2/5/09 9:31 AM Rate of Inflation: The rate of inflation can be measured by the percent change in the CPI, or: Inflation rate = (current CPI ? previous CPI)/previous CPI How did we bring down inflation? - reduce the money supply (interest rates rose) Nominal 2000 GDP = $60 (real and nom GDP0 ) 100 oranges @ $.20 80 apples @ $.50 Nominal 2004 GDP = $86 120 oranges @ $.27 90 apples @ $.60 Real 2004 GDP = 69 120 oranges @ $.20 = $24 90 apples @ $.50 = $45 86/60 = 1.43 43% increase how much of this was the result of inflation and how much was the result of the actually growth of the product in the economy (Real GDP1 / Nom GDP0 ) * (Nom GDP1 / Real GDP1 ) = (Nom GDP1 / Nom GDP0 ) = 86/60 Real growth = 69/60 = 1.15 15% increase in the amount of product Inflation = 86/69 = 1.2464 24% of the change in the GDP value is a result of inflation when you see the nominal change in the value of the economy, two things that cause those changes are inflation and real growth. We saw a 40% change in the value of products in the economy, so 15% of that was due to real growth and 24% was due to inflation Trade off between Inflation and Unemployment: If we want to control inflation, we?re going to have to do something?s with unemployment and vice versa ? Phillip?s curve Lower inflation (4%) higher unemployment (9%) Lower unemployment (4%) higher inflation (10%) Stagflation = high inflation and high unemployment (doesn?t fit Phillip?s curve, but happens) Anytime the Phillip's curve is going to hold is only in the short term ? within a year or two. When you start talking about the long run, the economy changes and you can?t talk about the relationship between unemployment and inflation. As you see increases in demand, prices will go up demand pull As long as increased demand is offset by increased supply, we won?t see an increase in inflation Contraction in the aggregate supply - We have the goods, but for some reason all the prices go up which effects all the prices in the economy= price push inflation perfect example for what happened in the 70?s with oil prices when the oil shock hit, all prices in the economy went up 2 types of inflation = demand pull and price push *** Interest rate = exchange rate between earlier money and later money As interest rates are rising, it?s saying that people want to consume now. They?re saying that if you want them to save, you have to pay them a higher interest rate. If interest rates and low, it?s saying that people are willing to save, and spend the money later Discount rate Cost of capital Opportunity cost of capital required return Future Values: Suppose you invest $1,000 for one year at 5% per year. What is the future falue in one year? Interest = 1,000 (.05) = 50 Value in one year = principal + interest = 1,000 +50 = 1,050 Future Value (FV) = 1000(1+.05) = 1,050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1,000(1.05)(1.05) = 1,000(1.05)^2 = 1,102.50 FV = PV (1 + r)^t FV = future value PV = present value r = period interest rate, expressed as a decimal t= number of periods future value interest factor = (1 + r)^t Effects of Compounding Simple interest ? only earn interest on principal Compound interest ? earn interest on principal and on interest Consider the previous example: FV with simple interest = 1,000 + 50 +50 = 1,100 FV with compound interest = 1,102.50 The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment Future Values ? Example 2 $1,000 for 5 years FV = 1,000(1.05)^5 = 1,276.28 Present Values: How much do I have to invest today to have some amount in the future? PV = FV / (1 +r)^t or PV = FV (1 + r)^-t When we talk about discounting, we mean finding the present value of some future amount. When we talk about the ?value? of something, we are talking about the present value unless we specify ? Present Value -Example Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today? PV = 10,000 / (1.07)^1 = 9,345.79 You want to begin saving for you daughter?s college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today? PV = 150,000 / (1.08)^17 = 40,540.34 For a given interest rate ? the longer the time period, the lower the present value. What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10% 5 years: PV = 500 / (1.1)^5 = 310.46 10 years: PV = 500 / (1.1)^10 = 192.77 For a given time period ? the higher the interest rate, the smaller the present value. What is the present value of $500 received in 5 years if the interest rate is 10%? 15%? Rate = 10%: PV = 500/(1.1)^5 = 310.46 Rate = 15%: PV = 500/(1.15)^5 = 248.58 There is an inverse relation ship between present values and interest rates Multiple Cash Flows- Find the PV of each cash flows and add them ? 12% interest rate: Year 1 CF: 200 / (1.12)^1 = 178.57 Year 2 CF: 400 / (1.12)^2 = 318.88 Year 3 CF: 600 / (1.12)^3 = 427.07 Year 4 CF: 800 / (1.12)^4 = 508.41 Total PV = 1,432.93 if the interest was 10% instead of 12%, the PV will increase Bond Definitions: Bond ? instrument where a company borrows money from somewhere else- contract that says how much you borrowed, going to pay, interest, etc. Par value (face value) ? what you?re going to get at the end of the bond?s life as a payment Coupon rate ? rate of interest that you?re going to be payed on that bond Coupon payment = par value * coupon rate Maturity date = when you?re getting the par value back Yield or Yield to maturity ? interest that the market says you ought to be earning Bond value = PV of coupons + PV of par As interest rates increase, present values decrease So, as interest rates increase, bond prices decrease and vice versa Valuing a Bond with Annual Coupons Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? Coupon: Par Value * Coupon Rate 1000 * .10 = 1000 B= PV of coupons + PV of par B = 369.50 + 593.45 = 963.04 anytime the coupon is less than the yield, the bond value will be less than par.*** anytime the coupon is greater than the yield, the bond value will be above par.*** Coupon rate stays the same for the life of the bond, but the value of the bond can change depending on the yield to maturity 2/5/09 9:31 AM 2/5/09 9:31 AM
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