Chapters 4 and 5.pptx

Chapter 4 Future Value, Present Value, and Interest Rates © 2017 McGraw-Hill Education. All Rights Reserved. Authorized only for instructor use in the classroom. No reproduction or distribution without the prior written...

Chapter 4 Future Value, Present Value, and Interest Rates © 2017 McGraw-Hill Education. All Rights Reserved. Authorized only for instructor use in the classroom. No reproduction or distribution without the prior written consent of McGraw-Hill Education.  Learning Objectives 1. Compare the value of monetary payments using present value and future value. 2. Apply present value to a stream of payments using internal rate of return and bond valuation. 3. Explain the difference between real and nominal interest rates and how each is calculated. © 2017 McGraw-Hill Education. All Rights 4-2 Reserved.  Introduction Credit is one of the critical mechanisms we have for allocating resources. Although interest has historically been unpopular, this comes from the failure to appreciate the opportunity cost of lending. Interest rates – Link the present to the future. – Tell the future reward for lending today. – Tell the cost of borrowing now and © 2017 McGraw-Hill Education. All Rights 4-3 Reserved.  Valuing Monetary Payments Now and in the Future We must learn how to calculate and compare rates on different financial instruments. We need a set of tools: – Future value – Present value © 2017 McGraw-Hill Education. All Rights 4-4 Reserved.  Future Value and Compound Interest Future value is the value on some future date of an investment made today. – $100 invested today at 5% interest gives $105 in a year. So the future value of $100 today at 5% interest is $105 one year from now. – The $100 yields $5, which is why interest rates are sometimes called a yield. – This is the same as a simple loan of © 2017 McGraw-Hill Education. All Rights 4-5 Reserved.  Future Value and Compound Interest If the present value is $100 and the interest rate is 5%, then the future value one year from now is: $100 + $100(0.05) = $105 This also shows that the higher the interest rate, the higher the future value. In general: FV = PV + PV(i) = PV(1 + i) © 2017 McGraw-Hill Education. All Rights 4-6 Reserved.  Future Value and Compound Interest The higher the interest rate or the higher the amount invested, the higher the future value. Most financial instruments are not this simple, so what happens when time to repayment varies. When using one-year interest rates to compute the value repaid more than one year from now, we must consider compound interest. – Compound interest is the interest on the interest. © 2017 McGraw-Hill Education. All Rights 4-7 Reserved.  Future Value and Compound Interest What if you leave your $100 in the bank for two years at 5% yearly interest rate? The future value is: $100 + $100(0.05) + $100(0.05) + $5(0.05) = $110.25 $100(1.05)(1.05) = $100(1.05)2 In general FVn = PV(1 + i)n n=years © 2017 McGraw-Hill Education. All Rights 4-8 Reserved.  Future Value and Compound Interest Table 4.1: Computing the future value of $100 at 5% annual interest © 2017 McGraw-Hill Education. All Rights 4-9 Reserved.  Future Value and Compound Interest Converting n from years to months is easy, but converting the interest rate is harder. – If the annual interest rate is 5%, what is the monthly rate? Assume im is the one-month interest rate and n is the number of months, then a deposit made for one year will have a future value of $100(1 + im)12. © 2017 McGraw-Hill Education. All Rights 4-10 Reserved.  Future Value and Compound Interest We know that in one year the future value is $100(1.05) so we can solve for im: (1 + im)12 = (1.05) (1 + im) = (1.05)1/12 = 1.0041 These fractions of percentage points are called basis points. – A basis point is one one-hundredth of a percentage point, 0.01 percent. © 2017 McGraw-Hill Education. All Rights 4-11 Reserved.  Invest $100 at 5% annual interest How long until you have $200? The Rule of 72: – Divide the annual interest rate into 72 – So 72/5=14.4 years. – 1.0514.4 = 2.02 © 2017 McGraw-Hill Education. All Rights 4-12 Reserved.  Present Value Financial instruments promise future cash payments so we need to know how to value those payments. Present value is the value today (in the present) of a payment that is promised to be made in the future. Or, present value is the amount that must be invested today in order to realize a specific amount on a given future date. © 2017 McGraw-Hill Education. All Rights 4-13 Reserved.  Present Value Solve the Future Value Formula for PV: FV = PV × (1+i), so This is just the future value calculation inverted. 4-  Present Value We can generalize the process as we did for future value. Present Value of payment received n years in the future: 4-  Present Value From the previous equation, we can see that present value is higher: 1. The higher future value of the payment,. 2. The shorter time period until payment, n. 3. The lower the interest rate, i. © 2017 McGraw-Hill Education. All Rights 4-16 Reserved.  How Present Value Changes Doubling the future value of the payment, without changing the time of the payment or the interest rate, doubles the present value. The sooner a payment is to be made, the more it is worth. © 2017 McGraw-Hill Education. All Rights 4-17 Reserved. Figure 4.1: Present Value of $100 at 5% Interest © 2017 McGraw-Hill Education. All Rights 4-18 Reserved. Table 4.2: Present Value of $100 Payment Higher interest rates are associated with lower present values, no matter what the size or timing of the payment. At any fixed interest rate, an increase in the time reduces its present value. © 2017 McGraw-Hill Education. All Rights 4-  We can turn a monthly growth rate into a compound-annual rate using what we have learned in this chapter. – Investment grows 0.5% per month – What is the compound annual rate? FVn= PV(1+i)n = 100x(1.005)12 = 106.17 Compound annual rate = 6.17% (Note: 6.17 > 12x0.05 = 6.0) © 2017 McGraw-Hill Education. All Rights 4-20 Reserved.  Internal Rate of Return Imagine that you run a tennis racket company and that you are considering purchasing a new machine. – Machine costs $1 million and can produce 3000 rackets per year. – You sell the rackets for $50, generating $150,000 in revenue per year. – Assume the machine is only input, have certainty about the revenue, no maintenance and a 10 year lifespan. © 2017 McGraw-Hill Education. All Rights 4-21 Reserved.  Internal Rate of Return If you borrow $1 million, is the revenue enough to make the payments? We need to compare the internal rate of return to the cost of buying the machine. The interest rate that equates the present value of an investment with its cost. © 2017 McGraw-Hill Education. All Rights 4-22 Reserved. Internal Rate of Return Balance the cost of the machine against the revenue. – $1 million today versus $150,000 a year for ten years. To find the internal rate of return, we take the cost of the machine and equate it to the sum of the present value of each of the yearly revenues. – Solve for i - the internal rate of return. © 2017 McGraw-Hill Education. All Rights 4-23 Reserved.  Internal Rate of Return: Example Solving for i, i = 0.0814 or 8.14% So long as your interest rate at which you borrow the money is less than 8.14%, then you should buy the machine. © 2017 McGraw-Hill Education. All Rights 4-24 Reserved.  What is the present value of the expected losses associated with a preventable future disaster? – Discount rates – Scale of future losses © 2017 McGraw-Hill Education. All Rights 1-25 Reserved.  Bond Basics A bond is a promise to make a series of payments on specific future dates. Bonds create obligations, and are therefore thought of as legal contracts that: – Require the borrower to make payments to the lender, and – Specify what happens if the borrower fails to do so. © 2017 McGraw-Hill Education. All Rights 4-26 Reserved.  Bond Basics The most common type of bond is a coupon bond. – Issuer is required to make annual payments, called coupon payments. – The annual interest the borrower pays (ic), is the coupon rate. – The date on which the payments stop and the loan is repaid (n), is the maturity date or term to maturity. – The final payment is the principal, face value, or par value of the bond. © 2017 McGraw-Hill Education. All Rights 4-27 Reserved.  Coupon Bond Called a coupon bond as buyer would receive a certificate with a number of dated coupons attached. Coupons © 2017 McGraw-Hill Education. All 4-28 Rights Reserved.  Valuing the Principal Assume a bond has a principle payment of $100 and its maturity date is n years in the future. The present value of the bond principal is: – The higher the n, the lower the value of the payment. © 2017 McGraw-Hill Education. All Rights 4-29 Reserved.  Valuing the Coupon Payments These resemble loan payments. The longer the payments go, the higher their total value. The higher the interest rate, the lower the present value. The present value expression gives us a general formula for the string of yearly coupon payments made over n years. © 2017 McGraw-Hill Education. All Rights 4-30 Reserved.  Valuing the Coupon Payments Plus Principal We can just combine the previous two equations to get: The value of the coupon bond, PCB, rises when – The yearly coupon payments, C, rise and – The interest rate, i, falls. © 2017 McGraw-Hill Education. All Rights 4-31 Reserved.  Bond Pricing The relationship between the bond price and interest rates is very important. – Bonds promise fixed payments on future dates, so the higher the interest rate, the lower their present value. The value of a bond varies inversely with the interest rate used to calculate the present value of the promised payment. © 2017 McGraw-Hill Education. All Rights 4-32 Reserved.  Pay down your debt – The opportunity cost of investing in a retirement fund is the interest rate you are paying on your mortgage, credit card, loan, etc. – No riskless investment is likely to match the rate you receive when you reduce the size of your debt © 2017 McGraw-Hill Education. All Rights 1-33 Reserved.  Real and Nominal Interest Rates Borrowers care about the resources required to repay. Lenders care about the purchasing power of the payments they received. Neither cares solely about the number of dollars, they care about what the dollars buy. © 2017 McGraw-Hill Education. All Rights 4-34 Reserved.  Real and Nominal Interest Rates Nominal Interest Rates (i) – The interest rate expressed in current- dollar terms. Real Interest Rates (r) – The inflation adjusted interest rate. © 2017 McGraw-Hill Education. All Rights 4-35 Reserved.  Real and Nominal Interest Rates The nominal interest rate you agree on (i) must be based on expected inflation ( e ) over the term of the loan plus the real interest rate you agree on (r). i=r+ e This is called the Fisher Equation. The higher expected inflation, the higher the nominal interest rate. © 2017 McGraw-Hill Education. All Rights 4-36 Reserved.  Figure 4.2: Nominal Interest Rate, Inflation Rate and Real Interest Rate © 2017 McGraw-Hill Education. All Rights 4-37 Reserved.  This figure shows the nominal interest rate and the inflation rate in 50 countries and the euro area in early 2016. 4-  Real and Nominal Interest Rates Financial markets quote nominal interest rates. When people use the term interest rate, they are referring to the nominal rate. We cannot directly observe the real interest rate; we have to estimate it. r=i- e © 2017 McGraw-Hill Education. All Rights 4-39 Reserved.  Chapter 5 Understanding Risk © 2017 McGraw-Hill Education. All Rights Reserved. Authorized only for instructor use in the classroom. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1-  Learning Objectives 1. Interpret risk as a measure of uncertainty about payoffs. 2. Explain how to quantify risk. 3. Define risk aversion and explain the role risk premium plays in the risk-return tradeoff. 4. Explain the difference between idiosyncratic and systematic risks. 5. Demonstrate how to reduce risk through hedging and diversification. © 2017 McGraw-Hill Education. All Rights 5-41 Reserved.  Defining Risk According to the dictionary, risk is “the possibility of loss or injury.” For outcomes of financial and economic decisions, we need a different definition. Risk is a measure of uncertainty about the future payoff to an investment, assessed over some time horizon and relative to a benchmark. © 2017 McGraw-Hill Education. All Rights 5-42 Reserved.  Defining Risk 1. Risk is a measure that can be quantified. – The riskier the investment, the less desirable and the lower the price. 2. Risk arises from uncertainty about the future. – We do not know which of many possible outcomes will follow in the future. 3. Risk has to do with the future payoff of an investment. – We must imagine all the possible payoffs and the likelihood of each. © 2017 McGraw-Hill Education. All Rights 5-43 Reserved.  Defining Risk 4. Definition of risk refers to an investment or group of investments. – Investment described very broadly. 5. Risk must be assessed over some time horizon. – In general, risk over shorter periods is lower. 6. Risk must be measured relative to some benchmark - not in isolation. – A good benchmark is the performance of a group of experienced investment advisors or money managers. © 2017 McGraw-Hill Education. All Rights 5-44 Reserved.  Measuring Risk In determining expected inflation or expected return, we need to understand expected value. – The investments return out of all possible values. © 2017 McGraw-Hill Education. All Rights 5-45 Reserved.  Possibilities, Probabilities, and Expected Value Probability theory states that considering uncertainty requires: – Listing all the possible outcomes. – Figuring out the chance of each one occurring. Probability is a measure of the likelihood that an event will occur. It is always between zero and one. Can also be stated as frequencies. © 2017 McGraw-Hill Education. All Rights 5-46 Reserved.  Possibilities, Probabilities, and Expected Value We can construct a table of all outcomes and probabilities for an event, like tossing a fair coin. © 2017 McGraw-Hill Education. All Rights 5-47 Reserved.  Possibilities, Probabilities, and Expected Value If constructed correctly, the values in the probabilities column will sum to one. Assume instead we have an investment that can rise or fall in value. – $1,000 stock which can rise to $1,400 or fall to $700. – The amount you could get back is the investment’s payoff. – We can construct a similar table and determine the investment’s expected value - the average or most likely outcome. © 2017 McGraw-Hill Education. All Rights 5-48 Reserved. Possibilities, Probabilities, and Expected Value Expected value is the mean - the sum of their probabilities multiplied by their payoffs. Expected Value = 1/2($700) + 1/2($1,400) = $1,050 © 2017 McGraw-Hill Education. All Rights 5-49 Reserved.  Possibilities, Probabilities, and Expected Value What if $1,000 Investment could 1. Rise in value to $2,000, with probability of 0.1 2. Rise in value to $1,400, with probability of 0.4 3. Fall in value to $700, with probability of 0.4 4. Fall in value to $100, with probability of 0.1 © 2017 McGraw-Hill Education. All Rights 5-50 Reserved.  Possibilities, Probabilities, and Expected Value Expected Value = 0.1 × ($100) + 0.4 × ($700) + 0.4× ($1,400) +0.1× ($2,000) = $1,050 © 2017 McGraw-Hill Education. All Rights Reserved. 5-51  Possibilities, Probabilities, and Expected Value Using percentages allows comparison of returns regardless of the size of initial investment. – The expected return in both cases is $50 on a $1,000 investment, or 5 percent. Are the two investments the same? – No - the second investment has a wider range of payoffs. Variability equals risk. © 2017 McGraw-Hill Education. All Rights 5-52 Reserved.  Measures of Risk It seems intuitive that the wider the range of outcomes, the greater the risk. A risk free asset is an investment whose future value is known with certainty and whose return is the risk free rate of return. – The payoff you receive is guaranteed and cannot vary. Measuring the spread allows us to measure the risk. © 2017 McGraw-Hill Education. All Rights 5-53 Reserved.  Variance and Standard Deviation The variance is the average of the squared deviations of the possible outcomes from their expected value, weighted by their probabilities. 1. Compute expected value. 2. Subtract expected value from each of the possible payoffs and square the result. 3. Multiply each result times the probability. 4. Add up the results. © 2017 McGraw-Hill Education. All Rights 5-54 Reserved. Variance and Standard Deviation 1. Compute the expected value: ($1400 x ½) + ($700 x ½) = $1,050. 2. Subtract this from each of the possible payoffs and square the results: $1,400 – $1,050 = ($350)2 = 122,500(dollars)2 and $700 – $1,050 = (–$350)2 =122,500(dollars)2 3. Multiply each result times its probability and add up the results: ½ [122,500(dollars)2] + ½ [122,500(dollars)2] =122,500(dollars)2 4. The Standard deviation is the square root of the variance: © 2017 McGraw-Hill Education. All Rights 5-55 Reserved.  Variance and Standard Deviation Standard deviation is the (positive) square root of the variance standard deviation = The standard deviation is more useful because it deals in normal units, not squared units (like dollars-squared). We can calculate standard deviation into a percentage of the initial investment. We can compare other investments to this one. Given a choice between two investments with equal expected payoffs, most will choose the one with the lower standard deviation. – The greater the standard deviation, the higher the risk. © 2017 McGraw-Hill Education. All Rights 5-56 Reserved. Variance and Standard Deviation We can see Case 2 is more spread out - higher standard deviation - therefore it carries more risk. © 2017 McGraw-Hill Education. All Rights Reserved. 5-57  Value at Risk Sometimes we are less concerned with spread than with the worst possible outcome – Example: We don’t want a bank to fail Value at Risk (VaR): The worst possible loss over a specific horizon at a given probability. For example, we can use this to assess whether a fixed or variable-rate mortgage is better. © 2017 McGraw-Hill Education. All Rights 5-58 Reserved.  Value at Risk For a mortgage, the worst case scenario means you cannot afford your mortgage and will lose you home. – Expected value and standard deviation do not really tell you the risk you face, in this case. VaR answers the question: how much will I lose if the worst possible scenario occurs? © 2017 McGraw-Hill Education. All Rights 5-59 – Reserved.  Systemic risks are threats to the system as a whole, not to a specific household, firm or market. Common exposure to a risk can threaten many intermediaries at the same time. A financial system may contain critical parts without which it cannot function. Obstacles to the flow of liquidity pose a catastrophic threat to the financial © 2017 McGraw-Hill Education. All Rights 5-60 Reserved.  Risk Aversion, the Risk Premium, and the Risk- Return Tradeoff Most people do not like risk and will pay to avoid it because most of us are risk averse. – Insurance is a good example of this. A risk averse investor will always prefer an investment with a certain return to one with the same expected return but any amount of uncertainty. Therefore, the riskier an investment, the higher the risk premium. – The compensation investors required to hold the risky asset. © 2017 McGraw-Hill Education. All Rights 5-61 Reserved. Risk Aversion, the Risk Premium, and the Risk- Return Tradeoff © 2017 McGraw-Hill Education. All Rights 5-62 Reserved.  Sources of Risk: Idiosyncratic and Systematic Risk All risks can be classified into two groups: 1. Those affecting a small number of people but no one else: Idiosyncratic or unique risks 2. Those affecting everyone: Systematic or economy-wide risks © 2017 McGraw-Hill Education. All Rights 5-63 Reserved.  Sources of Risk: Idiosyncratic and Systematic Risk Idiosyncratic risks can be classified into two types: 1. A risk is bad for one sector of the economy but good for another. A rise in oil prices is bad for car industry but good for the energy industry. 2. Unique risks specific to one person or company and no one else. © 2017 McGraw-Hill Education. All Rights 5-64 Reserved. Sources of Risk: Idiosyncratic and Systematic Risk © 2017 McGraw-Hill Education. All Rights 5-65 Reserved.  Reducing Risk through Diversification Some people take on so much risk that a single big loss can wipe them out. – Traders call this “blowing up.” Risk can be reduced through diversification, the principle of holding more than one risk at a time. – This reduces the idiosyncratic risk an investor bears. One can hedge risks or spread them among many investments. © 2017 McGraw-Hill Education. All Rights 5-66 Reserved.  Hedging Risk Hedging is the strategy of reducing idiosyncratic risk by making two investments with opposing risks. If one industry is volatile, the payoffs are stable. Let’s compare three strategies for investing $100: Invest $100 in GE. Invest $100 in Texaco. Invest half in each company. © 2017 McGraw-Hill Education. All Rights 5-67 Reserved.  Hedging Risk Investing $50 in each stock to ensure your payoff. Hedging has eliminated your risk entirely. © 2017 McGraw-Hill Education. All Rights 5-68 Reserved.  Spreading Risk You can’t always hedge as investments don’t always move in a predictable fashion. The alternative is to spread risk around. – Find investments whose payoffs are unrelated. We need to look at the possibilities, probabilities and associated payoffs of different investments. © 2017 McGraw-Hill Education. All Rights 5-69 Reserved.  Spreading Risk Let’s again compare three strategies for investing $1,000: Invest $1,000 in GE. Invest $1,000 in Microsoft. Invest half in each company. © 2017 McGraw-Hill Education. All Rights 5-70 Reserved.  Spreading Risk We can see the distribution of outcomes from the possible investment strategies. This figure clearly shows spreading risk lowers the spread of outcome and lowers the risk. © 2017 McGraw-Hill Education. All Rights 5-71 Reserved.  Spreading Risk The more independent sources of risk you hold in your portfolio, the lower your overall risk. As we add more and more independent sources of risk, the standard deviation becomes negligible. Diversification through the spreading of risk is the basis for the insurance business.© 2017 McGraw-Hill Education. All Rights 5-72 Reserved.