An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures
ID: 2614558 • Letter: A
Question
An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.3%. Bond C pays a 12% annual coupon, while Bond Z is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 9.3% over the next 4 years, calculate the price of the bonds at each of the following years to maturity. Round your answer to the nearest cent. Years to Maturity Price of Bond C Price of Bond Z
4 Price of bond c Price of bond z
3
2
1
0
Explanation / Answer
Years to maturity Price of Bond C Price of bond Z 4 $ 1,086.90 $ 700.68 3 $ 1,067.98 $ 765.84 2 $ 1,047.30 $ 837.07 1 $ 1,024.70 $ 914.91 0 $ 1,000.00 $ 1,000.00 Working: Bond C: a. 4 years to Maturity Par Value $ 1,000 Annual Coupon $ 1,000 x 12% = $ 120 Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.093)^-4)/0.093 i 9.3% = 3.2185 n 4 Present Value of single 1 = (1+i)^-n Where, = (1+0.093)^-4 i 9.3% = 0.7007 n 4 Present Value of coupon $ 120 x 3.2185 = $ 386.22 Present Value of Par value $ 1,000 x 0.7007 = $ 700.68 Current Price $ 1,086.90 b. 3 years to maturity Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.093)^-3)/0.093 i 9.3% = 2.518 n 3 Present Value of single 1 = (1+i)^-n Where, = (1+0.093)^-3 i 9.3% = 0.766 n 3 Present Value of coupon $ 120 x 2.5178 = $ 302.14 Present Value of Par value $ 1,000 x 0.7658 = $ 765.84 Current Price $ 1,067.98 c. 2 years to maturity Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.093)^-2)/0.093 i 9.3% = 1.7520 n 2 Present Value of single 1 = (1+i)^-n Where, = (1+0.093)^-2 i 9.3% = 0.8371 n 2 Present Value of coupon $ 120 x 1.7520 = $ 210.24 Present Value of Par value $ 1,000 x 0.8371 = $ 837.07 Current Price $ 1,047.30 d. 1 year to maturity Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.093)^-1)/0.093 i 9.3% = 0.9149 n 1 Present Value of single 1 = (1+i)^-n Where, = (1+0.093)^-1 i 9.3% = 0.9149 n 1 Present Value of coupon $ 120 x 0.9149 = $ 109.79 Present Value of Par value $ 1,000 x 0.9149 = $ 914.91 Current Price $ 1,024.70 e. 0 year to maturity Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.093)^-0)/0.093 i 9.3% = 0 n 0 Present Value of single 1 = (1+i)^-n Where, = (1+0.093)^-0 i 9.3% = 1 n 0 Present Value of coupon $ 120 x 0 = 0 Present Value of Par value $ 1,000 x 1.0000 = $ 1,000.00 Current Price $ 1,000.00 Bond Z a. 4 Years to maturity Price of Bond 1000 x (1.093^-4) = $ 700.68 b. 3 Years to maturity Price of Bond 1000 x (1.093^-3) = $ 765.84 c. 2 Years to Maturity Price of Bond 1000 x (1.093^-2) = $ 837.07 d. 1 Year to maturty Price of Bond 1000 x (1.093^-1) = $ 914.91 e. 0 year to maturity Price of Bond 1000 x (1.093^-0) = $ 1,000.00
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