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Face Value: Also known as the par value and stated on the face of the bond. It represents the amount borrowed by the firm, which it promises to repay after a specified period.
Coupon rate: A bond carries a specific rate of interest, which is also called as the coupon rate.
Maturity: A bond is issued for a specified period. It is to be repaid on maturity.
Redemption Value: The value, which the bondholder gets on maturity, is called the redemption value. A bond is generally issued at a discount (less than par value) and redeemed at par.
Market Value: A bond may be traded on a stock exchange. Market value is the price at which the bond is usually bought or sold in the market.
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Bond Value
A bond, whose par value is Rs. 1,000, bears a coupon rate of 12 per cent and has a maturity period of 3 years. The required rate of return on the bond is 10 per cent. What is the value of this bond?
Solution
Annual interest payable = 1,000 * 12% = 120
Principal repayment at the end of 3 years = Rs. 1,000
The value of the bond
= 120 (PVIFA 10%, 3 yrs) + Rs. 1,000 (PVIF 10%, 3 yrs)
= 120 (2.487)+1,000 (0.751)
= 298.44 + 751
= Rs. 1,049.44
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A bond, whose par value is Rs. 1000, bears a coupon rate of 12 per cent payable semi-annually and has a maturity period of 3 years. The required rate of return on bond is 10 per cent. What is the value of this bond?
Solution
Semi-annual interest payable = 1,000 x 12 per cent/2= 60
Principal repayment at the end of 3 years = Rs. 1,000
The value of the bond
= 60 (PVIFA 10%/2, 6 pds) + Rs. 1,000 (PVIF 10%/2, 6 pds) =
60 (5.0746) + 1,000 (0.746) = 304.48 + 746 = 1,050.48
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The face value of the bond is Rs. 1,000, coupon rate is 11 per cent, years to maturity is seven years. The required rate of return is 13 per cent, and then the present value of the bond is
110 x PVIFA (13 per cent, 7) + 1,000 (PVIF 13 per cent, 7)
110(4.423)+1,000 (0.425) = 911.53
One year from now, when the maturity period will be six years, the present value of the bond will be
110 x PVIFA (13 per cent, 6) + 1,000 (PVIF 13 per cent, 6)
110 (3.998) + 1,000 (0.480) = 919.78
Similarly, when maturity period is 5, 4, 3, 2, 1 the Bond value will become 929.87, 940.14, 952.71, 966.48, 982.35, respectively.
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Current yield = Coupon interest/current market price
If a bond of face value Rs. 1,000, carrying a coupon interest rate of 8 per cent, is quoted in the market at Rs. 800, then the
Current yield of the bond is = 8 per cent * 1,000/800 = 10 per cent
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YIELD-TO-MATURITY OF BOND
It is the rate of return earned by an investor, who purchases a bond and holds it until the maturity.
Numerical problems on YTM
Consider a Rs. 1,000 par value bond, whose current market price is Rs. 850/-. The bond carries a coupon rate of 8 per cent and has the maturity period of nine years. What would be the rate of return that an investor earns if he purchases the bond and holds until maturity?
Solution
If kd is the yield to maturity then,
850 = 80 (PVIFA kd per cent, 9 yrs) + 1,000 (PVIF kd, 9 yrs)
To calculate the value of kd, we have to try several values:
= 80 (PVIFA 12 per cent, 9) + 1,000 (PVIF 12 per cent, 9)
= 80x 5.328+ 1,000 x (0.361)
= 426.24 + 361 =787.24
Since, the above value is less than 850, we have to try with value less than 12 per cent. Let us try with
kd =10 per cent
= 80 (PVIFA 10 per cent, 9) + 1,000 (PVIF 10 per cent, 9) = 80
x 5.759 + 1.000 * 0.424 = 884.72
From the above it is clear that kd lies between 10% and 12%. Now we have to use linear interpolation in the range of 10% and 12%. Using it, we find that kd is equal to the following:
(884.72-850) / (884.72-787.24)
34.72 / 97.48 = 10%.+
.71=10.71%
Therefore, the yield to maturity is 10.71%
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