Annuities

1
Annuities

• Chapter 11

2
Annuities

• Equal Cash Flows at Equal Time Intervals
• Ordinary Annuity (End) Cash Flow At End Of Each
  Period
• Annuity Due (Begin) Cash Flow At Beginning Of
  Each Period
• Examples
• Savings Plan Save 50 at the end of each month
• Savings Plan How Much Do I have to put in bank
  each month for 35 years to become a millionaire?
• Borrow Money What is my monthly payment if I
  borrow 190,000?
• Asset Valuation How much should I pay for a
  machine if it will yield Cash Flow of 10,000 at
  the each of each year for the next 15 years?

3
Annuities

• Annuity Definition
• A level steam of cash flows for a fixed period of
  time
• Each payment is for the same amount
• Payments are referred to as PMT
• The time between PMT is always the same
• Timing for annuities
• Ordinary Annuity (Savings Plans, Mortgage
  contracts)
• PMT are made at the end of each period
• The day you sign the contract, you do not make a
  PMT
• Annuity due (Lease contracts)
• PMT are made at the beginning of each period

4
Types of Annuities

• Savings plan
• If I put 50 (PMT) in the bank at the end of each
  month for 50 years, how much will I have when I
  retire? What is the future value?
• Future value of future cash flows valuation
• If I want to be a millionaire, how much do I have
  to put in the bank at the end of each month. What
  is the PMTFV?
• Loan (DEBT) periodic payment
• If I take out a loan for 190,000, what is the
  monthly payment amount paid at the end of each
  month (PMT)? What is the PMTPV?
• Present value of future cash flows valuation
• If I know the asset will give me 10,000 (PMT) at
  the end of each year for the next 15 years, what
  should I pay for this asset today? What is the
  present value?

5
Math Book Formulas Ordinary Annuity (End)
6
Math Book Formulas Ordinary Annuity (End)
7
Variables
8
FV PMTFV for for Ordinary Annuity (End)

• Excel Functions

• FV (Savings Plan) FV(rate , nper , -PMT)
• PMT (Savings Plan) PMT(rate , nper , , FV)
• Skip PV arguments (put 2 commas) If you put
  PV in, it just means you had so in bank to
  start

• Math Formulas

• FV PMT((1i/n)(xn)-1)/(i/n)
• PMT FV/(((1i/n)(xn)-1)/(i/n))

9
FV PMTFV for Annuity Due (Begin)

• Excel Functions

• FV (Savings Plan) FV(rate , nper , -PMT , , 1)
• PMT (Savings Plan) PMT(rate , nper , , FV , 1)
• Skip PV arguments (put 2 commas) If you put
  PV in, it just means you had so in bank to
  start

• Math Formulas

• FV PMT((1i/n)(xn)-1)/(i/n)(1i/n)
• PMT FV/(((1i/n)(xn)-1)/(i/n))/(1i/n)

10
PV PMTPV for Ordinary Annuity (End)

• Excel Functions

• PMT (Borrower Loan) PMT(rate , nper , PV) PV
  positive cuz bank lends it to you (regardless of
  whether you immediately pay the loan out)
• PV (Asset Valuation) PV(rate , nper , PMT)PMT
  positive cuz cash come into business, PV negative
  cuz that is max you should pay for asset

• Math Formulas

• PMT PV/(((1i/n)-(xn)-1)/(i/n))
• PV PMT((1i/n)-(xn)-1)/(i/n)

11
PV PMTPV for Annuity Due (Begin)

• Excel Functions

• PMT (Borrower Loan) PMT(rate , nper , PV, ,1)
  Skip FV arguments (put 2 commas)
• PV positive cuz bank lends it to you
  (regardless of whether you immediately pay the
  loan out)
• PV (Asset Valuation) PV(rate , nper , PMT,
  ,1)PMT positive cuz cash come into business,
  PV negative cuz that is max you should pay for
  asset

• Math Formulas

• PMT PV/(((1i/n)-(xn)-1)/(i/n))/(1i/n)
• PV PMT((1i/n)-(xn)-1)/(i/n)(1i/n)

12
PMTPV for Ordinary Annuity (End)

• Excel Functions

• PMT (Withdraw During Retirement) PMT(rate ,
  nper , -PV) PV negative cuz you put in bank,
  PMT positive cuz you get money in each period

13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)