1 / 16

Annuities

Annuities. Chapter 11. 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

olisa
Télécharger la présentation

Annuities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 forfor Ordinary Annuity (End) Math Formulas: 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… FV =PMT*((1+i/n)^(x*n)-1)/(i/n) PMT =FV/(((1+i/n)^(x*n)-1)/(i/n))

  9. FV & PMTFV for Annuity Due (Begin) Math Formulas: 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… FV =PMT*((1+i/n)^(x*n)-1)/(i/n)*(1+i/n) PMT =FV/(((1+i/n)^(x*n)-1)/(i/n))/(1+i/n)

  10. PV & PMTPVfor Ordinary Annuity (End) Math Formulas: 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 PMT =PV/(((1+i/n)^-(x*n)-1)/(i/n)) PV =PMT*((1+i/n)^-(x*n)-1)/(i/n)

  11. PV & PMTPVfor Annuity Due (Begin) Math Formulas: 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 PMT =PV/(((1+i/n)^-(x*n)-1)/(i/n))/(1+i/n) PV =PMT*((1+i/n)^-(x*n)-1)/(i/n)*(1+i/n)

  12. PMTPVfor 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

More Related