Finance ( FV / PV)

Finance

• Finance is the study of value
• Is a way of thinking and a set of tools that reflects a way of thinking
• The most applicable decision-making system

Value Creation

Is about two key components

1. Time
2. Uncertainty

Time Value of Money

• Almost every decision involves
• Time
• Money
• Never compare money over the time without a rate.
• Always use time lines

Basic Terms

n = periods of time

r  = Interest rate (%)

FV = Future Value

• Compounding - is the finance term
• Initial Payment plus accumulated Interest
• Formula - 
• FV = P + r*P 
• FV = (1+r)*P     For one period
•      For any period

PV = Present Value

• Discounting - is the finance term
• PV = FV / (1+r)^n

Using Excel

Present Value

The formula is =PV(Rate, Nper, Pmt, Fv, Type)
Where:

• Rate: Is the interest rate expressed in decimal format (Ex: 0.10 ) or if is annually (Ex: 0.10/12)
• Nper: The number of periods
• Pmt: 
• Value 0 for PV of single cash flow
• Establish the amount of money you will deposit for the time period Nper
• Ex. How much money do I need today to pay 200 for 10 years
• Fv: The value of the money in the future 
• Type: Indicates whether the payment is due at the beginning of the period (type 1) or at the end (type 0).  By default the type is 0

Future Value

The formula is =FV(Rate, Nper, Pmt, Pv, Type)
Where:

• Rate: Is the interest rate expressed in decimal format (Ex: 0.10 ) or if is annually (Ex: 0.10/12)
• Nper: The number of periods
• Pmt: 
• Value 0 for FV of single cash flow
• Establish an amount to know the future value like a pension with a regular payment. 
• Ex. Each month I pay 10000 to my account.
• Another example is the amount each month you pay for your mortgage.
• Pv: The value today 
• Type: Indicates whether the payment is due at the beginning of the period (type 1) or at the end (type 0).  By default the type is 0

Multiple Payments

Terms

• C - Cash flow
• PMT - Payment

Annuity

• Is represente by PMT

Formula in excel
This is to know the amount of periodical payments to get the known final amount. 

=pmt( rate, nper, pv, [fv], [type])

• pv - is 0 if you do know have to amount inn each payment
• fv - is the amount of money you want to get at the end of the periods

Interest Component

Is the interest you are paying per the current borrowed amount 

Future Value on an Annuity

• Assumption
• The first payment of the annuity occurs one period from now.
• This calculate for example the amount of money I will get from my pension if I deposit an amount of money each month for n years

Present Value on an Annuity

• This calculate for example the amount of money I need now to expense for the next n years. 
• Ex. How much money do I now to expend 10000 per year during the next 20 years
• In excel use PV(rate, nper, pmt)

Efective Anual Rate

Where:

• r is the annual rate 
• Also know as stated 
• k is the number of periods
• EAR is also know as real

Perpetuity

A set of equal payments that are paid for ever, with or without growth.

Stock is an example of perpetuity
Bond is not an example because it is limited in time

PV of Perpetuity

                                                 
Where:

• C is the payment
• R the rate

PV of a Constant Growth Perpetuity

Where:

• C is the payment
• R the rate
• g is the growth rate

Present Value of an Annuity growing at rate g