4	5	Total net benefits
Project A	10	10	10	10	10	50
Project B	12	11	10	9	8	50
Project C	8	9	10	11	12	50

Refer to the information above. Which project offers the greatest present value at a discount rate of 13%?

Select one:

a. Project C

b. Project B

c. Project A

d. The projects are equal in the present value of their net benefits

Answer 1

As per the information provided in the question the EPA is considering among water quality projects (A,B and C)

Discounting rate (i) = 13%

Project A

Present Value = 10(P/A,i,N)

Present Value = 10(P/A,13%,5) =10(3.5172) = $35.172

Project B

Present Value = 12(P/F,i,N) + 11(P/F,i,N) + 10(P/F,i,N) + 9(P/F,i,N) + 8(P/F,i,N)

Present Value = 12(P/F,13%,1) + 11(P/F,13%,2) + 10(P/F,13%,3) + 9(P/F,13%,4) + 8(P/F,13%,5)

Present Value = 12(0.8850) + 11(0.7831) + 10(0.6931) + 9(0.6133) + 8(0.5428)

Present Value = 10.62 + 8.6141 + 6.931 + 5.5197 + 4.3424 = $36.0272 (should be selected)

Project C

Present Value = 8(P/F,i,N) + 9(P/F,i,N) + 10(P/F,i,N) + 11(P/F,i,N) + 12(P/F,i,N)

Present Value = 8(P/F,13%,1) + 9(P/F,13%,2) + 10(P/F,13%,3) + 11(P/F,13%,4) + 12(P/F,13%,5)

Present Value = 8(0.8850) + 9(0.7831) + 10(0.6931) + 11(0.6133) + 12(0.5428)

Present Value = 7.08 + 7.0479 + 6.931 + 6.7463 + 6.5136 = $34.3188

While comparing the present value of three projects (Project A, B and C),

Project B should be selected for greatest present value.

Answer Option B – Project B