Two mutually exclusive projects are being considered and one of them must be sel

Question

Two mutually exclusive projects are being considered and one of them must be selected. Project A requires an initial investment of $500,000, annual O&M costs of 200,000, and will have a useful life of 8 years. Project B requires an initial investment of $800,000, annual O&M costs of 150,000, and will have a useful life of 9 years. Both projects are estimated to yield $350,000 per year in revenues. The salvage value of the equipment used in each project at the end of their respective useful lives is $50,000 and $40,000, respectively.
a. Compute the payback period for Project A considering a MARR of 15%. (ANS: 4.96 years)
b. Compute the payback period for Project B considering aMARR of 15%. (ANS: 6.56 years)

Explanation / Answer

Net annual benefit (NAB) = Annual revenue - Annual O&M cost

Project A: $(350,000 - 200,000) = $150,000

Project B: $(350,000 - 150,000) = $200,000

Since MARR is given, we have to computed discounted payback period (DPBP) which is the time by when cumulative discounted net annual benefit is zero. Note that in year 0, NAB equals initial investment.

For project A, DPBP lies between years 4 & 5.

DPBP = 4 + (Absolute value of cumulative discounted NAB, year 4 / Discounted NAB, year 5)

= 4 + (71,753 / 74,577) = 4 + 0.96 = 4.96 years

For project B, DPBP lies between years 6 & 7.

DPBP = 6 + (Absolute value of cumulative discounted NAB, year 6 / Discounted NAB, year 7)

= 6 + (43,103 / 75,187) = 6 + 0.56 = 6.56 years

PROJECT - A Year NAB ($) PV factor @15% Discounted NAB ($) Cumulative Discounted NAB ($) 0 -5,00,000 1.0000 -5,00,000 -5,00,000 1 1,50,000 0.8696 1,30,435 -3,69,565 2 1,50,000 0.7561 1,13,422 -2,56,144 3 1,50,000 0.6575 98,627 -1,57,516 4 1,50,000 0.5718 85,763 -71,753 5 1,50,000 0.4972 74,577 2,823 PROJECT - B Year NAB ($) PV factor @15% Discounted NAB ($) Cumulative Discounted NAB ($) 0 -8,00,000 1.0000 -8,00,000 -8,00,000 1 2,00,000 0.8696 1,73,913 -6,26,087 2 2,00,000 0.7561 1,51,229 -4,74,858 3 2,00,000 0.6575 1,31,503 -3,43,355 4 2,00,000 0.5718 1,14,351 -2,29,004 5 2,00,000 0.4972 99,435 -1,29,569 6 2,00,000 0.4323 86,466 -43,103 7 2,00,000 0.3759 75,187 32,084

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