Ch. 4 (BUS G-345; Money, Banking; and Capital Markets; Self)

Ch. 4 (BUS G-345; Money, Banking; and Capital Markets;...

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Unformatted text preview: Chapter 4: Understanding Interest Rates After this chapter you should have an understanding of the following. 1.What present value is and how to calculate the present value of bonds. 2.Understand the definitions of interest rates, yield to maturity, current yield, and rate of capital gain. 3.Understand interest—rate risk. 4.Understand and apply the Fisher equation. 5.Understand the differences between nominal and real interest rates. 6.Understand the difference between ex ante and ex post interest rates. 27‘ 0' W fl a")? "" .1: Is it possible for a market to have a negative rate of return? V435 ML 664:4 quyfem ( {4% Max—m? ma Is it possible for very high interest rates on short- term bonds to indicate a lose credit market as opposed to a tight credit market? V55 1 W “Wi— To answer the above questions, we have to know how to evaluate the value of bonds. In particular, the value of the _fQ_L_1r general types of credit market instruments in consideration for such things as inflation and income tax. l.Simple Loan a saga [m4 (ampwmdrby) g 2.Fixed Payment Loan ’Mov’flgjagflfi , pay/wads “f 3.Coupon Bond 4.Discount Bond hy‘flwfi ymf‘a grpA 555575 (30!! (V m- if? How to calculate Present Value Basic idea is that money received in the future is not as/yaluable as money received today. WM If you were to put $1,000 in the bank today and it paid a simple interest rate of 10% to you at the end of the year, you would have $1,100 at the end of the year. This can be written as the following, Let i = the interest rate, PV = Present Value, @194- F“ = future cash flow and I1: number of periods, then your cash flow one year from now is fl/ _ q or : PV*(1+i)n - F” In this case 1,100 = 1000 a 1:" If we left the $1,000 in the bank for two years we would have $1,100 after the first and $1,210 after the second. F \/ W = We: . ' Note that we can rearrange this equation to find the presednt value of future cash flow. i PV = @F/ (1+1)n ./ To calculate present value we will need to discount future cash flows by the discount factor, 1/ (l + opportunity cost)“, when the interest rate is the opportunity cost than the discount factor becomes l/(l + i)”, for each period n and add up the PV of those cash flows. More generally, N PV = ;) {CF11 * [ 1/ (1+in)"]} For example: Suppose that you own a bond that will give you a cash flow of $1,000 for 3 years and at the end of the four year give you acash flow of $1 ,100. If the interest rate is 10%What is the PV of this bond? W: The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today. I The yield to maturity is what economist generally considers being the market interest rate. Let’s calculate the Yield to Maturity for four types of credit market instruments, Simple Loan, Fixed Payment Loan, Coupon Bond, Discount Bond. Simple Loan From our earlier example if the amount borrowed is $1,000 and the end of the year cash flow to repay the loan is $1 ,100, what is the yield to maturity of this credit instrument? For simple loans, the simple interest rate equals Fixed Payment Loan (or fully amortized loan) is a loan where principle and interested are paid by a fixed amount at predetermined intervals for the duration of the loan. LV = loan value (present value) FP = fixed yearly payment (Cash Flow) 11 = number of years until maturity - P Lve= PP + FP + PP .+...+ F 1+i a+o2 a+o3 0+0" a MIL/i Md: will pay a fixed “stated” interest rate (also called the coupon rate) or coupon payment every year until the maturity date. At the maturity date it will pay the face value or par value of the bond. P = price of coupon bond C = yearly coupon payment 4%???" _’ f; i' " F 4}: ._ a: . F = face value of the bond n = years to maturity date C C A C C F P=———+_ ,,+ _ l+...+_ _+ I Hi (l+f)“' (1+z')’ (1+i)” (1+i)” Let’s look at an example of different loan values (their PV “‘price”) and yields to maturities. Table 1: Yields to Maturity on a 10%-Coupon— Rate Bond Maturing in Ten Years (Face Value = $1,000) 0 When the coupon bond is priced at its face value, theyield to maturity equals [am mr‘ e. o The price of a coupon bond and the yield to maturity are m wow/53C related a The yield to maturity is Maw than the coupon rate when the bond price is below its facexalue _ We”? 352‘ Pmfifiboflv MEI/M525 ““““““ H- ——W 2:056 C's-far}... 66/15 .27" ;ch fleets 0% WWW? Consol or Mil: A bond with no maturity date that does not repay principal but pays fixed coupon payments forever. (a. I. L,” {d . W v :i P = C it /' R = price of the consol C : yearly interest payment if 2 yield to maturity of the consol can rewriteabove equationas this: x", = C/ I: For coupon bonds, this equation gives the current yield, an easy to calculate approximation to the yield to maturity Discount Bond or zero—coupon bond does not pay any cpupons (or yearly interest payments). It just pays the face value of the bond at maturity. Money is then made by the holder of the bond only through the difference in the purchase price and par value of the bond (ortheir selling price if sold before maturity) For any one year discount bond: i = (F - P) / P @LW Fahd/c1 [C] F = Face value of the discount bond P = current price of the discount bond The yield to maturity equals the increase in price over the year divided by the initial price. As with a coupon bond, the yield to maturity is negatively related to the current bond price. Let’s consider the difference between Interest rates and rates of return. 10 Rate of Return:_ The payments to the owner plus the change in value expressed as a fraction of the purchase price. VH7 V! r“! -' r’ '" ’ ” " 0w RET = C/Pt + (Pu — Pt) / Pt RET = return from holding the bond from time t to time t + 1 Pt = price of bond at time t Pu = price of the bond at time t + l C = coupon payment OR = current yield = i0 (Pu - Pt) /Pt = rate of capital gain = g o The return equals the yield to maturity only if the WIS the time to maturity Link-,1} 9.3} - M 0 A liifieininterest rates is associated with a fall in bond prices, resulting in a cap_i_t_al_loss if time to maturity/is longer than the holding period a The more distant @QIMW, the greater the sizeef the percentage prieeehepge associated with an interest—rate_change 11 ' WW, the lower the rate of return theloeeurs as a result of an increase in the interest rate Mmsmurwmm 0 Even if a bond has a substantial initial interest rate, its return ean be negative if interest rates rise Table 2: One-Year Returns on Different-Maturity lO%—C0up0n—Rate Bonds When Interest Rates Rise from 10% to 20% 101/ f; /, 05:3, [‘5 5 /, 2.00 ft? m??? [VAC-av 6 %& 5 Cpl/CM MW) 660% lit/“CWWJ-Zocrflz) (x) = 2 55%., e ,[gemsIMk is the possible reduction in returns associated with changes in market interest rates. 0 Prices and returns for long-term bonds are We than those for shorter-term bonds 0 There is generally no interest—rate risk for any bond whose time to maturity matches the holding period 13 Real and Nominal Interest Rates 0 Nominal interest rate makes no allowance for inflation 0 Real interest rate is adjusted for changes in price level so it more accurately reflects the w. m Whorrowing A 0 IE? ante real interest rate is adjusted for M changes in the price level L. 0 Ex p’o‘st real interest rate is adjusted for actual changes in the price level . k ‘- . 'I. . - l {. .,_- _ _I ,..[_. Fisher E uation: i 9—— ir + rte i = nominal interest rate ir = real interest rate are I expected inflation rate When the real interest rate is low, there are greater incentives to borrow and fewer incentives " . (b252,) r 5‘5; 14 FIGURE 1: Real and Nominal Interest Rates (Three-Month Treasury Bill), 195 3—2008 Interest Rate (%) 16 12 Nominal Rate Estimated Real Rate 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 ...
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Ch. 4 (BUS G-345; Money, Banking; and Capital Markets;...

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