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Unformatted text preview: 1,000(PVIF6%,16) = $70(PVIFA6%,16) + $1,000(PVIF6%,16) = $696.82 = $1,101.06 222 The percentage change in price is calculated as: Percentage change in price = (New price – Original price) / Original price ∆ PFaulk% = ($696.82 – 783.24) / $783.24 = –0.1103 or –11.03% ∆ PGonas% = ($1,101.06 – 1,216.76) / $1,216.76 = –0.0951 or –9.51% If the YTM declines from 10 percent to 8 percent: PFaulk PGonas = $30(PVIFA4%,16) + $1,000(PVIF4%,16) = $70(PVIFA4%,16) + $1,000(PVIF4%,16) = $883.48 = $1,349.57 = +0.1280 or 12.80% ∆ PFaulk% = ($883.48 – 783.24) / $783.24 ∆ PGonas% = ($1,349.57 – 1,216.76) / $1,216.76 = +0.1092 or 10.92% All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates. 16. The bond price equation for this bond is: P0 = $960 = $37(PVIFAR%,18) + $1,000(PVIFR%,18) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.016% This is the semiannual interest rate, so the YTM is: YTM = 2 × 4.016% = 8.03% The current yield is: Current yield = Annual coupon payment / Price = $74 / $960 = .0771 or 7.71% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + 0.04016)2 – 1 = .0819 or 8.19% 17. The company should set the coupon rate on its new bonds equal to the required return. The required return can be observed in the market by finding the YTM on outstanding bonds of the company. So, the YTM on the bonds currently sold in the market is: P = $1,063 = $50(PVIFAR%,40) + $1,000(PVIFR%,40) 223 Using a spreadsheet, financial calculator, or trial and error we find: R = 4.650% This is the semiannual interest rate, so the YTM is: YTM = 2 × 4.650% = 9.30% 18. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is onehalf of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $84/2 × 4/6 = $28 And we calculate the clean price as: Clean price = Dirty price – Accrued interest = $1,090 – 28 = $1,062 19. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is onehalf of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $72/2 × 2/6 = $12.00 And we calculate the dirty price as: Dirty price = Clean price + Accrued interest = $904 + 12 = $916.00 20. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0842 = $90/P0 P0 = $90/.0842 = $1,068.88 Now that we have the price of the bond, the bond price equation is: P = $1,068.88 = $90{[(1 – (1/1.0781)t ] / .0781} + $1,000/1.0781t We can solve this equation for t as follows: $1,068.88 (1.0781)t = $1,152.37 (1.0781)t – 1,152.37 + 1,000 152.37 = 83.49(1.0781)t 1.8251 = 1.0781t t = log 1.8251 / log 1.0781 = 8.0004 ≈ 8 years The bond has 8 years to maturity. 224 21. The bond has 10 years to maturity, so the bond price equation is: P = $871.55 = $41.25(PVIFAR%,20) + $1,000(PVIFR%,20) Using a spreadsheet, financial calculator, or trial and error we find: R = 5.171% This is the semiannual interest rate, so the YTM is: YTM = 2 × 5.171% = 10.34% The current yield is the annual coupon payment divided by the bond price, so: Current yield = $82.50 / $871.55 = .0947 or 9.47% 22. We found the maturity of a bond in Problem 20. However, in this case, the maturity is indeterminate. A bond selling at par can have any length of maturity. In other words, when we solve the bond pricing equation as we did in Problem 20, the number of periods can be any positive number. Challenge 23. To find the capital gains yield and the current yield, we need to find the price of the bond. The current price of Bond P and the price of Bond P in one year is: P: P0 = $90(PVIFA7%,5) + $1,000(PVIF7%,5) = $1,082.00 P1 = $90(PVIFA7%,4) + $1,000(PVIF7%,4) = $1,067.74 Current yield = $90 / $1,082.00 = .0832 or 8.32% The capital gains yield is: Capital gains yield = (New price – Original price) / Original price Capital gains yield = ($1,067.74 – 1,082.00) / $1,082.00 = –0.0132 or –1.32% The current price of Bond D and the price of Bond D in one year is: D: P0 = $50(PVIFA7%,5) + $1,000(PVIF7%,5) = $918.00 P1 = $50(PVIFA7%,4) + $1,000(PVIF7%,4) = $932.26 Current yield = $50 / $918.00 = 0.0545 or 5.45% Capital gains yield = ($...
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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 TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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