Minas

CAPITAL BUDGET SYSTEMS (NPV, IRR, Payback)
First, realize that the value of money changes over time You are capitalizing to know the value of the money X in t2

t1

t2

x (1 + i )

n

i isthe interest rate or a requested rate of return for an investment.

You are discounting to know the value of the money X on t1

t1

x n (1 + i )

t2

n is the period number

So, whenanalyzing if an investment is worth or not, you need to compare the value of the money in the same moment, not at different times.

NPV, net present value (VAN valor actual neto in Spanish) is obtainedby calculating the sum of present values of the individual cash flows that will be occurring at different time periods. You have to assign a desired rate of return that you would be happy with. Ifincoming cash flows are higher than the initial outgoing (your NPV is positive), it is fine to proceed with a project

And here is an example. You invest 800.000 and will be getting cash flows for irfor 6 years as follows: Year 1 100.000 Year 2 150.000 Year 3 175.000 Year 4 200.000 Year 5 250.000 Year 6 300.000 You want a rate of return of 7%, or you might want to do something different withyour money.

NPV = -800.000 +

100.000 150.000 175.000 200.000 250.000 300.000 + + + + + (1 + 0.07)1 (1 + 0.07) 2 (1 + 0.07) 3 (1 + 0.07) 4 (1 + 0.07) 5 (1 + 0.07) 6
ESTIMATED NET CASH FLOW 100.000150.000 175.000 200.000 250.000 300.000 NPV PRESENT VALUE -800.000 93.458 131.016 142.852 152.579 178.247 199.903 98.054

PERIOD 0 1 2 3 4 5 6

Positive result, so OK

In Excel, as simple as toapply this formula to see the value of the whole sum of cash flows

Another method to analyse investments is the Internal rate of Return IRR (TIR tasa interna de retorno in Spanish) That it simplyis to make NPV=0. This is to say, IRR is the interest rate that makes NPV=0. Are you happy with it?

0 = -800.000 +

100.000 150.000 175.000 200.000 250.000 300.000 + + + + + (1 + i )1 (1 + i )...