Question

A water treatment plant is considering implementing a new treatment technology to treat water at lower costs. They are deciding between two options: · Option A has an expected life of 24 years. It would require a one-time up-front cost of $2.25 million to install and would then yield net benefits of $180,000 at the end of each of the 24 years.

· Option B has an expected life of 24 years. It would require a one-time up-front cost of $180,000 to install and would then yield net benefits of $40,000 at the end of each of the 24 years.

a) Using a real discount rate of 5 percent: · What is the present value of the total benefits of Option A? Option B? (Show your work either here in in an attached spreadsheet.)

· What is the net present value of the total benefits of Option A? Option B? Show your work. · Which project should the treatment plant choose? Defend your answer.

b) If instead of a discount rate of 5 percent, they use a discount rate of 3%, which project should the treatment plant choose? Defend your answer.

Answer 1

Part 1) We have the following information

	Option A	Option B
Initial cost ($)	2,250,000	180,000
Annual benefits ($)	180,000	40,000
Life in years (n)	24	24
Interest rate (i)	5% or 0.05	5% or 0.05

Option A

PV(5%) = – First Cost + Annual benefit(P/A, i, n)

PV(5%) = – 2,250,000 + 180,000(P/A, 5%, 24)

PV(5%) = – 2,250,000 + 180,000[((1+0.05)²⁴ – 1)/0.05(1+0.05)²⁴]

PV(5%) = – 2,250,000 + (180,000 × 13.799)

PV(5%) = – 2,250,000 + 2,483,755.52

PV(5%) = 233,755.52

Option B

PV(5%) = – First Cost + Annual benefit(P/A, i, n)

PV(5%) = – 180,000 + 40,000(P/A, 5%, 24)

PV(5%) = – 180,000 + 40,000[((1+0.05)²⁴ – 1)/0.05(1+0.05)²⁴]

PV(5%) = – 180,000 + (40,000 × 13.799)

PV(5%) = – 180,000 + 551,945.67

PV(5%) = 371,945.67

Since, the present value of Option B is higher so it should be selected.

Part 2) We have the following information

	Option A	Option B
Initial cost ($)	2,250,000	180,000
Annual benefits ($)	180,000	40,000
Life in years (n)	24	24
Interest rate (i)	3% or 0.03	3% or 0.03

Option A

PV(3%) = – First Cost + Annual benefit(P/A, i, n)

PV(3%) = – 2,250,000 + 180,000(P/A, 3%, 24)

PV(3%) = – 2,250,000 + 180,000[((1+0.03)²⁴ – 1)/0.03(1+0.03)²⁴]

PV(3%) = – 2,250,000 + (180,000 × 16.936)

PV(3%) = – 2,250,000 + 3,048,397.58

PV(3%) = 798,397.58

Option B

PV(3%) = – First Cost + Annual benefit(P/A, i, n)

PV(3%) = – 180,000 + 40,000(P/A, 3%, 24)

PV(3%) = – 180,000 + 40,000[((1+0.03)²⁴ – 1)/0.03(1+0.03)²⁴]

PV(3%) = – 180,000 + (40,000 × 16.936)

PV(3%) = – 180,000 + 677,421.68

PV(3%) = 497,421.68

Since, the present value of Option A is higher so it should be selected.