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Business Finance (MGT 232)

Business Finance (MGT 232). Lecture 6. Time Value of Money. Overview of the Last Lecture. 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. Uneven Cash Flows.

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Business Finance (MGT 232)

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  1. Business Finance(MGT 232) Lecture 6

  2. Time Value of Money

  3. Overview of the Last Lecture • 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

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

  5. Uneven Cash Flows Ali will receive the set of cash flows below. What is the Present Value at a discount rate of 10%? 0 1 2 3 4 5 10% Rs.600 Rs.600 Rs.400 Rs.400 Rs.100 PV0

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

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

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

  9. Frequency of Compounding General Formula: FVn = PV(1 + [i/m])mn n: Number of Years m: Compounding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n PV0 :PV of the Cash Flow today

  10. Frequency of Compounding

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

  12. Impact of Frequency QrtlyFV Monthly FV= Daily FV=

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

  14. Impact of Frequency For Present Value:

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

  16. BW’s Effective Annual Interest Rate 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= ( 1 + 6% / 4 )4 - 1 = 1.0614 - 1 = .0614 or 6.14%!

  17. Effective Annual Interest Rate 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?

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

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

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