9) A 30-year, 10% semiannual coupon bond with a par value of $1,000 may be calle
ID: 2673093 • Letter: 9
Question
9) A 30-year, 10% semiannual coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,100. The bond sells for $1,050. (Assume that the bond has just been issued.)What is the bond's yield to maturity? Round your answer to two decimal places.
%
What is the bond's current yield? Round your answer to two decimal places.
%
What is the bond's capital gain or loss yield? Round your answer to two decimal places.
%
What is the bond's yield to call? Round your answer to two decimal places.
10) Absalom Motors's 15% coupon rate, semiannual payment, $1,000 par value bonds that mature in 20 years are callable 4 years from now at a price of $1,050. The bonds sell at a price of $1,205.42, and the yield curve is flat. Assuming that interest rates in the economy are expected to remain at their current level, what is the best estimate of the nominal interest rate on new bonds? Round your answer to two decimal places.
Explanation / Answer
1. YTM we have Period = 30 yrs. Semiannual bond So nper = 2*30 = 60 perios. Par Value = FV = $1000 Coupon = 10% Semiannual. So PMT = 10%*$1000/2 = $50 Current price of bond = PV = $1050 So Semiannual YTM = Rate = Rate(nper,pmt,PV,FV) = Rate(60,50,-1050,1000) = 4.75% So YTM = 2*4.75% = 9.49% .........................Ans (1) 2. Current Yield = Annual coupon/Current Bond price = 2*$50/$1050 = 9.52% ...Ans (2) 3. What is the bond's capital gain or loss yield? Capital Gain Yield =CGY= (P1-P0)/P0 Where: P0 = Original price of the Bond P1 = Current/Selling price of the Bond so CGY = (1050-1000)/1000 = 5.00% .............Ans (3) 4. What is the bond's yield to call? ie YTC we have Period = 4 yrs. Semiannual bond So nper = 2*4 = 8 perios. Par Value = $1000 Coupon = 10% Semiannual. So PMT = 10%*$1000/2 = $50 Current price of bond = PV = $1050 Call price = FV = $1100 So Semiannual YTC = Rate = Rate(nper,pmt,PV,FV) = Rate(8,50,-1050,1100) = 5.26% So YTC = 2*5.26% = 10.51% .........................Ans (4) 10) YTC: we have Period = 4 yrs. Semiannual bond So nper = 2*4 = 8 perios. Par Value = $1000 Coupon = 15% Semiannual. So PMT = 15%*$1000/2 = $75 Current price of bond = PV = $1205.42 Call price = FV = $1050 So Semiannual YTC = Rate = Rate(nper,pmt,PV,FV) = Rate(8,75,-1205.42,1050) = 4.87% So YTC = 2*4.87% = 9.73% .............(A) YTM: we have Period = 20yrs. Semiannual bond So nper = 2*20 = 40 perios. Par Value = $1000 Coupon = 15% Semiannual. So PMT = 15%*$1000/2 = $75 Current price of bond = PV = $1205.42 Maturity price = FV = $1000 So Semiannual YTM = Rate = Rate(nper,pmt,PV,FV) = Rate(40,75,-1205.42,1000) =6.11% So YTM = 2*6.11% =12.23% .........(B) The bond is selling at a large premium, which means that its coupon rate is much higher than the going rate of interest. Therefore, the bond is likely to be called—it is more likely to be called than to remain outstanding until it matures. Thus, it will probably provide a return equal to the YTC rather than the YTM. So, there is no point in calculating the YTM; just calculate the YTC = 9.73%. This would be close to the going rate, and it is about what Absalom Motors's would have to pay on new bonds.
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