Net Present Value Npv

Examples Of Net Present Value (NPV), ROI and

Payback Analysis

Introduction

Terms and Definitions

Net Present Value - Method of calculating the expected net monetary gain or loss from a project by discounting all expected future cash inflows and outflows to the present point in time.

Discount Rate - Also known as the hurdle rate or required rate of return, is the rate that a project must achieve in order to be accepted rather than rejected.

Return on Investment - Expected income divided by the amount originally invested

Payback Analysis - The number of years needed to recover the initial cash outlay.

Formulas

Net Present Value = t=1..n A * (1+r)-t OR t=1..n A/ (1+r)t

Where A = Cash flow

r = Required rate of return

t = year of cash flow

n = the nth year

Return On Investment = (Discounted Benefits - Discounted Costs) / Discounted Costs

Payback Period = Years taken to repay initial outlay .

Eg. Project Z Outlay = $ 4000

Yearly cash flows = $2000

Payback period = 2yrs

Examples

* Required rate of Return = 10%

Project A Year 1 Year 2 Year 3 Year 4 Year 5 Total Total Discounted

Benefits $ - $2,000.00 $ 3,000.00 $ 4,000.00 $ 5,000.00 $14,000.00 $ 9,743.00

Costs $ 5,000.00 $1,000.00 $ 1,000.00 $ 1,000.00 $ 1,000.00 $ 9,000.00 $ (7,427.00)

Cash Flow $ (5,000.00) $1,000.00 $ 2,000.00 $ 3,000.00 $ 4,000.00 $ 5,000.00 $ 2,316.00

Project B Year 1 Year 2 Year 3 Year 4 Year 5 Total

Benefits $ 1,000.00 $2,000.00 $ 4,000.00 $ 4,000.00 $ 4,000.00 $15,000.00 $ 10,783.00

Costs $ 2,000.00 $2,000.00 $ 2,000.00 $ 2,000.00 $ 2,000.00 $10,000.00 $ (7,582.00)

Cash Flow $ (1,000.00) $ - $ 2,000.00 $ 2,000.00 $ 2,000.00 $ 5,000.00 $ 3,201.00

Net Present Value

Project A

Year 1 = -$5000 * (1 + .1)-1 = -$4545

Year 2 = $1000 * (1 + .1)-2 = $826

Year 3 = $2000 * (1 + .1)-3 = $1503

Year 4 = $3000 * (1 + .1)-4 = $2049

Year 5 = $4000 * (1 + .1)-5 = $2484

NPV = $2316

Project B

Year 1 = -$1000 * (1 + .1)-1 = -$909

Year 2 = $ 0 * (1 + .1)-2 = $0

Year 3 = $2000 * (1 + .1)-3 = $1503

Year 4 = $2000 * (1 + .1)-4 = $1366

Year