**Bond Value 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.

- A Bond is a form of debt raised by the issuer of the bond.
- Issuer of the bonds pays interest to the purchaser for using his money.
- Terms associated with bonds: Face value, Coupon rate, Maturity, Redemption value, Market value.
- Face value and redemption value may be different but these are fixed and known.
- Market value of the bond may be different form the face value and keeps changing.

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.

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### Terms Associated with Bonds

**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

- The purchaser of the bonds gets regular interest payments as also the redemption amount on maturity.
- The interest on bond (also called coupon rate) is fixed at the time of its issue. But interest rate in the market keeps changing, and, therefore, market price of bond also changes.
- The market price or intrinsic value of a bond is different from the face value if the coupon rate is different from the market interest rate at that particular time.
- Market value is equal to PV of all the coupon receipts and redemption value discounted at the prevailing market rate.

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, 982.35,respectively.

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**YTM**

**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

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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.

- Current yield =coupon interest/current market price.
- E.g. if face value of a bond is Rs 50, coupon rate is 8% pa, and market price is Rs 40, then the current yield=4/40=0.1 or 10%
- Yield to Maturity(YTM) is that discount rate at which all future cash flows equal the present market value.

### 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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For two bonds X and Y having face value of Rs. 1.000, coupon rate of 10 per cent each, years to maturity is three and six years respectively.

Market value of bond X at YTM of 10 per cent is

100 PVIFA (10 per cent, 3) + 1.000 PVIF (10 per cent, 3) = 1,000

Market Value of Bond Y at YTM of 10 per cent is

100 PVIFA (10 per cent, 6) + 1,000 PVIF (10 per cent, 6) = 1,000

Now market value of bond X at YTM of 11 per cent is

100 PVIFA (11 per cent, 3) + 1,000 PVIF (11 per cent, 3) = 975

And Market Value of Bond Y at YTM of 11 per cent is

100 PVIFA (11 per cent, 6) + 1,000 PVIF (11 per cent, 6) = 958

Change in price for X on increasing YTM by 1 per cent is (1,000 – 975)/l,000 = 2.5 per cent Change in price for Y on increasing YTM by 1 per cent is (1,000 – 958)/1,000 = 4.2 per cent

Thus, longer-term bond is more sensitive to interest rate change than short-term bond.

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Consider a bond having a face value of Rs. 1,000 with a coupon rate of 10 per cent and maturity period of five years. Let the YTM be 10 per cent. Market price of the bond will be equal to Rs. 1,000.

A 1 per cent increase in YTM to 11 per cent changes price to Rs. 963.04 (100 PVIFA 11 per cent, 5 + 1000 PBV1F 11 per cent, 5), a decrease of 3.7 per cent.

A decrease of 1 per cent YTM to 9 per cent changes the price to Rs. 1,039 (100 PVIFA 9 per cent, 5 + 1,000 PVIF 9 per cent, 5) an increase of 3.9 per cent.

Thus, an increase in bond’s yield caused a price decrease that is smaller than the price increase caused by an equal size decrease in yield.

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A bond of face value of Rs. 1,000 par value X bond with a coupon rate of 12 per cent maturity period of six years and YTM of 10 per cent. The market value of the bond will be Rs. 1,087.

Consider another identical bond Y but with differing YTM of 20 per cent. The market value of this bond will be Rs. 734.

If the YTM increase by 20 per cent, i.e. YTM of bond X rises to 12 per cent (10 x 1.2) and bond Y rises to 24 per cent (i.e., 20 x 1.2) then the market value of both bonds will change to:

**Bond ABC: **120 PVIFA (12 per cent, 6) + 1,000 PVIF (12 per cent. 6) = Rs. 1,000

**Bond XYZ: **120 PVIFA (24 per cent, 6) + 1,000 PVIF (24 per cent, 6) = 638

Market value of ABC bond with a lower YTM decreased by 8 per cent whereas in case of XYZ bond with an higher YTM the decrease is 13 per cent.

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**Theorems for Bond Valuation**

- When the required Rate of Return is equal to the coupon rate, the value of the Bond is equal to its par value.
- When the required rate of return (Kd) is greater than the coupon rate, the value of the bond is less than its par value.
- When the required rate of return is less than the coupon rate, the value of the bond is greater than its par value etc.,
- Effect of change in market interest rate
- Effect of maturity period
- Bond price is inversely related to YTM
- Interest rate elasticity= %age change in price/%age change in YTM .This is always negative as both move in opposite direction.