# Net Present Value Npv

**Topics:**Net present value, Investment, Rate of return

**Pages:**6 (831 words)

**Published:**March 26, 2012

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 5 = $2000 * (1 + .1)–5 = $1242

NPV = $3201

Return On Investment

= (Discounted Benefits – Discounted Costs) / Discounted Costs

Project A

= ($9747-$7427) / $7427 = .31 or 31%...

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