Financial functions

NPV Value today of a set of future cash flow PV=Present value of a series of cash flows NPV= PV-time zero cash flow (cost of the asset)

NPV NPV(interest, range) Net present value of a sequence of cash flows at the «discount rate» Assumption: first cash flows after one period Not net (function misnamed!) Cash flows evenly spaced

IRR IRR(cash flows, guess) Computes the internal rate of return of a sequence of cash flows (IRR makes the NPV=0) Guess is the starting point for the algorithm Useful if more than one IRR is present Cash flows evenly spaced IRR includes all the arguments (including the first neagtive one)

IRR and loan tables Show the division of the investment cash flows between: Investment income =IRR*principal balance at the beginning of the year Return of the investment principal

Multiple IRRs To find the extra IRR use the «guess» extra argument The guess is the starting point for the algorithm that excel uses to fing the IRR Guess has to be close to the IRR Graph the NPV see points in which the function crosses the x-axis Recall the Theorems!!

Payment PMT(rate; n.periods; pv; [future value]; type) This function calculates the payment necessary to pay off a loan with equal payments over a fixed number of periods See also loan Tables

Loan table Flat payment schedule: Take a loan for 10.000 Euro, interest rate =7% per year, to pay off the loan and the interests over 6 years: PMT gives the annual payment Payment is split into Interest and repayment of principal

Present value PV(rate; n.periods; payment; [future value]; type) Calculates the present value of an annuity Payment negative if pv positive

Future value FV(rate; n.periods; payment; [present value]; [type]) Computes the future value of a series of deposits (annuity) Type (0=end of the period, 1= at the beginning) default=0

XNPV XNPV(rate; values; dates) Calculates the net present value for a series of cash flows when dates are unevenly spaced All cash flow should be indicated (also the first one) Tools|Add-Ins |Analysis Toolpack

XIRR XIRR(values (cash flow payments); dates (schedule of dates); [guess]) Calculates the IRR for cashflows unevenly spaced Annual IRR