Question

Assume you have a 1-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 8% coupon rate and pays the $80 coupon once per year. The third has a 10% coupon rate and pays the $100 coupon once per year. a. If all three bonds are now priced to yield 8% to maturity, what are their prices? (Round your answers to 2 decimal places. Omit the "$" sign in your response.) 10% Coupon Current prices Zero Coupon $ 8% Coupon $ b. If you expect their yields to maturity to be 8% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each? (Round your answers to 2 decimal places. Omit the "$& %" signs in your response.) Zero Coupon 8% Coupon 10% Coupon Current prices Pre-tax rate of return After-tax rate of return c. If you expect their yields to maturity to be 7% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each? (Round your answers to 2 decimal places. Omit the "$& %" signs in your response.) Zero Coupon 8% Coupon 10% Coupon Current prices Pre-tax rate of return After-tax rate of return

Answer 1

a)

8% Based on finite GP 2 a) Zero Coupon 8% Coupon 10% coupon YTM 4 Coupon 80 100 5 YTM Multiple for Coupon 6.71 6.71 6 YTM Multiple for Face Value 0.46 0.46 0.46 7 Value of Coupon 0 $ 536.81 $ 671.01 8 Value of Face Value 463.19 $ 463.19 $ 463.19 9 Current Price $ 463.19 $ 1,000.00 $ 1,134.20 11

b)

12 b) 8% Based on finite GP 15 Coupon 16 Tax Rate 17 Post Tax Coupon 18 Coupon Received 19 YTM Multiple for Coupon 20 YTM Multiple for Face Value 21 Value of Coupon 22 Value of Face Value 23 Current Price 24 Capital Gain 25 Capital Tax Rate 26 Post Tax Cap Gain 27 Total Gain 28 Pre Tax ROI 29 Post Tax ROI Zero Coupon 8% Coupon 10% coupon YTM 0 80 100 30% 30% 30% - $ 56.00 $ 70.00 - $ 56.00 $ 70.00 6.25 6.25 0.50 0.50 0.50 - $ 499.75 $ 624.69 500.25 $ 500.25 $ 500.25 500.25 $ 1,000.00 $ 1,124.94 37.06 S - $ (9.26) 20% 20% 20% 29.64 $ - $ (9.26) 29.64 $ 56.00 $ 60.74 8.0% 8.0% 8.0% 6.4% 5.6% 5.4%

c)

32 33 C) 0 7% Based on finite GP 36 Coupon 37 Tax Rate 38 Post Tax Coupon 39 Coupon Received 40 YTM Multiple for Coupon 41 YTM Multiple for Face Value 42 Value of Coupon 43 Value of Face Value 44 Current Price 45 Capital Gain 46 Capital Tax Rate 47 Post Tax Cap Gain 48 Total Gain 49 Pre Tax ROI 50 Post Tax ROI Zero Coupon 8% Coupon 10% coupon YTM 80 100 30% 30% 30% $ 56.00 $ 70.00 • $ 56.00 $ 70.00 6.52 6.52 0.54 0.54 0.54 . $ 521.22 $ 651.52 543.93 $ 543.93 $ 543.93 543.93 $ 1,065.15 $ 1,195.46 80.74 $ 65.15 $ 61.26 20% 20% 20% 64.59 $ 52.12 $ 61.26 64.59 $ 108.12 $ 131.26 17.4% 14.5% 14.2% 13.9% 10.8% 11.6%