1. Financial functions

2. 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)

3. 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

4. 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)

5. 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

6. 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!!

7. 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

8. Loan table Flat payment schedule:
Take a loan for 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

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

10. 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

11. 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

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