Calculation of YTM – CS Professional Study Material

Chapter 16 Calculation of YTM – CS Professional Banking Law and Practice Notes is designed strictly as per the latest syllabus and exam pattern.

Calculation of YTM – CS Professional Banking Law and Practice Study Material

Question 1.
Attempt the following:
What are the various constituents of financial markets? How are these regulated? (Dec 2009, 5 marks)
Constituents of financial markets
Money Market : Money market is a place for trading in money and short term financial assets that are close substitutes to money. It provides an avenue for equilibrating the short term surplus funds of the lenders / investors with short term requirements of borrowers with call notice money forming a sizable portion of it. In India money market is regulated by RBI.

Capital Market: Capital market is the market for long term funds. It refers to all the facilities and institutional arrangements for borrowing and lending term funds. Demand of long term money capital arises mainly from the private sector manufacturing industries and government for economic development. The supply of funds comes mainly from the individual saver, corporate savings, banks, insurance companies, specialized financing agencies and the government.

Capital Markets are divided into Primary Market and Secondary Market. Primary market covers public, corporates, existing stock holders, etc. The Primary Market refers to the setup that helps the industry to raise funds by issuing different types of securities which are issued directly to the investors. Secondary Markets cover recognized stock exchanges and spot markets. Secondary market refers to the market for subsequent sale and purchase of securities.

Calculation of YTM - CS Professional Study Material

G-sec Market: Government Securities Market: This is the most dominant segment of debt marketing in terms of market capitalization, trading volume and number of participants. The market for government securities comprises the securities issued by the Central /State Governments and the state sponsored entities.

In the recent past local bodies like the municipal corporation have also begun to tap the debt market for funds. The Government mobilizes funds mainly through issue of dated securities and T – bills. The major investors in sovereign papers are the banks, insurance companies and Financial Institutions which generally do so to meet statutory requirements. Primary dealers are dealers who deal in Government securities.

Forex Market: Forex market refers to trading in currencies. It is the market where foreign currencies are traded, it is a round the clock market. Global markets where the change in volume of transactions and large transactions take place. The various segments of forex market are spot market, forward market and derivatives market. The main players in the fore market are the authorized dealers.

Following are the important instruments for raising funds from the market Following are Capital Market Instruments: (Governed by SEBI)
(i) Equity Shares: The equity share holders are the part owner of the company. These shares can be obtained either through the Initial Public Offerings (IPOs), Further/Follow-on-Public Offerings (FPOs), Qualified Institutions Placements (QIP)/Private Placements/Right Issues (Primary Markets) and can also be bought in the stock markets after the stocks are listed (Secondary Market). Issue of equity provide long-term capital in the company.

Calculation of YTM - CS Professional Study Material

(ii) Preference Share: Preference shareholders are entitled for fixed dividend over other equity shareholders and in case of surplus, preference is given in distribution of income, over equity shareholders. In case of liquidation, their claim would rank above the equity shareholders. Companies can issue redeemable preference shares.

(iii) Debenture: A debenture holder enjoys a fixed rate of interest payable half yearly/yearly, on a fixed date. The principal amount is repayable on the date of redemption. Debentures may be secured or unsecured. Debenture holders are creditors of the company.

(iv) Bond: A bond is issued in the form of a negotiable certificate/ document against indebtedness. Bonds and debentures are same. Government or Local Authorities issues bonds but corporate entities give name of such borrowings Debenture or Bond. Bonds are of various types based on security convertability etc.

Following are Money Market Instruments: (Governed by RBI)
(v) Commercial Paper (CP): CP is issued by companies with high credit ratings, in the form of promissory notes, at discount but repayable at par, to their holder at maturity.

(vi) Certificate of Deposit (CD): A CD is issued by a bank at discount to be redeemable at per on the maturity date. Minimum amount ₹ 1,00,000 and period 7 days to one year. CDs are issued in the form of usance promissory note.

Calculation of YTM - CS Professional Study Material

Question 2.
(a) Explain the following terms with reference to ‘Bonds’ :
(i) Coupon rate
(ii) Yield to Maturity
(iii) Redemption value. (June 2019) (3 marks)
(b) Based on the behaviour of the bond market, a set of theorems for bond valuation has been developed. State briefly these theorems used for the purpose of bond valuation. (9 marks)
(a) Terms with reference to Bonds
(i) Coupon Rate: The interest rate on the debt security is termed as coupon rate, (stated interest rate on a fixed income security / specified interest rate on a fixed maturity security which is fixed at the time of issue).

(ii) Yield to Maturity: It represents the overall return on a debt security if it is retained till maturity with an assumption that all interest payments will be reinvested at the current yield on the security. It represents the total income one can receive on a debt security say a bond. (It is the theoretical internal rate of return earned by an investor who buys the bond today at the market price, assuming that the bond will be held till maturity and that all coupon and principal payments are made on schedule).

(iii) Redemption value: The maturity value that a debt security holder(bond) may get. It may be at par value at premium(higher than par value) or at a discount (less than par value).

Calculation of YTM - CS Professional Study Material

(b) Theorems for Bond Value
Based on the behavior of the bond market a set of theorems for bond valuation has been put forward by some authors. The theorems are as under:

  1. When the required rate of return(‘r’) is equal to the coupon rate the value of the bond is equal to the par value.
  2. When the required rate of return is greater than its coupon rate the value of the bond will be less than its par value.
  3. When the required rate of return is less than the coupon rate the value of the bond will be greater than its par value.
  4. When the required rate of return is greater than coupon rate the discount on the bond decreases as it approaches maturity.
  5. When the required return is less than coupon rate the premium on the bond declines as it approaches maturity.
  6. Bond price is inversely proportional to it’s YTM.
  7. The longer the term to maturity, for a given differene between YTM and Coupon rate, the greater will be the change in price with changes in price.
  8. For an equal size increase or decrease in YTM, the bond price changes are not symmetrical. That is to say, in given maturity of a bond, the bond price change will be greater with a decrease in bond’s YTM, than the change in bond price with an equal increase in bond’s YTM.
  9. Other things being the same, for a given change in YTM, the percentage of price change in-respect of high coupon rate bond will be smaller than in case of bonds of low coupon rate.
  10. A change in YTM affects the bonds with higher YTM in comparison to bonds with lower YTM.

Calculation of YTM - CS Professional Study Material

Question 3.
Company has issued two series of bonds A and B. They have the following characteristics: (Dec 2019)

Bond A Bond B
Face Value ₹ 100 ₹ 100
Coupon Rate 14% 14%
Current market price ₹ 100 ₹ 100
Term to maturity 4 years 7 years
Coupon Payment Annually Annually

(i) Compute the YTM of Bond A and B.
(ii) If the interest rates fall by 1%, what would be the new market price of the bonds ?
(iii) What is the percentage change in the price of two bonds ? What did you notice regarding the percentage price change in case of Bonds A and B identical in all respects, except term to maturity ?

Calculation of YTM - CS Professional Study Material

Note :
1. Present Value (PV) interest factor of annuity (PVIFA), 13% for 4 years = 2.9745, 13% for 7 years = 4.4226.
2. Present value (PV) of ₹ 1 that is (1 + r)n where r = interest rate, n = number of period until receipt. Present value, where r (13%) and n (period) 4 years, PV = 0.613 and r (13%) and n (period) 7 years, PV = 0.425). (6 marks)
(i) Since the bonds are available at their respective face values, the YTM of the Bond A and B will be equal to their coupon rates, i.e. 14%.

(ii) After the interest rate fell by 1 %
The market price of Bond A is
= 14 × PVIFA (13%, 4) + 100 (13%, 4)
= 14 × 2.974+ (100 × 0.613)
= 41.636 + 61.30
= ₹ 102.94
The market price of Bond B is
= 14 × PVIFA (13%, 7) + 100 (13%, 7)
= 14 × 4.423 + (100 × 0.425)
= 61.922 + 42.50
= ₹ 104.42

(iii) Percentage price change in case of Bond A is
= \(\frac{102.94-100}{100}\)
= 2.94%
Percentage price change in case of Bond B is
= \(\frac{104.42-100}{100}\)
= 4.42%
We observe that for a decrease in YTM by 1 % the bond having longer term to maturity experience a price change that is more than the price change for a bond that is having a shorter term to maturity.

Calculation of YTM - CS Professional Study Material

Question 4.
From the following information, calculate: (Aug 2021, 6 marks)
(i) Market Value at given YTM and
(ii) Duration of the Bond.
Bond Face Value ₹ 1,000/-.
Coupon: 7%.
Maturity: 5 Years YTM: 9%
Present Value Interest Factor for an-Annuity @ 7% / 5 Years = 4.1002. Present Value Interest Factor for Single Cash Flows @ 7%.
1st Year : 0.9346
2nd Year : 0.8734
3rd Year : 0.8163
4th Year : 0.7629
5th Year : 0.7130
(i) The Market Value at YTM of 9%
= 70 (4.1002)+ 1000 (0.7130)
= 287.014
= 1000.014

(ii) Duration of bond is calculated as under:

Year Cash Flow PV Factor Present Value @7% Proportion of Bond Value Proportion of Bond value x time year
1 70 0.9346 65.4220 0.0654 0.0654
2 70 0.8734 6101380 0.0611 0.1222
3 70 0.8163 57.1410 0.0571 0.1713
4 70 0.7629 53.1410 0.0534 0.2136
5 1070 0.7130 762.9100 0.7628 3.814
1000.0140 4.3865

Hence, the Duration of the Bond is 4.3865.

Calculation of YTM - CS Professional Study Material

Question 5.
Consider a ₹1,000 par value bond, whose current market price is ₹ 850/-. The bond carries a coupon rate of 8 percent and has a maturity period of nine years. What would be the rate of return that an investor earns if he purchases the bond and holds it until maturity? (6 marks)

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