**Debt**

DEBT means a sum of money due by certain and expresses agreement. In a less technical sense, it means a claim for money. Loans from banks or financial institutions are one of the popular forms of debt.

**Bonds**

Debt capital consists of mainly bonds and debentures. The holder of debt capital does not receive a share of ownership of the company when they provide funds to the firm. Rather, when a company first issues debt capital, the providers of debt capital purchase a debenture, which involves lending money to the firm. In return for loaning this money, bond holders have a right to certain guaranteed payments during the life of the bond.

For example : a company issued a bond of a face value of Rs. 100 carrying a coupon rate of 10 per cent for ten years. This entitles the bondholder to receive Rs. 10 (10 per cent of Rs. 100) for ten years as interest. At the end of tenth year, the bondholder is also entitled to receive back the invested amount of Rs. 100. Irrespective of the level of profits or losses, which company makes during that period of ten years, the bondholder is entitled to receive the coupon interest during that period.

**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.

………………………………………………………………………………………………………………**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

………………………………………………………………………………………………………………

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.**…………………………………………………………………………………………………………**

**CURRENT YIELD ON BOND**

It measures the rate of return earned on a bond, if it is purchased at its current market price and if the coupon interest is received.

**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

………………………………………………………………………………………………………………

**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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