Bond Investment: Caiib Paper 1 (Module B), Unit 6
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So, here we are providing “Unit 6: Bond Investment” of “Module B: Business Mathematics” from “Paper 1: Advanced Bank Management (ABM)”.
The Article is Caiib Unit 6: Bond Investment
- Debt is a sum of money borrowed by one entity, namely the borrower from another entity, namely the lenders. Due to the unavailability of liquid cash, Governments, corporations(big and small) and individuals often raise debts to make payments for varied purposes.
- For instance, an organization may borrow from a bank or raise money from other sources to fund its working capital requirements. Another instance is a student purchasing an education loan from a bank to fund his/her education. This is a form of contract which allows the borrower to borrow money with the condition that the money is to be paid back at a later date(specified in the agreement), with added interest.
- Governments raise debts to cover their deficit finances which help pay for ongoing activities as well as major capital projects. This debt may be issued in the form of loans or by issuing bonds.
Bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest (the coupon) to use and/or to repay the principal at a later date, termed maturity. A bond is a formal contract to repay borrowed money with interest at fixed intervals (ex semi annual, annual, sometimes monthly).
Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure. Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in the company (i.e., they are owners), whereas bondholders have a creditor stake in the company (i.e., they are lenders). Another difference is that bonds usually have a defined term, or maturity, after which the bond is redeemed, whereas stocks may be outstanding indefinitely.
- 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.
How Do Bonds Work?
Consider a government bond as an example. Suppose the Indian Government raised money by selling 6 per cent coupon, 2012 maturity, and Treasury bonds. Each bond has a face value of Rupees 1,000/-. Because the coupon rate is 6 per cent, the government makes coupon payments of 6 per cent of Rupees 1,000 or Rupees 60 each year. When the bond matures in July 2012, the government must pay the face value of the bond, Rupees 1000, in addition to the final coupon payment.
Suppose you have purchased this bond in the year 2009. If you plan to hold this bond till maturity, then the cash flow is shown on the time line below. The initial cash flow is negative and equal to the price you have to pay for the bond. Thereafter the cash flows
equal the annual coupon payment, until the maturity date. On maturity you receive the face value of the bond, Rupees 1,000, in addition to the final coupon payment.
Dealers and brokers quote the figures or the prices which prevail in the bond market. This is essentially part of the debt market and you can see the prices quoted on the National Stock Exchange or NSE in the papers. Details such as the rate of interest, the year of maturity, price are reported in NSE website/ financial papers. A sample of some such trades is given as follows:
Bond Prices and Yields
In this example we examined the cash flows for a 6 per cent treasury bond. How much would you be willing to pay for this stream of cash flows? To find out we have to compare with the interest rate on similar securities prevailing at that point in time. Let us presume the interest rate on three year maturities offer a return of 5.6 per cent. Thus we use this rate as the discount rate to value the cash flows from the bond.
PV= 60/(1+r)+ 60/(1+r)^2+ 1060/(1+r)^2
Bond Prices are usually quoted as a percentage of their face value. Thus we can say that our 6 per cent treasury bonds are worth 101.077 per cent of face value, and its price would usually be quoted as 101.077.
As you can notice that the coupon or interest payments on bonds and debentures are an annuity. In other words, the holder of our 6 per cent treasury bond receives a regular stream of Rupees 60 for three years. Thus we can also use the annuity formula to value the coupon payments and then add on the present value of the final payment or final face value.
PV = PV (Coupons) plus PV (face value)
= PV (A, r, n) plus PV (face value)
=PV (60, 0.056,3) plus PV(1000)
=60*0.177584/0.056*1.177584 plus 1000divided by1.177584 is equal to 10.65504divided by 0.0659447 plus 849.19
=161.58 plus 849.19 is equal to 1010.77
If we need to value a bond of many years to run before maturity, it is usually better to use the annuity formula and separate the coupon or interest payments from the face value.
Bond Prices and Interest Rates
As interest rates change, so do bond prices. For example, suppose that investors demanded an interest rate of 6 per cent on 3 year Treasury bonds. What would be the price of the Treasury bond valued earlier? Just repeat the last calculation with a discount rate of r is equal to 0.06
PV at 6%=60/1.06+60/(1.06)^2+1060/(1.06)^3
Thus when the interest rate is the same as the coupon rate (6% in our example), the bond sells for its face value.
Now if, we discount the cash flows at a rate higher than the bond’s coupon rate, the bond is worth less than its face value. Let us see the following example.
Investors will pay Rupees 1,000 for a six per cent 3 year Treasury bond, when the interest rate is 6 per cent. Suppose that the interest rate is 10% when coupon is 6%. Now what is the value of the bond? We just repeat our initial calculation but with r is equal to 0.10
The bond sells for 90.055 per cent of face value.
We conclude that
- When the market interest rate exceeds the coupon rate, bonds sell for less than face value;
- When the market interest rate is below the coupon rate, bonds sell for more than face value.
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?
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%.+
Therefore, the yield to maturity is 10.71%
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