Net Present Value Npv
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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