Chapter 14 - Bond Prices and Yields
8. 9.
The bond price will be lower. As time passes, the bond price, which is now above par value, will approach par.
Yield to maturity: Using a financial calculator, enter the following: n = 3; PV = ?953.10; FV = 1000; PMT = 80; COMP i This results in: YTM = 9.88%
Realized compound yield: First, find the future value (FV. of reinvested coupons and principal:
FV = ($80 * 1.10 *1.12. + ($80 * 1.12. + $1,080 = $1,268.16
Then find the rate (yrealized . that makes the FV of the purchase price equal to $1,268.16:
$953.10 ? (1 + yrealized .3 = $1,268.16 ? yrealized = 9.99% or approximately 10%
Using a financial calculator, enter the following: N = 3; PV = ?953.10; FV = 1,268.16; PMT = 0; COMP I. Answer is 9.99%.
10.
a. Zero coupon Current prices
b. Price 1 year from now Price increase Coupon income Pretax income
Pretax rate of return Taxes*
After-tax income
After-tax rate of return
c. Price 1 year from now Price increase Coupon income Pretax income
Pretax rate of return Taxes?
After-tax income
After-tax rate of return $463.19
$500.25 $ 37.06 $ 0.00 $ 37.06 8.00% $ 11.12 $ 25.94 5.60%
$543.93 $ 80.74 $ 0.00 $ 80.74 17.43% $ 19.86 $ 60.88 13.14%
8% 10% coupon coupon $1,000.00 $1,134.20
$1,000.00 $1,124.94 $ 0.00 ? $ 9.26 $ 80.00 $100.00 $ 80.00 $ 90.74 8.00% 8.00% $ 24.00 $ 28.15 $ 56.00 $ 62.59 5.60% 5.52%
$1,065.15 $1,195.46 $ 65.15 $ 61.26 $ 80.00 $100.00 $145.15 $161.26 14.52% 14.22% $ 37.03 $ 42.25 $108.12 $119.01 10.81% 10.49%
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Chapter 14 - Bond Prices and Yields
* In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year-end is
treated as a capital loss and therefore is not treated as an offset to ordinary income.
? In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary income (see part (b); the remainder of the price increase is taxed as a capital gain.
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Chapter 14 - Bond Prices and Yields
11. a. On a financial calculator, enter the following:
n = 40; FV = 1000; PV = –950; PMT = 40
You will find that the yield to maturity on a semiannual basis is 4.26%. This implies a bond equivalent yield to maturity equal to: 4.26% * 2 = 8.52% Effective annual yield to maturity = (1.0426)2 – 1 = 0.0870 = 8.70%
b. Since the bond is selling at par, the yield to maturity on a semiannual basis is the same as the semiannual coupon rate, i.e., 4%. The bond equivalent yield to maturity is 8%.
Effective annual yield to maturity = (1.04)2 – 1 = 0.0816 = 8.16%
c. Keeping other inputs unchanged but setting PV = –1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semiannual basis. 12.
Effective annual yield to maturity = (1.0376)2 – 1 = 0.0766 = 7.66%
Since the bond payments are now made annually instead of semiannually, the bond equivalent yield to maturity is the same as the effective annual yield to maturity. [On a financial calculator, n = 20; FV = 1000; PV = –price; PMT = 80]
The resulting yields for the three bonds are:
Bond Equivalent Yield
Bond Price =
Effective Annual Yield
$950 8.53% 1,000 8.00 1,050 7.51
The yields computed in this case are lower than the yields calculated with semiannual payments. All else equal, bonds with annual payments are less attractive to investors because more time elapses before payments are
received. If the bond price is the same with annual payments, then the bond's yield to maturity is lower.
13.
Bond
Price $400.00 500.00 500.00 385.54 463.19 400.00
Maturity (years. 20.00 20.00 10.00 10.00 10.00 11.91
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Equivalent YTM 4.688% 3.526 7.177 10.000 8.000 8.000
Chapter 14 - Bond Prices and Yields
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