Question

Here’s a table giving the benefits and costs of a project in each period and stuff.

Period	0	1	2	3
Benefits	$0	$250	$250	$250
Costs	$400	$25	$25	$300

A. Calculate the net present value of this project using a discount rate of 3%.

B. Calculate the net present value of this project using a discount rate of 7%.

C. Calculate the benefit cost ratio of this project using a discount rate of 5%.

D. Based on your answers to A, B and C, make a guess as to the internal rate of return for this project.

E. Discuss whether this project should be done, based on your answers to the above questions.

Answer 1

Period	0	1	2	3
Benefits	$0	$250	$250	$250
Costs	$400	$25	$25	$300
Net Cash Flow	-400	225	225	-50

A. Calculate the net present value of this project using a discount rate of 3%.

NPW = -400 + 225 (P/A, 3%, 2) – 50(P/F, 3%, 3)

NPW = -400 + 225 (1.91347) – 50(.91514) = -15.22

B. Calculate the net present value of this project using a discount rate of 7%.

NPW = -400 + 225 (P/A, 7%, 2) – 50(P/F, 7%, 3)

NPW = -400 + 225 (1.80802) – 50(.81630) = -34

C. Calculate the benefit cost ratio of this project using a discount rate of 5%.

PW of Cost = 400 + 25 (P/A, 5%, 2) + 300 (P/F, 5%, 3)

PW of Cost = 400 + 25 (1.85941) + 300 (.86384) = 706

PW of Revenues = 250(P/A, 5%, 3)

PW of Revenues = 250(2.72325) = 681

Benefit Cost Ratio = PW of Benefits / PW of Cost

Benefit Cost Ratio = 681 / 706 = .96

D. Based on your answers to A, B and C, make a guess as to the internal rate of return for this project.

Based on the Present Worth calculations the IRR must be below 3%. At 3% the NPW is negative, and we need to reduce it to get a positive NPW, so that we can use the interpolation formula. Hence, the IRR must be below 3%.

E. Discuss whether this project should be done, based on your answers to the above questions.

The project should be rejected. In the benefit cost ratio also, its coming less than one. The project should not be done.