2. Annuities Chapter 11

3. 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?

4. 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

5. 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 PMT FV ? 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 PMT PV ? 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?

6. 5 Math Book Formulas Ordinary Annuity (End):

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9. FV & PMT FV for for Ordinary Annuity (End) Math Formulas: FV =PMT*((1+i/n)^(x*n)-1)/(i/n) PMT =FV/(((1+i/n)^(x*n)-1)/(i/n)) 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… 8

10. FV & PMT FV for Annuity Due (Begin) Math Formulas: 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) 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… 9

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

12. PV & PMT PV for Annuity Due (Begin) Math Formulas: 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) 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 11

13. PMT PV 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 12

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