1. 4-1 Business Finance (MGT 232) Lecture 5

2. 4-2 Time Value of Money

3. 4-3 Time Value of Money Simple Interest rate Compounding Interest rate Future Value Graphical Representation Why we use Compounding Present Value Graphical Representation Overview of the Last Lecture

4. 4-4 Types of Annuities Ordinary Annuity Ordinary Annuity: Payments or receipts occur at the end of each period. Annuity Due Annuity Due: Payments or receipts occur at the beginning of each period. u An Annuity u An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.

5. 4-5 Examples of Annuities Student Loan Payments Car Loan Payments Insurance Premiums Mortgage Payments Retirement Savings

6. 4-6 Parts of an Annuity 0 1 2 3 Rs.100 Rs.100 Rs.100 (Ordinary Annuity) End End of Period 1 End End of Period 2 Today Equal Equal Cash Flows Each 1 Period Apart End End of Period 3

7. 4-7 Parts of an Annuity 0 1 2 3 Rs.100 Rs.100 Rs.100 (Annuity Due) Beginning Beginning of Period 1 Beginning Beginning of Period 2 Today Equal Equal Cash Flows Each 1 Period Apart Beginning Beginning of Period 3

8. 4-8 Future Value Annuity - FVA Future Value annuity is the future value of the series of equal payments for specified equidistant periods Ordinary Annuity Annuity Due

9. 4-9 FVA n FVA n = R(1+i) n-1 + R(1+i) n-2 +... + R(1+i) 1 + R(1+i) 0 Ordinary Annuity - FVA R R R n 0 1 2 n n+1 FVA n R = Periodic Cash Flow Cash flows occur at the end of the period i%...

10. 4-10 Example of an Ordinary Annuity - FVA Rs.1,000 Rs.1,000 Rs.1,000 3 0 1 2 3 4 7% Cash flows occur at the end of the period Suppose a bank is offering 7% interest rate at an equal amount of deposit of Rs. 1000 at the end of each year for the next 3 years. What amount you will have at the end of 3 years if you deposit equal payments of Rs. 1000 each.

11. 4-11 FVA n FVA 3 Rs.3,215 FVA n = R (FVIFA i%,n ) FVA 3 = Rs.1,000 (FVIFA 7%,3 ) = Rs.1,000 (3.215)=Rs.3,215 Valuation Using Table

12. 4-12 FVAD n FVA n FVAD n = R(1+i) n + R(1+i) n-1 +... + R(1+i) 2 + R(1+i) 1 = FVA n (1+i) Future Value Annuity Due FVAD R R R R R n-1 0 1 2 3 n-1 n FVAD n i%... Cash flows occur at the beginning of the period

13. 4-13 Example of an Annuity Due -- FVAD Rs.1,000 Rs.1,000 Rs.1,000 3 0 1 2 3 4 7% Cash flows occur at the beginning of the period Suppose a bank is offering 7% interest rate at an equal amount of deposit of Rs. 1000 at the beginning of each year for the next 3 years. What amount you will have at the end of 3 years if you deposit equal payments of Rs. 1000 each.

14. 4-14 FVAD n FVAD n = R (FVIFA i%,n )(1+i) FVAD 3 Rs.3,440 FVAD 3 = Rs.1,000 (FVIFA 7%,3 )(1.07) = Rs.1,000 (3.215)(1.07)= Rs.3,440 Valuation Using Table

15. 4-15 Present Value Annuity - PVA Present Value annuity is the present value of the series of equal payments for specified equidistant periods Ordinary Annuity Annuity Due

16. 4-16 PVA n PVA n = R/(1+i) 1 + R/(1+i) 2 +... + R/(1+i) n Present Value Ordinary Annuity - PVA R R R n 0 1 2 n n+1 PVA n R = Periodic Cash Flow i%... Cash flows occur at the end of the period

17. 4-17 Example of an Ordinary Annuity -- PVA Rs.1,000 Rs.1,000 Rs.1,000 3 0 1 2 3 4 7% Cash flows occur at the end of the period Suppose you will need Rs. 10,000 after 3 years that will require equal amount of deposit of Rs. 1000 at the end of each year for the next 3 years. What lump sum amount you should deposit today if the bank is offering an interest rate of 7%?

18. 4-18 PVA n PVA 3 Rs.2,624 PVA n = R (PVIFA i%,n ) PVA 3 = Rs.1,000 (PVIFA 7%,3 ) = Rs.1,000 (2.624) =Rs.2,624 Valuation Using Table

19. 4-19 PVAD n PVA n PVAD n = R/(1+i) 0 + R/(1+i) 1 +... + R/(1+i) n-1 = PVA n (1+i) Present Value Annuity Due PVAD R R R R n-1 0 1 2 n-1 n PVAD n R: Periodic Cash Flow i%... Cash flows occur at the beginning of the period

20. 4-20 Example of an Annuity Due -- PVAD Rs.1,000 Rs.1,000 Rs.1,000 3 0 1 2 3 4 7% Cash flows occur at the beginning of the period Suppose you will need Rs. 10,000 after 3 years that will require equal amount of deposit of Rs. 1000 at the beginning of each year for the next 3 years. What lump sum amount you should deposit today if the bank is offering an interest rate of 7%?

21. 4-21 PVAD n PVAD n = R (PVIFA i%,n )(1+i) PVAD 3 Rs.2,808 PVAD 3 = Rs.1,000 (PVIFA 7%,3 )(1.07) = Rs.1,000 (2.624)(1.07) = Rs.2,808 Valuation Using Table

22. 4-22 1. Read problem thoroughly 2. Determine if it is a PV or FV problem 3. Create a time line 4. Put cash flows and arrows on time line 5. Determine if solution involves a single CF, annuity stream(s), or mixed flow 6. Solve the problem Steps to Solve Time Value of Money Problems

23. 4-23 Summary Annuity Types of Annuity Future Value Annuity Ordinary Annuity Annuity Due Present Value Annuity Ordinary Annuity Annuity Due Steps to Solve Time Value of Money Problems