Question

PRACTICE PROBLEM ON CAPITAL BUDGETING TECHNIQUES: NPV AND IRR

Suppose you have to choose between two mutually exclusive investment projects with the following cash flows (all numbers are in $1,000s):

	t=0	t=1	t=2
Project A	-$400	$250	$300
Project B	-$200	$140	$179

Both projects have a discount rate of 9%. Determine the Payback Period, Net Present Value (NPV) and the IRR for each project. Which is the better project based on NPV? And how can you use the IRR criterion to obtain the correct (i.e., value maximizing) project choice?

Answer 1

Project A:

Payback period:

Cumulative cash flow for year 0 = -400

Cumulative cash flow for year 1 = -400 + 250 = -150

Cumulative cash flow for year 2 = -150 + 300 = 150

150 / 300 = 0.5

Payback period = 1 + 0.5 = 1.5 years

Net present value:

Net present value = Present value of cash inflows - present value of cash outflows

Net present value = -400 + 250 / (1 + 0.09)¹ + 300 / (1 + 0.09)²

Net present value = $81.86

IRR:

IRR is the rate of return that makes NPV equal to 0

Net present value = -400 + 250 / (1 + R)¹ + 300 / (1 + R)²

Using trial and error method, i.e., after trying various value for R, lets try R as 23.32%

Net present value = -400 + 250 / (1 + 0.2332)¹ + 300 / (1 + 0.2332)²

Net present value = 0

Therefore, IRR is 23.32%

Project B:

Payback period:

Cumulative cash flow for year 0 = -200

Cumulative cash flow for year 1 = -200 + 140 = -60

Cumulative cash flow for year 2 = -60 + 179 = 119

60 / 179 = 0.34

Payback period = 1 + 0.34 = 1.34 years

Net present value:

Net present value = Present value of cash inflows - present value of cash outflows

Net present value = -200 + 140 / (1 + 0.09)¹ + 179 / (1 + 0.09)²

Net present value = $79.10

IRR:

IRR is the rate of return that makes NPV equal to 0

Net present value = -200 + 140 / (1 + R)¹ + 179 / (1 + R)²

Using trial and error method, i.e., after trying various value for R, lets try R as 35.87%

Net present value = -200 + 140 / (1 + 0.3587)¹ + 179 / (1 + 0.3587)²

Net present value = 0

Therefore, IRR is 35.87%

Based on NPV, project A is better as it has a higher NPV

Based on IRR, project B is better.