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Unformatted text preview: UNIVERSITY OF ILLINOIS College of Business - Department of Finance - Finance 300 (Financial Markets) Professor James Jackson Coupon Bonds: Current Yield, Capital Gain and Yield To Maturity Question: Does Current Yield (CY) + Average Capital Gain (Avg. k Gain) = Yield To Maturity (YTM)? Answer: No. Current Yield (CY) + Annual Capital Gain = Yield To Maturity (YTM). Example #1 Coupon Face Annual Coupon YTM Semi-Annual \$1,000.00 \$60.00 4.00% Bond price with 10 years to maturity (TTM) = \$1,163.51 (solve using financial calculator or spreadsheet) Face – Price = \$1000 - \$1,163.51 = -\$163.51 Total k Gain % = -\$163.51 / \$1,163.51 = -0.1405 CY % = \$60.00 / \$1,163.51 = 0.0516 Avg. k Gain = (-\$163.51 / \$1,163.51) / 10.00 = -0.0141 CY + Avg. k Gain = 0.0516 + (-0.0141) = 0.0375 Annual k Gain % = (\$1,149.92 - \$1,163.51) / \$1,163.51 = -0.0117 Approximate YTM = CY + Annual k Gain =0.0516 - 0.0117 = 0.0399 Approximate YTM TTM Price Face - Price Total k Gain % CY % Avg. k Gain CY + Avg. k Gain Annual k Gain % CY + Annual k Gain 10.0 \$1,163.51-\$163.51-0.1405 0.0516-0.0141 0.0375-0.0117 0.0399 9.0 \$1,149.92-\$149.92-0.1304 0.0522-0.0145 0.0377-0.0123 0.0399 8.0 \$1,135.78-\$135.78-0.1195 0.0528-0.0149 0.0379-0.0130 0.0399 7.0 \$1,121.06-\$121.06-0.1080 0.0535-0.0154 0.0381-0.0137 0.0399 6.0 \$1,105.75-\$105.75-0.0956 0.0543-0.0159 0.0383-0.0144 0.0399 5.0 \$1,089.83-\$89.83-0.0824 0.0551-0.0165 0.0386-0.0152 0.0398 4.0 \$1,073.25-\$73.25-0.0683 0.0559-0.0171 0.0388-0.0161 0.0398 3.0 \$1,056.01-\$56.01-0.0530 0.0568-0.0177 0.0391-0.0170 0.0398 2.0 \$1,038.08-\$38.08-0.0367 0.0578-0.0183 0.0395-0.0180 0.0398 1.0 \$1,019.42-\$19.42-0.0190 0.0589-0.0190 0.0398-0.0190 0.0398 0.5 \$1,009.80-\$9.80-0.00971 0.059417-0.009708738 0.04971 UNIVERSITY OF ILLINOIS...
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