Lecture 2_Student_2 slides.pdf - FIN222 Lecture 2 CH4 Time...

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FIN222 Lecture 2 CH4: Time Value of Money: Valuing CF Streams CH5: Interest Rates Learning Outcome 1 - Continued 1. Demonstrate an understanding of how financial system works and calculate the value of different types of cash flow streams including financial assets such as shares and bonds. 2
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3 Lecture 2 Reading Lecture 3 Reading 4.1 4.2 4.3 4.4 - Growing Perpetuity 4.5 Solving for the cash Flows - Solving for the number of periods 5.1 5.2 5.3 Inflation and real vs nominal rates 5.3 -Yield curve and Discount rates -Yield curve and The economy 6.1 6.2 -Zero-coupon bond cash flows 6.3 6.4 -Interest rate changes and bond prices -Interest rate risk and bond prices -Bond prices in practice 6.5 Notations 4 FV =Future Value PV = Present value r = Interest rate n = Number of periods m= Frequency of compounding APR= Annual Percentage Rate EAR = Effective Annual Rate g= growth rate k = the period where the first cash flow occurs (not in the text book)
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5 Reminder from Lecture 1 Time value of money A dollar today is worth more than a dollar tomorrow. Which one of these assets would you rather own? The interest rate plays a role of converting cash across time! |_____|_____|_____|_____|_____|_____|_____|_____| Asset 1 Year 0 1 2 3 4 5 6 7 8 $100 |_____|_____|_____|_____|_____|_____|_____|_____| Asset 2 Year 0 1 2 3 4 5 6 7 8 $100 |_____| $1 > $1 $105 5% Simple Interest vs Compound Interest Simple Interest Interest is only earned on principal (of $10). Compound Interest (assume annual compounding!) Interest is earned on both principal and previously earned interest . Compound interest method –Simple interest method = Amount of interest on interest 0 1 $10+10*0.1 =$11 2 $11+10*0.1 =$12 3 $12+10*0.1 =$13 $10 0 1 $10+10*0.1 =$11 2 $11+ *0.1 = 3 $12.1+ *0.1 = $10 $11 $12.1 $12.1 $13.31 1 FV C( rn) 1 n FV C( r) 6
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7 0 1 $1 10% $1.1 0 1 $1 0.5 5% 5% $1.1025 0 1 $1 0.25 2.5% $1.1038 0.5 0.75 2.5% 2.5% 2.5% FV n =C (1+r/ m ) m n m =No of times per year that interest is compounded $1(1+ 0.1 ) 1 = $1.1 FV? when more than one compounding period is involved? $1(1+ = $1.1025 2x1 0.1/2 ) 4x1 $1(1+ 0.1/4 ) = $1.1038 Rate per period Total No of periods r=10% Example 1: Future Value Your aunt is planning to invest in a bank deposit that will pay 7.5% per annum compounding semi-annually . If she has $5,000 to invest, how much will she have at the end of four years ? 8
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Example 2: Present Value Megan expects to need $50,000 as a down payment on a house in six years . How much does she need to invest today in an account paying 7.25% per annum compounding quarterly? 9 Example 3. What is the present value of a cash flow of $10,000 to be received in five years given an interest rate of 6% p.a. over five years (a) compounded annually, (b) compounded monthly? (a) Annual compounding: (b) Monthly compounding: 10 Lesson : The more frequently interest payments are compounded, the smaller the PV of $XX for a given period.
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INTEREST QUOTES AND ADJUSTMENT APR vs EAR The most common way to quote interest rates is in terms of an Annual Percentage Rate (APR) APR represents The amount of simple interest earned in one year = the amount of interest earned without the effect of compounding APR < the ACTUAL amount of interest if m > 1
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