Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

37 if the ytm suddenly falls to 6 percent plaurel

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Unformatted text preview: ]15 } / .076) + €1,000[1 / (1 + .076)15] P = €1,070.18 219 6. Here we are finding the YTM of an annual coupon bond. The fact that the bond is denominated in yen is irrelevant. The bond price equation is: P = ¥87,000 = ¥5,400(PVIFAR%,21) + ¥100,000(PVIFR%,21) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 6.56% Since the coupon payments are annual, this is the yield to maturity. 7. The approximate relationship between nominal interest rates ( R), real interest rates (r), and inflation (h) is: R=r+h Approximate r = .05 –.039 =.011 or 1.10% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r)(1 + h) (1 + .05) = (1 + r)(1 + .039) Exact r = [(1 + .05) / (1 + .039)] – 1 = .0106 or 1.06% 8. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) R = (1 + .025)(1 + .047) – 1 = .0732 or 7.32% 9. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) h = [(1 + .17) / (1 + .11)] – 1 = .0541 or 5.41% 10. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) r = [(1 + .141) / (1.068)] – 1 = .0684 or 6.84% 220 11. The coupon rate, located in the first column of the quote is 6.125%. The bid price is: Bid price = 119:19 = 119 19/32 = 119.59375% × $1,000 = $1,195.9375 The previous day’s ask price is found by: Previous day’s asked price = Today’s asked price – Change = 119 21/32 – (–17/32) = 120 6/32 The previous day’s price in dollars was: Previous day’s dollar price = 120.1875% × $1,000 = $1,201.875 12. This is a premium bond because it sells for more than 100% of face value. The current yield is: Current yield = Annual coupon payment / Asked price = $75/$1,347.1875 = .0557 or 5.57% The YTM is located under the “Asked yield” column, so the YTM is 4.4817%. The bid-ask spread is the difference between the bid price and the ask price, so: Bid-Ask spread = 134:23 – 134:22 = 1/32 Intermediate 13. Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. The bond price equation is: P = C(PVIFAR%,t) + $1,000(PVIFR%,t) Miller Corporation bond: P0 = $45(PVIFA3.5%,26) + $1,000(PVIF3.5%,26) P1 = $45(PVIFA3.5%,24) + $1,000(PVIF3.5%,24) P3 = $45(PVIFA3.5%,20) + $1,000(PVIF3.5%,20) P8 = $45(PVIFA3.5%,10) + $1,000(PVIF3.5%,10) P12 = $45(PVIFA3.5%,2) + $1,000(PVIF3.5%,2) P13 = $1,168.90 = $1,160.58 = $1,142.12 = $1,083.17 = $1,019.00 = $1,000 Modigliani Company bond: P0 = $35(PVIFA4.5%,26) + $1,000(PVIF4.5%,26) = $848.53 P1 = $35(PVIFA4.5%,24) + $1,000(PVIF4.5%,24) = $855.05 P3 = $35(PVIFA4.5%,20) + $1,000(PVIF4.5%,20) = $869.92 P8 = $35(PVIFA4.5%,10) + $1,000(PVIF4.5%,10) = $920.87 P12 = $35(PVIFA4.5%,2) + $1,000(PVIF4.5%,2) = $981.27 P13 = $1,000 All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity lengths. 221 Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond. 14. Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 8 percent. If the YTM suddenly rises to 10 percent: PLaurel PHardy = $40(PVIFA5%,4) + $1,000(PVIF5%,4) = $964.54 = $40(PVIFA5%,30) + $1,000(PVIF5%,30) = $846.28 The percentage change in price is calculated as: Percentage change in price = (New price – Original price) / Original price ∆ PLaurel% = ($964.54 – 1,000) / $1,000 = –0.0355 or –3.55% ∆ PHardy% = ($846.28 – 1,000) / $1,000 = –0.1537 or –15.37% If the YTM suddenly falls to 6 percent: PLaurel PHardy = $40(PVIFA3%,4) + $1,000(PVIF3%,4) = $1,037.17 = $40(PVIFA3%,30) + $1,000(PVIF3%,30) = $1,196.00 ∆ PLaurel% = ($1,037.17 – 1,000) / $1,000 = +0.0372 or 3.72% ∆ PHardy% = ($1,196.002 – 1,000) / $1,000 = +0.1960 or 19.60% All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates. Notice also that for the same interest rate change, the gain from a decline in interest rates is larger than the loss from the same magnitude change. For a plain vanilla bond, this is always true. 15. Initially, at a YTM of 10 percent, the prices of the two bonds are: PFaulk PGonas = $30(PVIFA5%,16) + $1,000(PVIF5%,16) = $70(PVIFA5%,16) + $1,000(PVIF5%,16) = $783.24 = $1,216.76 If the YTM rises from 10 percent to 12 percent: PFaulk PGonas = $30(PVIFA6%,16) + $...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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