# Bond and Percent

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• Published : November 5, 2012

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Bond P is a premium bond with a 12 percent coupon. Bond D is a 6 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 9 percent, and have five years to maturity. The current yield for Bonds P and D is percent and percent, respectively. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))|

If interest rates remain unchanged, the expected capital gains yield over the next year for Bonds P and D is percent and percent, respectively. (Do not include the percent signs (%). Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))|

Explanation:
To find the capital gains yield and the current yield, we need to find the price of the bond. The current price of Bond P and the price of Bond P in one year is:|
P:| P0 = \$120(PVIFA9%,5) + \$1,000(PVIF9%,5) = \$1,116.69|
|   |
| P1 = \$120(PVIFA9%,4) + \$1,000(PVIF9%,4) = \$1,097.19|
|   |
| Current yield = \$120 / \$1,116.69 = .1075 or 10.75%|
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| The capital gains yield is:|
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| Capital gains yield = (New price – Original price) / Original price| |   |
| Capital gains yield = (\$1,097.19 – 1,111.69) / \$1,116.69 = –.0175 or –1.75%| |   |
| The current price of Bond D and the price of Bond D in one year is:|
D:| P0 = \$60(PVIFA9%,5) + \$1,000(PVIF9%,5) = \$883.31|
|   |
| P1 = \$60(PVIFA9%,4) + \$1,000(PVIF9%,4) = \$902.81|
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| Current yield = \$60 / \$883.81 = .0679 or 6.79%|
|   |
| Capital gains yield = (\$902.81 – 883.31) / \$883.31 = +.0221 or +2.21%|
All else held constant, premium bonds pay high current income while having price depreciation as maturity nears; discount bonds do not pay high current income but have price appreciation as maturity nears. For either bond, the total return is still 9%, but this return is distributed differently between current income and capital gains|

One More Time Software has 9.2 percent coupon bonds on the market with nine years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. The current yield on the bonds is percent, the YTM is percent, and the effective annual yield is percent. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16.))|

Explanation:
The bond price equation for this bond is:|

P0 = \$1,068 = \$46(PVIFAR%,18) + \$1,000(PVIFR%,18)|

Using a spreadsheet, financial calculator, or trial and error we find:|
R = 4.06%|

This is the semiannual interest rate, so the YTM is:|

YTM = 2 × 4.06% = 8.12%|

The current yield is:|

Current yield = Annual coupon payment / Price = \$92 / \$1,068 = .0861 or 8.61%|
The effective annual yield is the same as the EAR, so using the EAR equation:|
Effective annual yield = (1 + 0.0406)2– 1 = .0829 or 8.29%|

Grohl Co. issued 11-year bonds a year ago at a coupon rate of 6.9 percent. The bonds make semiannual payments. If the YTM on these bonds is 7.4 percent, the current bond price is \$ . (Do not include the dollar sign (\$). Round your answer to 2 decimal places. (e.g., 32.16))|

Explanation:
To find the price of this bond, we need to realize that the maturity of the bond is 10 years. The bond was issued one year ago, with 11 years to maturity, so there are 10 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is:|

P = \$34.50(PVIFA3.7%,20) + \$1,000(PVIF3.7%,20) = \$965.10|

Kiss the Sky Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for \$1,045. At this price, the bonds yield 7.5 percent. The coupon rate on the bonds is percent. (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))|

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