1. 4-1 Business Finance (MGT 232) Lecture 6

2. 4-2 Time Value of Money

3. 4-3 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 Overview of the Last Lecture

4. 4-4 When we have UNEQUAL Payments over UNEQUAL number of periods We cant use Annuity… Uneven Cash flow Stream… Uneven Cash Flows

5. 4-5 Present Value 10% Ali will receive the set of cash flows below. What is the Present Value at a discount rate of 10%? Uneven Cash Flows 5 0 1 2 3 4 5 Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 PV 0 10%

6. 4-6 piece-at-a-time piece 1.Solve a “piece-at-a-time” by discounting each piece back to t=0. How to Solve? 5 0 1 2 3 4 5 R R R R R R R R R R i% PV

7. 4-7 “Piece-At-A-Time” 5 0 1 2 3 4 5 Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 10% Rs.545.45Rs.495.87Rs.300.53Rs.273.21 Rs. 62.09 Rs.1677.15 = PV of the Mixed Flow PV of Uneven Cashflow Stream

8. 4-8 “Piece-At-A-Time” 5 0 1 2 3 4 5 Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 10% FV of Uneven Cashflow Stream

9. 4-9 General Formula: PV FV n = PV(1 + [i/m]) mn n: Number of Years m: Compounding Periods per Yeari: Annual Interest Rate FV n,m : FV at the end of Year n PV 0 : PV 0 : PV of the Cash Flow today Frequency of Compounding

10. 4-10 Frequency of Compounding CompoundingInterest Year (i/m)No of Periods (nxm) Annually Semi-Annually Quarterly Monthly Daily

11. 4-11 Rs.1,000 Ali has Rs.1,000 to invest for 2 years at an annual interest rate of 12%. Annual FV = Semi FV = Impact of Frequency

12. 4-12 Qrtly FV Monthly FV= Daily FV= Impact of Frequency

13. 4-13 Rs.1,000 Ali has to make equal payments of Rs.1,000 to for 3 years at an annual interest rate of 12% in order to have some amount in future. Annual FV = Semi FV = Impact of Frequency

14. 4-14 For Present Value: Impact of Frequency

15. 4-15 The actual rate of interest earned (paid) after adjusting the nominal rate for factors such as the number of compounding periods per year. Formula: Effective Annual Interest Rate

16. 4-16 EAR Basket Wonders (BW) has a Rs.1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)? EAR EAR= ( 1 + 6% / 4 ) 4 - 1 = 1.0614 - 1 6.14%! =.0614 or 6.14%! BW’s Effective Annual Interest Rate

17. 4-17 Suppose you borrow either through credit card which charges 12 % per month for a year or through bank loan with 12% interest rate that is compounded quarterly. What should you choose? Effective Annual Interest Rate

18. 4-18 Loan Amortization If a loan is to be repaid in equal periodic payments, it is said to be amortized loan. It is an application of compounding interest and annuity. Example: Car Loan, Mortgage Loan, Student Loan

19. 4-19 1.Calculate the payment per period. 2.Determine the interest in Period t. (interest x Beg. Amt) principal payment 3.Compute principal payment in Period t. (Payment - interest from Step 2) principal payment 4.Determine ending balance in Period t. (Balance - principal payment from Step 3) 5.Start again at Step 2 and repeat. Steps to Amortizing a Loan

20. 4-20 Summary Uneven Cash flow Streams Frequency of Compounding FV and PV Compounding Effective Annual Rate Loan Amortization