Time Value II.pptx for answers in business studies

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1. Time Value Cont’d Annuities

2. To highlight –before embarking on this The use of a time line Multiple rates over time and series of cash-flows Notes on sources of finance sent to email Quiz: PV FV NO. of Years Rate 8,000 88,756 21% 1,000 2,000 9 600 7 14% 500 6 12%

3. Annuity An annuity is a series of cash flows of equal amount, occurring at even intervals. There are 2 types of annuities : An ordinary annuity – Payments occur at the end of each period An annuity due – Payments occur at the beginning of each period Ordinary annuities are the most common.

4. Formula Present Value of an Annuity: Ordinary: Annuity due: (1+r)  

5. Example Consider a five payment annuity , with payments of Kshs . 5,000 at the end of each of the next five years. If the appropriate discount rate is 14%, What is the present value of this annuity ? If the appropriate discount rate is 10%, What is the present value of this annuity ?

6. Applying the PVA formula Our PMT =5,000 r= 14% n=5yrs =17,165.40  

7. Reading off the tables( PVIFA r,n ) PVIFA r,n signifies the column(rate) and row(period) intersection we should read off:

8. PVIFA 14%,5 From the table we see that at the intersection of the 14% column and the 5 period row we have : 3.4331 Thus, PV= 5,000(3.4331) = 17,165.5 Notice there’s a slight decimal difference due to rounding

9. Amortization : Amortize derives from the latin admortire meaning to kill . This is why we talk of mortality rate in the social sciences when implying the death rate. We here, in finance, are interested in killing off a loan to zero or repaying it completely using regular payments. Loan amortization is therefore the process of calculating the loan payments that amortize the loaned amount.

10. Example Consider a loan amount of Kshs.1,000,000. If its repaid in 4 annual installments (at the end of each year) and the interest rate is 16% p.a what’s the repayment amount? In essence we are making PMT the subject in; We thus get ;  

11.   PMT = 357,375.0695 =357,375.07  

12. Alternatively, using the PVIFA r,n tables From ; PVIFA 16%,4 we read off the intersection

13. PVIFA 16%,4 PMT = 357,372.5967 Again observe the rounding off difference  

14. Amortization table

15. Quiz Suppose you take out a 15 year mortgage of Kshs . 15,000,000 at an interest rate of 16.8% p.a repayable monthly ; construct an amortization table for the first 4 months What is the loan balance by the end of the 5 th year?