In the previous article we had introduced debt market instruments, the purpose of this article is to give an insight into the different measures used to value debt instruments.

First of all let us start with a few terms that will be used. Face value refers to the value of the instrument. Market price refers to the current price the instrument is quoting at in a debt market. A 12% GOI-2008, has a face value of Rs 100 but it may be quoting Rs 103 in the secondary market, which is known as the market price.

The return on the debt market instrument is known as yield. There are different ways of looking at return. There will always be the fixed return on the instrument that is known as the coupon rate. For example a 12% GOI-2008, G-SEC, give 12% interest per annum paid bi yearly. This return is based on the face value and not on the market value. This rate of interest is also known as the coupon rate. The coupon rate is fixed and it does not vary with the life of the instrument and this is exactly the reason what makes the government securities attractive (or unattractive). Therefore, irrespective of what price the person buys a security the coupon rate will always be fixed (12% in the example).

The other low risk investment avenue is fixed deposits. Firstly, fixed returns are not as high as the interest rate offered in bonds. And secondly the return on the fixed deposits is always fixed. Therefore, in any scenario there is no opportunity for a price appreciation or depreciation. Depending on the macro environment the government cuts or hikes interest rates (lending rates). This causes the bank to adjust their borrowing and lending rate. A bank has to always lend at a rate greater than it borrows at. This is known as the spread and this is a major source of the banks income. For example if money is available to the bank at 10% it may it lend at 11%. In case the lending rates decline then most likely the banks pass on the advantage to the borrowers (assuming strong competitive forces) and vice-versa for a hike in borrowing rates. In this scenario the G-SEC become attractive as they continue to offer 12% returns.

The problem with the coupon is that it is not based on the market price. But for someone who buys the fixed income instrument from the market it does not give a realistic picture. Suppose the bond was bought at a market price greater than the face value, then the coupon rate though constant will mean lower returns for the investor. For example if a G-Sec with 12% coupon was bought at a market price of Rs 104, the return or the current yield will be much lower.

Coupon Rate
Current Yield = -------------- * 100
Purchase Price

Suppose Ramesh buys 12% GOI-2008 at Rs 102 and Suresh buys the same instrument at Rs 104 then be current yield for Ramesh 11.76% is and that for Suresh is 11.53%.

Yield to maturity (YTM) measures the effective return on a bond that is bought at market price. For a given bond we know the market price, the face value and coupon rate therefore, we determine what rate of discount will bring the future cash flows to the present market value and this is the actual return on the instrument.

YTM is discount rate that equates present value of the all the cash inflows to the cost price of the government security (market price), which is actually the Internal Rate of Return of the government security. The concept of Yield to Maturity assumes that the future cash flows are reinvested at the same rate at which the original investment was made.

The Net Present Value (NPV) can be calculated as follows:

I/2 I/2 I/2 I/2+FV
Market price = ---- + ---- + ---- ........... ------
(1+r) (1+r)^{2} (1+r)^{3} (1+r)^{n}

where I/2 = annual interest rate payable half yearly

r = discount rate or YTM

n = number of half years remaining to maturity

The approximate Yield to Maturity (YTM) can be computed as per the formula given below:

YTM* I+(F-M)/N
---------- = ---------
*(Approx.) (F+M)/2

where

I = Annual interest Rate

F = Face value of bond

M = Market price of the bond

N = Number of years to maturity

Suppose Ramesh buys 12% GOI-2008 at Rs 102 and Suresh buys the same instrument at Rs 104 then the yield to maturity using approximation is

For Ramesh,

12+(100-102)/7
YTM = --------------- = 11.59%
(100+102)/2

For Suresh,
12+(100-104)/7
YTM = -------------- = 11.20%
(100+104)/2

**Maturity Date** |
**Coupon** rate (%) |
**Last traded** quantity (Nos) |
**Last traded** price (Rs) |
**Coupon** (%) |
**Current** yield (%) |
** Years to** Maturity |
**Yield To** Maturity (%) |

1-Sep-02 |
11.15 |
3,000 |
103.52 |
11.15 |
10.77 |
1.5 |
8.65 |

23-Mar-04 |
12.50 |
500 |
110.41 |
12.50 |
11.32 |
3.0 |
8.53 |

22-Apr-05 |
9.90 |
1,000 |
105.31 |
9.90 |
9.40 |
4.0 |
8.35 |

10-Apr-06 |
11.68 |
500 |
112.55 |
11.68 |
10.38 |
5.0 |
8.62 |

28-May-07 |
11.90 |
500 |
114.38 |
11.90 |
10.40 |
6.0 |
8.86 |

31-Aug-08 |
11.40 |
500 |
112.65 |
11.40 |
10.12 |
7.0 |
9.02 |

7-Apr-09 |
11.99 |
500 |
114.20 |
11.99 |
10.50 |
8.0 |
9.53 |

28-Jul-10 |
11.30 |
1,000 |
111.95 |
11.30 |
10.09 |
9.0 |
9.41 |

29-Jan-11 |
12.32 |
500 |
114.90 |
12.32 |
10.72 |
10.5 |
10.14 |

Source NSE website
Price Interest rate relationship:

The price of a government security is inversely related to the market interest rate. As the interest rate increases price decreases and therefore, the yield increases. However, if the interest rates fall the G-Sec become expensive and therefore, the yield falls.

Therefore, if the market price is equal to face value of the government security, then the current yield, coupon yield and Yield to maturity will all be equal to the coupon rate or interest payable on government security.

Coupon rate = Yield to maturity if, Market price = Face value

If Market Price is less than the face value of the government security the current yield and yield to maturity will be higher than the coupon yield than the coupon rate.

Coupon rate < Yield to maturity if, Market price < Face value

- In cases where the market price of the government security/bond is more than its face value the current yield and Yield to maturity will be lower than the coupon rate.

Coupon rate > Yield to maturity if, Market price > Face value

Zero coupon bonds that comprise the majority of G-Secs, are also traded. The disadvantage of these instruments is that there are no regular cash flows. The only cash inflow takes place at maturity. But this translates to an advantage that the yield gets locked. This is due to the fact that while calculating YTM there is an implicit assumption that the cash flows are reinvested at the same interest rate. As interest rates are prone to fluctuations, the yield too is variable.

In the next article we will take up how different factors affect the valuation of bonds.
To read on various factors affecting valuation of debt instruments please click here.

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