Week 4 Chapter 7 - Q&A - Calculator&Formula

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1. Interpreting bond yields [Z'LO 71] Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 per cent coupon bond sells at par. Two years from now, the required return on the same bond is 8 per cent. What is the Coupon rate on the bond then? The YTM? 1. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. Unlike YTM and required return, the coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond 1s still 10 per cent, and the YTM is 8 per cent. 3. Valuing bonds [~/ LO 7.2] Even though most corporate bonds in Australia make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a face value of €1000, 23 years to maturity and a coupon rate of 3.8 per cent paid annually. If the yield to maturity is 47 per cent, what is the current price of the bond? 3. The price of any bond is the PV of the interest payments, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P =€38({1 - [1/(1 + 0.047%)] }/0.047) + €1000[1/(1 + 0.047)%] P =€875.09 ‘We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as: PVIFz:=1/(1+R) which stands for Present Value Interest Factor PVIFAR:= ({1-[1/(1 + RY]}/R) which stands for Present Value Interest Factor of an Annuity These abbreviations are shorthand notation for the equations in which the interest rate and the number of periods is substituted into the equation and solved. We will use this shorthand notation in the remainder of the solutions key. 3 Enter 23 €38 N | PmT | Solve for €875.00 6. Bond prices[7LO 7.2] Patonga Ferry Services issued 15-year bonds a year ago at a coupon rate of 4.9 per cent. The bonds make semiannual payments and have a face value of $1000. If the YTM on these bonds is 4.5 per cent, what is the current bond price? 6. To find the price of this bond, we need to realise that the maturity of the bond is 14 years. The bond was issued 1 year ago, with 15 years to maturity, so there are 14 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is: P =$24.50(PVIFA225%.25) + $1000(PVIF225%28) P=$1041.22 6. Enter 28 4.5%/2 $49/2 $1000 Solve for $1041.22

7. Bondyields [[Z'LO 7.2] Quambone Farms issued 25-year bonds two years ago at a coupon rate of 5.3 per cent. The bonds make semiannual payments. If these bonds currently sell for 105 per cent of face value, what is the YTM? 7. Here we are finding the YTM of a semianaual coupon bond. The bond price equation is P =$1050 = $26 50(PVIFAz-. 15) + $1000(PVIFz-;16) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator or trial and error, we find: R=2467% © MeGrow-Hil Australia Ross,Fundamentais of Corporate Finance, 8 Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM =2 x 2.467% YTM =4.93% 7. Enter 46 =$1050 $53/2 $1000 N PV Solve for 2.467% 2.467% x2=4.93% 9. Zero coupon bonds [(7/LO 7.2] You find a zero coupon bond with a face value of $10000 and 17 years to maturity. If the yield to maturity on this bond is 4.2 per cent, what is the price of the bond? Assume semiannual compounding periods. 9. To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: P =$10 000(PVIF2.10%34) P =$4933.16 9. Enter 34 =$10 000 Solve for $4933.16 112 Valuing bonds [[Z/LO 7.2] Thirroul Surf Club has a bond outstanding with a coupon rate of 2.8 per cent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 3.4 per cent, and the bond has a face value of $5000. What is the price of the bond? 11. To find the price of this bond, we need to find the present value of the bond’s cash flows. So, the price of the bond is: P =$70(PVIFA1 70%.32) + $5000(PVIF1 70%32) P =$4632.13 11 Enter 32 3.4%/2 +$140/2 =$5000 Solve for $4623.13

15, Nominal versus real returns [/LO 7.4] Say you own an asset that had a total return last year of 1165 per cent.If the inflation rate last year was 275 per cent, what was your real return? 15. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates and inflation, 1s: (A+R) =1+ +7) r=[(1+0.1165)/(1.0275)] - 1 7=0.0866, or 8.66% 15. Calculator solution not available in eText 20, Interestrate fisk [7'LO 7.2] Bond J has a coupon rate of 3 per cent. Bond K has a coupon rate of 9 per cent. Both bonds have 14 years to maturity, make semiannual payments and have a YTM of 6 per cent. If interest rates suddenly rise by 2 per cent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 per cent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds? 20. Assume the face value of both bonds is $1000. Initially, at a YTM of 6 per cent, the prices of the two bonds are: Py =$15(PVIFA3%28) + $1000(PVIF3%.28) =$718.54 Px =$45(PVIFA3%2s) + $1000(PVIF3s,28) =$1281.46 If the YTM rises from 6 per cent to 8 per cent: Py = $15(PVIFA42,25) + $1000(PVIF 4, 28) =$583.42 Pg = $45(PVIFA42,25) + $1000(PVIF 42, 28) =$1083.32 The percentage change in price is calculated as: Percentage change in price = (New price — Original price)/Original price APf% =($583.42-718.54)/$718.54 =-0.1880, or -18.80% APg% =($1083.32-1281.46)/$1281.46 =-0.1546, or —15.46% If the YTM declines from 6 per cent to 4 per cent: P; =$15(PVIFA2228) + $1000(PVIF22 ) =$893.59 Px = $45(PVIFA2%.28) + $1000(PVIF2%.2) =$1532.03 AP1% =($893.59 —718.54)/$718.54 =0.2436, or 24.36% APK% =($1532.03 — 1281.46)/$1 281.46 =0.1955, or 19.55% All things being equal, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates.

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20. Initially, at a YTM of 6 per cent, the prices of the fwo bonds are: $1000 $718.54 $90/2 $1000 $1281.46 If the YTM rises from 6 per cent to 8 per cent: Ps Enter 28 $30/2 $1000 [ v | Solve for $583.42 AP;% = ($583.42 — 718.54)/$718.54 = -18.80% Px Enter 28 $90/2 $1000 v | Solve for $1083.32 APx% = ($1083.32 — 1281.46)/$1281.46 = —15.46% If the YTM declines from 6 per cent to 4 per cent: Ps Enter 28 4%/2 $30/2 $1000 [ ovir | Solve for $893.59 AP1% = ($893.59 — 718.54)/$718.54 =+ 24.36% Px Enter 28 $90/2 $1000 I Solve for $1532.03 APx% = ($1532.03 — 1281.46)/$1281.46 = + 19.55% All clse the same, the lower the coupon rate on a bond, the greater is ifs price sensitivity to changes in interest rates.

21 Bond yields [Z'LO 7.2] Wadalba Software has 6.4 per cent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 94.31 per cent of face value. What is the current yield on the bonds? The YTM? The effective annual yield? 21. The current yield is: Current yield = Annual coupon payment/Price Current yield = $64/$943.10 Current yield = 0.0679, or 6.79% Assuming the face value of the bond is $1000, the bond price equation for this bond 1s: Po=$943.10 = $32(PVIFARre.36) + $1 000(PVIFz2.36) Using a spreadsheet, financial calculator, or trial and error we find: R=3480% This s the semiannual interest rate, so the YTM is: YTM =2 x 3.480% YTM = 6.96% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + 0.03480)% — 1 Effective annual yield = 0.0708, or 7.08% 21. Enter 36 +$943.10 $64/2 $1000 Solve for 3.480% x 2 =6.96% Enter 2 crx Solve for 7.08% 25, Bond prices versus yields [(7/L0 7.2] a. What is the relationship between the price of a bond and its YTM? b. Explain why some bonds sell at a premium over face value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at face value? . What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at face value? 25. a. The bond price is the present value of the cash flows from a bond. The YTM is the interest rate used in valuing the cash flows from a bond. The bond price and YTM are inversely related. If the YTM increases, the bond price decreases and if the YTM decreases, the bond price increases. b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate. c. Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all cases, the current yield plus the expected one- period capital gains yield of the bond must be equal to the required return. 25. Calculator solution not available in eText

Chapter review and self-test problems [A Bond values A Mugee Industries bond has a 10 per cent coupon rate and a $1000 face value. Interest is paid semiannually and the bond has 20 years to maturity. If investors require a 12 per cent yield, what is the bond’s value? What is the effective annual yield on the bond? 7.2 Bond yields A South Ozzie company bond carries an 8 per cent coupon, paid semiannually. The face value is $1000 and the bond matures in six years. If the bond currently sells for $911.37, what is its yield to maturity? What is the effective annual yield? No Answers - Self Test

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Related Questions

Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond? What is the YTM on the bond?

s the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the YTM on the bond?

BASIC (Questions 1-17) 1. Interpreting Bond Yields Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond now? The YTM? LO 2 LO 2 2. Interpreting Bond Yields Suppose vou buy a 7 percent counon 20-vear

(a) You hold a consol that pays a coupon C in perpetuity. The current interest rate is i, and the average expectation in the market is that this will remainunchanged. What will be the price of the consol today? (b) In the next period however, the interest rate changes unexpectedly to i'. What is the new price of the bond? If the bond is sold at the beginning of that next period, what is the yield from the consol? Does the yield increase or decrease if i'> i? (c) Suppose alternatively that the market expects that the interest rate will change to i' after the initial period. What is the initial value of the consol, and whatis the yield from selling it after one period?

a) You hold a consol that pays a coupon in perpetuity. The current interest rate is i , and the average expectation in the market is that this will remain unchanged. What will be the price of the consol today? b) In the next period however, the interest rate changes unexpectedly to i 0. What is the new price of the bond? If the bond is sold at the beginning of that next period, what is the yield from the consol? Does the yield increase or decrease if 0 > i?

3. Suppose a bond with face value of $5,000 pays a semi-annual coupon of $60 and is currently priced at $4,200. What is a coupon rate? What is the current yield?

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $90.44, while a 2-year zero sells at $82.64. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 12% per year. Required: a. What is the yield to maturity of the 2-year zero? b. What is the yield to maturity of the 2-year coupon bond? c. What is the forward rate for the second year? d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year? e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis? Complete this question by entering your answers in the tabs below. Required A Required B Required C Required D Required E Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?…

What is a bond's yield to maturity (YTM)? A. The expected return you'll earn if the bond issuer defaults B. The return you have made if you sell the bond today C. The same as the bond's coupon rate D. The return you'll earn if you hold the bond to maturity and yields stay the same

Q1: A 20-year bond has a coupon rate of 8 percent, and another bond of the same maturity has a coupon rate of 15 percent. If the bonds are alike in all other respects, which will have the greater relative market price decline if interest rates increase sharply? Why?

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