Direct Transfer. Investment Banking. Investment Banking. Basic Concepts. Economics of Money and Banking. Basic Concepts

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1 Basic Concepts Economics of Money and Banking 2014 South Carolina Bankers School Ron Best University of West Georgia Risk and return: investors will only take on additional risk if they expect to receive adequate compensation How we measure risk and what we mean by adequate are the complicated parts of this concept 1 Basic Concepts Time value of money -- money has a time value associated with it -- a dollar today is worth more than a dollar tomorrow. This simply means that if you have the dollar today you can invest it so it will grow to be worth more over time. Direct Transfer Direct transfers of money and securities occur when a business sells its stocks or bonds directly to savers, without going through any type of financial institution. Borrower Promise Saver $$$ 2 3 Investment Banking An investment banker or brokerage firm serves as a middleperson and facilitates the issuance of securities These middlepersons: help borrowers design securities that will be attractive to investors, buy these securities from the corporations then resell them to savers in the primary markets. 4 Borrower Investment Banking Bor. secs Investment Banker Bor. secs $$ $$$ Savers When the process ends, savers have direct claims against the borrower. 5

2 Financial Intermediary Financial intermediaries such as a banks, mutual funds, or insurance companies: obtain funds from savers issue their own securities in exchange use these funds to purchase other securities literally create new forms of capital The existence of intermediaries greatly increases the efficiency of money and capital markets. 6 Borrower Financial Intermediary Bor claim % % $$ Financial Intermediary $$ % FI claim Savers Borrowers and Savers never have direct claims against one another. 7 The Cost of Money What do we call the price, or cost, of debt capital? The cost of money Production opportunities Time preferences for consumption The interest rate Expected inflation Risk 8 9 Production opportunities Time preference for consumption Refers to the productivity of the investment What does the project add to overall production? Does it: produce more, use less resources in production, etc. Refers to the need (or want) for consumption now versus the future Varies depending on situation If offered the same item : all people generally prefer to have it now instead of later 10 11

3 Expected inflation Inflation is the general rise is prices over time If prices are expected to rise, we need more money in the future to purchase goods Risk Risk is the existence of more than one outcome Risk encompasses the possibility that actual returns may be different from expected returns Any investment must cover this expected price increase What if there is no risk? The risk free rate of return should compensate investors for: their time preference for consumption the effect of inflation on buying power Nominal versus Real Returns The nominal or quoted return is the return that is seen The real return compensates investors for the use of their funds; it is the expected increase in an investor s wealth The inflation premium prices future inflation expectations into today s rates The market is putting its best guess about inflation into today s rates r f r* IP r f = r* + IP = Nominal (quoted) risk-free rate of return = Real risk free rate of return = i + ir* = Inflation premium Example of Inflation Premium Suppose prices rise by 5% You want a real return of 3% Goods that cost $100 before, will now cost $100(1+0.05) = $105 To purchase 3% more than before you need $105(1+0.03) = $

4 Example of Inflation Premium Thus, you need an 8.15% return (108.15/100) 1 = 8.15%) Effectively, you need to be compensated for expected inflation on your initial investment and your real return. r F = r* + i + (i)(r*) = (0.05)(0.03) Risk-Free Securities The closest approximation we have are government securities. Treasury bills return their promised return regardless of the economy. Are T-Bills completely risk-free? T-Bills are still exposed to the risk of unexpected changes in inflation What about risk? Risk is the possibility that more than one outcome may occur. Risk pertains to the possibility that actual returns will be different from the expected return The greater the chance (and range) of returns being different from the expected return, the riskier the investment. 20 Probability distribution -70 Firm Y 0 15 Firm X Expected Rate of Return 100 Rate of Return (%) 21 Risk Tolerance of Individuals Risk aversion is a dislike for risk. Risk averse individuals consider a trade-off between risk and return in making decisions. Risk averse investors require higher expected rates of return to compensate them for assuming higher levels of risk. 22 Expected vs. Actual Returns It is important to note that investors make their decision based on expected returns and risk. Actual returns may differ from expected returns, so actual returns are not always higher for higher risk investments in the short-run. In the long-run, higher returns do generally occur for higher risk assets. 23

5 Required return Investors will expect to receive the risk-free rate of return for any investment, since it can be obtained without any risk. They also will require additional expected return to compensate them for the risk of the asset. The return on any asset can be described by the following equation. Asset s required return = Risk-free rate of return + Asset s risk premium Risk Premiums What are some risks associated with debt securities? Default risk Liquidity risk Maturity risk Default Risk Premium Default risk is the risk that the borrower may default on the loan and not pay the interest or principal. Higher probability of default requires higher default risk premiums. Affected by economy? Affected by collateral? Liquidity Premium Liquidity refers to how quickly an asset can be converted into cash. Because liquidity is important, investors require liquidity premiums for assets that are more difficult (or have a penalty) to convert into cash. Maturity Risk Premium All else equal, the prices of longer-term securities are more effected by changes in interest rates. This is called interest rate risk and investors recognize the risk and charge a premium to compensate them for assuming the additional risk

6 Yield Curve The term structure of interest rates describes the relationship between longand short-term interest rates. The yield curve is the graph of interest rates for similar risk securities for different maturities Hypothetical Treasury Yield Curve Interest Rate (%) 1 yr 2.85% Maturity risk premium 10 yr 3.64% 30 yr 4.37% Inflation premium Real risk-free rate Years to Maturity 31 Yield Curve Shapes Upward sloping or normal Short-term yields are smaller than long-term yields Downward sloping or inverted Short-term yields are larger than longterm yields Yield Curve Shapes Upward sloping or normal As implied by the name normal, yield curves are usually upward sloping Downward sloping or inverted Often appear at the peak of the business cycle Investors seem to anticipate recession Expectations Hypothesis The EH contends that the shape of the yield curve depends on investors expectations about future interest rates. If interest rates are expected to increase, L-T rates will be higher than S-T rates, and vice-versa. Thus, the yield curve can slope up, down, or even bow. 34 Expectations Hypothesis Long-term rates are a geometric average of current and future short-term rates. EH says you can use the yield curve to find expected future interest rates. Assume: 1-year rate = 5% 2-year rate=7% (1+0.07) 2 = (1+0.05)(1 + year 2 rate) (1.1449)/(1.05) = (1 + year 2 rate) Year 2 rate = = 9.04% 35

7 Liquidity Premium Long-term securities are riskier than shortterm securities Over time, investors will have other opportunities/needs for funds and thus demand a premium to hold longer term securities Creates an upward bias to yield curve 36 Segmented Markets Different investors and borrowers are in varying maturity markets Supply and demand determine the interest rate separately for each maturity of securities Thus, there is no single market for securities, but instead a collection of markets defined by maturities 37 Preferred Habitat Investors prefer particular segments of the market They will move to other segments given sufficient inducement Supply and demand imbalances in various markets provide premiums for inducement 38 Federal Reserve System The Fed is the central bank of the United States. The central bank s primary role is to carry out monetary policy. By controlling the growth of money and credit, the Fed tries to ensure: that the economy grows at an adequate rate unemployment is kept low inflation is held down the value of the nation s currency is protected 39 Federal Reserve System The Fed is relatively free to pursue its goals due to its independence: The Fed raises its own funding from sales of its services and security trading so it does not depend on governmental allocations Board of Governors The center of authority is the Board of Governors. This body contains no more than 7 persons, each selected by the President and confirmed by the Senate. Members of the Board of Governors are appointed to 14 year terms The board regulates and supervises the activities of the 12 district Reserve banks and their branch offices (25)

8 Board of Governors Sets reserve requirements on deposits held by banks and other depository institutions Approves all changes in the discount rates posted by the 12 district banks Takes the lead in the system in determining open market policy Federal Open Market Committee FOMC has 12 voting member (7 members of Board of Governors and 5 district bank presidents) Specific task is to set policies that guide the conduct of open market operations (the buying and selling of securities by the Federal Reserve banks) Looks at the whole range of Fed policies and actions to influence the economy and financial system The Fed s Tools Open Market Policy Tool: Purchases and sales of securities (government and Federal agency bonds ) that are designed to move the reserves of depository institutions and interest rates Central bank sales (purchases) tend to decrease (increase) the growth of deposits and loans within the financial system (targets federal funds rate) 44 The Fed s Tools Discount Rate Policy Tool: Central banks are an important source of short-term funds for banks The discount rate is the rate charged by the Federal Reserve banks When the Fed loans reserves to borrowing institutions, the supply of legal reserves temporarily expands which may cause loans to expand 45 The Fed s Tools Reserve Requirements: Banks must place a percentage of transaction deposits in reserve Changes in the percentage of deposits that must be held in reserve can have a potent impact on credit expansion Lowers the amount of money available to lend Tends to increase interest rates (decreased supply) 46 Moral Suasion The bank tries to bring psychological pressure to bear on individuals and institutions to conform to its policies Testimony before Congress Letters and phone calls to those financial institutions that seem to stray from what the bank s objectives are Press releases from bank officials to encourage cooperation with their efforts 47

9 Interest Rates and Business Cycle Business cycle reflects the economic activity of an economy from good times to bad times back to good times Expansion Peak Contraction Trough Business Cycle Chart GDP or Economic Activity ($) Peak Expansion Contraction Expansio Difficult to determine starting and ending points of each phase Trough Units of Time Business Cycle Expansion Gaining economic strength Increases in GDP Unemployment tends to decrease Pressure developing to increase interest rate - Yield curve typically is normal Will begin to shift upward Will also rotate as ST rates more than LT rates 50 Business Cycle Peak Economy is at full production (capacity) - GDP may be growing at 3.0% to 3.5% Inflationary pressures Yield curve may become inverted - ST rates > LT rates - Borrowers will pay higher rate for ST rather than excessive LT rate for long time 51 Business Cycle Contraction Production (GDP) slows Unemployment increases Inventory builds Interest rates begin to fall - ST rates decrease more quickly than LT rates Bankruptcies increase Business Cycle Trough GDP may have negative growth rate Rates continue to fall - At some point, D M starts to increase - May require an economic shock Tax break Government spending 52 53

10 Months Business Cycle History in the U.S Contractions Expansions / Time Value of Money: Website Useful information related to the time value of money can be found on my UWG website. Sample Problems 1-19, 22, and are all examples of time value problems covered in the following pages. 55 Time Value of Money i% CF 0 CF 1 CF 2 CF 3 Time 0 is today Time 1 is the end of Period 1 (or the beginning of Period 2) If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year? 0 1 Year i=6% 100??? Future value What if we leave the money for two years? $100 (starting value = present value (PV)) 6 (interest = (0.06)(100) = 6) $106 (ending value = future value (FV)) FV = PV + PV (% change) FV = PV (1 + % change) FV = PV (1 + i) 58 $ 100 (present value (PV)) 6 (interest = 100*0.06 = 6) $ 106 (future value year 1 (FV 1 )) 6.36 (interest = 106*0.06 = 6.36) $ (future value year 2 (FV 2 )) Compound interest is interest earned on interest 59

11 How do we develop a formula for multiple periods? 106 = 100 ( ) FV 1 = PV ( 1 + i) = 106 ( ) FV 2 = FV 1 ( 1 + i) (but from above) FV 2 = PV (1 + i) (1 + i) FV 2 = PV (1 + i) 2 60 Future value In general, for any number of periods: FV n = PV (1 + i) n FV = future value PV = present value i = interest rate each period n = number of periods 61 Quoted or Nominal Rate Periodic Rate The nominal interest rate is the stated or quoted interest rate. i Nom is stated in contracts. Compounding periods per year (m) must also be given. Examples: 8%; compounded quarterly 8%, compounded daily (365 days) 62 Periodic rate = i Per = i Nom /m, where m is number of compounding periods per year. m = 4 for quarterly, 12 for monthly, and 360 or 365 for daily compounding. Examples: 8% comp. quarterly: i Per = 8%/4 = 2% 8% comp. daily (365): i Per = 8%/365 = % 63 Future value If interest is quoted on an annual basis and compounded during the year, we adjust the formula. Four Ways to Find FVs Solve the equation (using a regular calculator) FV n = PV (1 + i/m) n*m FV = future value PV = present value i = quoted annual interest rate n = number of years m = compounding periods per year 64 Use tables Use a spreadsheet Use a financial calculator 65

12 What is the FV of an initial $100 after 3 years if i = 10%? % FV =? FV 3 = PV(1 + i) 3 = $100(1.10) 3 = $100(1.331) = $ On calculator: Solve Equation 1.10 y x 3 = X = Use Interest Factor Tables 2% 4% 6% 8% 10% FV 3 = PV (FVIF) = 100 (1.3310) = Spreadsheet (Excel) Formulas can be entered into spreadsheets to calculate the time value of money, or you can use available financial functions. FV(rate,nper,pmt,pv,type) rate is the interest rate per period. nper is the number of periods. pmt is the payment amount per period. pv is the starting value. type indicates whether payments occur at the beginning or end of each period. 69 Spreadsheet (Excel) NOTE: pmt and type are for annuities. For lump sum problems set pmt equal to zero and ignore type. Enter =FV(0.1,3,0,-100) $ Answer 70 The Time Value Calculator All time value calculators work in a similar manner. Keys: N = number of time periods I = interest rate per time period PV = present value PMT = periodic payment amounts FV = future value 71

13 BA II Plus Getting Started Decimal places: Press 2nd then FORMAT Enter the number 4 then ENTER Press CE/C Periods per year Press 2nd then P/Y Enter the number 1 then ENTER Press CE/C 72 BA II Plus Getting Started To clear the display: Press CE/C To clear the time value keys (N, I/Y, etc.): Press 2nd then CLR TVM You should get in the habit of clearing the time value keys before starting a new problem. 73 HP 10B II Getting Started 2nd is the color second function key. Decimal places: Press 2nd then DISP Enter the number 4 Periods per year Press the number 1 Press 2nd then P/YR 74 HP 10B II Getting Started To clear the display: Press C To clear the time value keys (N, I/Y, etc.): Press 2nd then C ALL You should get in the habit of clearing the time value keys before starting a new problem. 75 Financial Calculator Solution BA II Plus What is the FV of an initial $100 after 3 years if i = 10%? Based on periods per year set equal to 1 76 To enter information: Press the number then the correct key Press the number 3 then N Press the number 10 then I/Y Press the number 100 then +/- then PV To get the solution: Press CPT then the item you are solving Press CPT then FV Answer:

14 HP 10B II To enter information: Press the number then the correct key Press the number 3 then N Press the number 10 then I/Y Press the number 100 then +/- then PV To get the solution: Press the key for the item you are solving Press FV Answer: What is the FV of an initial $100 after 3 years if the quoted annual interest rate is 10% with semi-annual compounding? 3x2 10/ Based on periods per year set equal to 1 79 Present value A present value is the amount we must begin with now so that with a given interest rate and time it will grow to be the future value. Solve FV n = PV(1 + i ) n for PV: FV PV = n = FV (1 + i) n 1 n 1 + i n We simply rearrange the equation to solve for the present value. Finding PVs is discounting. It is the reverse of compounding What is the PV of $ due in 3 years if i = 10%? Financial Calculator Solution i=10% PV =? PV = $ = $133.10(0.7513) = $ This means that you need to deposit $100 today earning 10% per year to have $ after 3 years. 83

15 What is the PV of $ received in 3 years if the quoted annual interest rate is 10% with semi-annual compounding? Solving for the Interest Rate What is annual interest rate are you promised if you must pay $1000 today to receive $1331 in 3 years? 3x2 10/ Based on periods per year set equal to 1 Note: PV and FV must have opposite signs Solving for the Interest Rate What quoted annual interest rate are you promised if you must pay $5000 today to receive $7500 in 3 years if interest is compounded quarterly? Solving for Time How many years will it take your money to quadruple if the annual interest rate is 10%? 3x Quoted annual rate = % x 4 = % 86 Note: PV and FV must have opposite signs. 87 Solving for Time How many years will it take your money to quadruple if the annual interest rate is 10% and interest is compounded monthly? Time Value It is easy to get bogged down in the formulas, so keep in mind the formula in words is quite simple. 10/ FV = PV + interest earned Years = (167.05)/12 = PV = FV interest earned 89

16 Time Value If interest rates go up, then interest earned goes up so: Time Value If interest rates go down, then interest earned goes down so: FV goes up (you add more interest over time) FV goes down (you add less interest over time) PV goes down (you can begin with less and reach the same goal) PV goes up (you need to start with more to reach the same goal) Time Value If the amount of time goes up, then interest earned goes up and: PV goes down (you can begin with less and reach the same goal) FV goes up (you add more interest over time) If the amount of time goes down, then interest earned goes down and: PV goes up (you must begin with more to reach the same goal) FV goes down (you add less interest) Effective Annual Rate (EAR) The annual rate of return after considering the effect of compounding of interest. The EAR is the annual rate that causes PV to grow to the same FV as within year compounding. i Nom m EAR = m The EAR is used to compare returns on investments with different compounding Effective Annual Rate (EAR) What is the EAR if the quoted annual rate is 10% with semi-annual compounding of interest. EAR = = (1.05) = = 10.25%. 94 EAR: Financial Calculator 2 10/ EAR = = 10.25% Any PV would grow to same FV at 10.25% annually or 10% semiannually. 95

17 What is the FV of $100 after 3 years under 10% semiannual compounding? What is the PV of $ received in 3 years under 10% semiannual compounding? 3x2 10/ x2 10/ Will the FV of a lump sum be larger or smaller if we compound more often, holding the nominal interest rate constant? Why? LARGER! If compounding is more frequent than once a year--for example, semiannually, quarterly, or daily--interest is earned on interest more often. 98 Semiannual Monthly Daily 3x2 10/ x12 10/ x365 10/ Will the PV of a lump sum be larger or smaller if we compound more often, holding the nominal interest rate constant? Why? Semiannual 3x2 10/ SMALLER! If compounding is more frequent than once a year--for example, semiannually, quarterly, or daily--interest is earned on interest more often so you can start with a smaller amount and reach the same goal in the same amount of time. Monthly Daily 3x12 10/ x365 10/

18 Annuities are sets of equal payments received at equal time intervals. Ordinary Annuity i% PMT PMT PMT Annuity Due i% PMT PMT PMT 102 What s the FV of a 3-year ordinary annuity of $100 at 10%? % FV = 331 The future value of the annuity is the sum of the future value of each payment. 103 FV of Ordinary Annuity You should be in end mode when you calculate the answer. 104 What s the PV of this ordinary annuity? % = PV The present value of the annuity is the sum of the present value of each payment. 105 PV of Ordinary Annuity Find the FV and PV if the annuity were an annuity due with annual compounding of interest Again, make sure you are in end mode when you calculate the answer % SWITCH TO Begin Mode: HP 10B: 2nd then BEG/END BA II+: 2nd then BGN then 2nd then Set then CE/C 107

19 Annuity Due Begin Mode 3 N 10 I/YR 0 PV 100 PMT FV $ Annuities Note that the only difference between an annuity due and an ordinary annuity is that each of the payments occur one period quicker Thus, each payment receives an extra year of interest Annuities The difference in the present value and future value of an ordinary annuity and annuity due with the same number of payments is one year s interest on the total = (331)( ) = ( )( ) Annuities Interest rates for annuities are often quoted on an annual basis, although compounding occurs during the year. To solve these problem, you must be sure that the periodic interest rate matches the payment period. For example, if the payments are monthly, they must be matched with a monthly interest rate What is the monthly payment if you finance $20,000 for five years with a quoted annual interest rate of 6.5%? (Payments begin one month after purchase.) What is the quoted annual interest rate for a lease if your payment is $399 per month for 36 months, the residual value is $15,000, and the car costs $24,627? (The first payment is due at inception.) 5x12 6.5/ END MODE BEGIN MODE Quoted annual = (0.6667)(12) = 8.0% 113

20 What s the value at the end of Year 3 of the following CF stream if the quoted interest rate is 10%, compounded semiannually? 0 i=5% % compounded semiannually is 5% each ½ year. 114 a. The cash flow stream is an annual annuity. First find EAR EAR = (1 + 2 ) 1 = 10.25%. b. Calculate FV using EAR as interest rate What is the PV of this uneven cash flow stream? 0 10% = PV Input in CFLO register: CF 0 = 0 CF 1 = 100 CF 2 = 300 CF 3 = 300 CF 4 = -50 Enter I = 10, then press NPV button to get NPV = $ (Here NPV = PV) TI-83: npv(10,0,{100,300,300,-50}) Enter 117 Uneven cashflows Suppose you are offered an investment that pays $10,000 per year the first 8 years, $20,000 per year the next 12 years, and $30,000 per year the following 15 years. If the appropriate discount rate is 9%, what is the present value of the investment? Input in CFLO register: CF 0 = 0 CF 1 = Frequency = 8 CF 2 = Frequency = 12 CF 3 = Frequency =15 Enter I = 9, then press NPV button to get NPV = $170,371 TI-83: npv(10,0,{10000,20000,30000},{8,12,15}) Enter

21 Uneven cashflows Suppose you are offered an investment that pays $10,000 per year the first 8 years, $20,000 per year the next 12 years, and $30,000 per year the following 15 years. If you invest all of the cashflows at an annual interest rate of 9%, what will be the future value of the cashflows at the end of the 35 years? Future value of uneven cashflows We first calculate the PV of the uneven CFs, and then calculate the FV. From previous problem we have: PV = 170, ,477, Suppose you are saving for retirement. You deposit $3000 at the end of each year in an account earning 10% per year. If you have 38 years until retirement, what will your account be worth at retirement? What happens if you decide that it s a little early to worry about retirement and you wait seven years to start saving? , ,092,130 Why is there such a large difference? What happens if you decide that it s a little early to worry about retirement and you wait another seven years to start saving? , If you waited to start saving, how much do you need to save each year to catch up? ,092,130 6, ,092,130 12,

22 Example The key in this example is that you will have $545,830 in 31 years regardless whether you start now or 7 years from now. However, if you start now, you will have an additional 7 years for the $545,830 to earn interest. Rule of 72 If you divide 72 by the annual interest rate, you will find approximately how many years it will take for your investment to double Albert Einstein was once asked: What do you consider the greatest invention of all time? His reply: Effect of Inflation In a previous example we found that investing $3000 annually for 38 years at a 10% annual rate of return resulted in a future value of $1,092,130. However, if inflation were 3% per year over the time period: Compound Interest! ,092, , Key Features of a Bond Bond Valuation Key features of bonds Bond valuation Measuring yield 1. Par value: Face amount; paid at maturity. (Usually $1,000 for corporate bonds.) 2. Maturity: Years until bond must be repaid. 3. Issue date: Date when bond was issued

23 Key Features of a Bond 4. Coupon interest rate: Stated interest rate (generally fixed). Multiply by par to get $ of interest. 5. Yield to maturity: rate of return earned on a bond held until maturity (also called the promised yield or expected return). 132 PV = Financial Asset Values The price of any asset should equal the present value (based on an appropriate discount rate) of its expected cash flows n k Value CF CF 1 CF 2... CF... + CF n n k 1 + k 1+k CF n 133 The discount rate (k i ) is the opportunity cost of capital (i.e., the rate that could be earned on alternative investments of equal risk). The expected cash flows of a bond are the interest payments and the par value. 134 What is the value of a 10-year, 10% coupon, $1000 par bond if k d = 10%? V B % V =? ,000 $100 $1, $ k d 1 + k 1+ k d d = $ $ $ = $1, V B m*n Formula INT/m t t 1 1 k /m 1 k /m d Par V B = value of bond N = number of years INT = annual coupon payment ($) Par = par value k d = annual discount rate m = number of coupon pmts each year d m*n 136 Calculator: The bond consists of a 10- year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:

24 PV annuity PV maturity value PV bond = = = $ $1, The calculator can calculate the present value of the annuity and maturity value in one step (always use end mode) , Bond Valuation using the calculator: N = total number of coupon payments I = discount rate (expected return; required return; yield-to-maturity) PV = price of the bond FV = Par value of bond PMT = coupon payment ($) each payment period USE THE END MODE 139 What would happen if rates rose by 3%, causing k = 13%? What would happen if rates fell, and k d declined to 7%? , When k d rises, above the coupon rate, the bond s value falls below par, so it sells at a discount. Price rises above par, and bond sells at a premium, if coupon > k d If coupon rate < k d, discount. If coupon rate = k d, par bond. Non-annual Coupon Payments All calculator entries represent the same items if coupon payments are made during the year. If coupon rate > k d, premium. The only difference is that the N, I, and PMT must be adjusted to account for the non-annual payments

25 Non-annual Coupon Payments What s the value of a 10-year, 12% quoted annual coupon bond with semi-annual coupon payments if k d = 10%? 2x10 10/2 120/ , Find the value of 10-year, 10% coupon, semiannual bond if k d = 13%. 2x10 13/2 100/ What is the yield to maturity (YTM)? YTM is the rate of return earned on a bond held to maturity. Also called the promised yield. What s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? The yield-to-maturity is determined by solving for the discount rate implied by the current selling price of the bond. All items are the same on the calculator, you just solve for I Find YTM if price were $1, Interest Rate (Price) Risk Interest rate (price) risk is the risk associated with the change in price of an asset when interest rates change. Holding all else equal, longer maturity bonds experience larger price changes when interest rates move

26 Price (interest rate) Risk Change in required return causes bond prices to adjust. k d 1-year Change 10-year Change 5% $1,048 $1, % +38.6% 10% 1,000 1, % -25.1% 15% Reinvestment Rate Risk CFs will have to be reinvested in the future If you invest in a multi-year bond, you get the same interest rate each year until maturity. If you invest in a one-year bond, you get the stated interest rate the first year. The next year you have to reinvest at the prevailing interest rate. 151 Interest rate and Reinvestment rate risk Long-term bonds: High interest rate risk, low reinvestment rate risk. Short-term bonds: Low interest rate risk, high reinvestment rate risk. Nothing is completely riskless! Do all bonds of the same maturity have the same price and reinvestment rate risk? No, low coupon bonds have less reinvestment rate risk but more price risk than high coupon bonds. WHY? Why Does It Matter? A bank s balance sheet primarily consists of financial claims (assets: securities and loans; liabilities: deposits and purchased funds; equity) As interests change: Revenue and expense fluctuates Value changes Typical Bank Balance Sheet Balance Sheet Cash Deposits Securities Borrowed Funds Loans Long-term Debt Premises Equity Other assets

27 Simple Bank: Accounts Account Amount Rate Maturity Cash Securities 100 4% 2 years Bus Loans 300 5% 1 year RE Loans 300 6% 3 years Cons Loans 200 7% 2 years Premises Checking Savings 400 2% 1 year* Time Accts 300 3% 2 years Equity (Assume all account values are at par. ) 156 Cash 50 Securities 100 Loans Business 300 RE 300 Consumer 200 Premises 50 Total Assets 1000 Simple Bank Balance Sheet Deposits Checking 200 Savings 400 Time Accts 300 Equity 100 Total Liab & Eq Net Interest Income This Year Amt Rate Interest Income Securities 100 X 4% = 4 Bus Loans 300 X 5% = 15 RE Loans 300 X 6% = 18 Cons Loans 200 X 7% = 14 Interest Expense Savings 400 X 2% = 8 Time Accts 300 X 3% = 9 Net Int Income NII Next Year if Rates Rise 1% Amt Rate Interest Income Securities 100 X 4% = 4 Bus Loans 300 X 6% = 18 RE Loans 300 X 6% = 18 Cons Loans 200 X 7% = 14 Interest Expense Savings 400 X 3% = 12 Time Accts 300 X 3% = 9 Net Int Income NII Next Year if Rates Fall 1% Amt Rate Interest Income Securities 100 X 4% = 4 Bus Loans 300 X 4% = 12 RE Loans 300 X 6% = 18 Cons Loans 200 X 7% = 14 Interest Expense Savings 400 X 1% = 4 Time Accts 300 X 3% = 9 Net Int Income Value at Current Rates Current value of financial claims in the bank. If rates change, value changes. N I PV PMT FV Secs BL RE Cons Sav Time

28 Immediate 1% Rate Increase N I PV PMT FV Secs BL RE Cons Sav Time Simple Bank: Rates Up 1% Cash 50 Securities Loans Business RE Consumer Premises Total Assets Market Value Deposits Checking 200 Savings Time Accts Equity Total Liab & Eq Immediate 1% Rate Decrease N I PV PMT FV Secs BL RE Cons Sav Time Simple Bank: Rates Down 1% Cash 50 Securities Loans Business RE Consumer Premises Total Assets Market Value Deposits Checking 200 Savings Time Accts Equity Total Liab & Eq

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