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  1. 1. LIVE PROJECT TO CALCULATE THE PRESENT VALUE AND YTM OF THE BOND Submitted by:- Mayuri Gariba Mudit Agrawal Nikhil Bakre Nikita Agrawal Pooja Zaveri   Submitted to:- MRS. Prashant Jain Faculty(F.M) 21/10/2008 PRESENT VALUE AND YTM
  2. 2.   Objective   Introduction   Formula   Data Calculation   21/10/2008 PRESENT VALUE AND YTM
  3. 3. <ul><li>To calculate Present Value(P O ) and Yield to Maturity(YTM) of a Bond </li></ul>21/10/2008 PRESENT VALUE AND YTM
  4. 4. <ul><li>BONDS:- </li></ul><ul><li>In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and is obliged to repay the principal and interest (the coupon) at a later date. </li></ul><ul><li>Bonds and stocks are both securities, but the major difference between the two is that stock-holders are the owners of the company whereas bond-holders are lenders to the issuing company. </li></ul>21/10/2008 PRESENT VALUE AND YTM
  5. 5. 21/10/2008 PRESENT VALUE AND YTM <ul><li>Another difference is that bonds usually have a defined term, or maturity, after which the bond is redeemed, whereas stocks may be outstanding indefinitely. </li></ul><ul><li>An exception is a consol bond, which is a perpetuity </li></ul><ul><li>(i.e., bond with no maturity). </li></ul>
  6. 6. 21/10/2008 PRESENT VALUE AND YTM
  7. 7. <ul><li>FACE VALUE:- </li></ul><ul><li>The face value of bonds usually represents the principal or redemption value . </li></ul><ul><li>  </li></ul><ul><li>Interest payments are expressed as a percentage of face value. </li></ul><ul><li>Before maturity, the actual value of a bond may be greater or less than face value, depending on the interest rate payable and the perceived risk of default. </li></ul>21/10/2008 PRESENT VALUE AND YTM
  8. 8. <ul><li>  </li></ul><ul><li>As bonds approach maturity, actual value approaches face value. </li></ul><ul><li>  </li></ul><ul><li>Its also called as Par value . </li></ul><ul><li>A BOND is generally issued at the par value of Rs 100 and sometimes Rs 1000. </li></ul>21/10/2008 PRESENT VALUE AND YTM
  9. 9. <ul><li>Coupon rate or Interest :- </li></ul><ul><ul><li>The coupon or coupon rate of a bond is the amount of interest paid per year expressed as a percentage of the face value of the bond. </li></ul></ul><ul><li>Maturity:-   </li></ul><ul><li>The bond's maturity date refers to a future date on which the issuer pays the principal to the investor. </li></ul><ul><li>Bond maturities usually range from one day up to 30 years or even more. </li></ul><ul><li>  </li></ul>21/10/2008 PRESENT VALUE AND YTM
  10. 10. <ul><li>Redemption value:- </li></ul><ul><li>  </li></ul><ul><ul><ul><li>The value which the bond holder gets on maturity is called Redemption value. </li></ul></ul></ul><ul><ul><ul><li>A bond may be redeemed at par, at premium (more than par) or at discount (less than par). </li></ul></ul></ul><ul><li>  </li></ul>21/10/2008 PRESENT VALUE AND YTM
  11. 11. <ul><li>When a bond sells at a discount, YTM > current yield > coupon yield. </li></ul><ul><li>When a bond sells at a premium, coupon yield > current yield > YTM. </li></ul><ul><li>When a bond sells at par, YTM = current yield = coupon yield amt </li></ul>21/10/2008 PRESENT VALUE AND YTM
  12. 12. <ul><li>Present Value:- </li></ul><ul><li>P O = I (PVIFA kd,n ) + F (PVIF kd,n ) </li></ul><ul><li>= I {(1+k) n – 1/k(1+k) n } + F {1/(1+k) n } </li></ul>21/10/2008 PRESENT VALUE AND YTM
  13. 13. <ul><li>  Yield to Maturity:- </li></ul><ul><li>  </li></ul><ul><li>YTM = {I+ (F-P)/n} / (F+P)/2 </li></ul><ul><li>Where:- </li></ul><ul><li>I = Annual Interest </li></ul><ul><li>kd = k = Required rate of return </li></ul><ul><li>n = Maturity period of bond </li></ul><ul><li>P o = Present Value of bond </li></ul><ul><li>F = Par value repayable at the maturity </li></ul><ul><li>P = Current market price of the bond </li></ul>21/10/2008 PRESENT VALUE AND YTM
  14. 14. 21/10/2008 PRESENT VALUE AND YTM Bond Holder Company name Mkt price (P) Annual Interest (I) ROR(kd = k ) Maturity period(n) Face value or Par value (F) Navin Shah Bank of Baroda 101.00 8.95% 10% 10yrs 1000 Hariom Gupta BSES Ltd. 96.00 5.95% 7% 15yrs 1000 Ankit Agrawal Canara bank 126.00 9.00% 11% 15yrs 1000 Narendra Jain CITICORP FINANCE LIMITED 195.00 10.25% 8% 3yrs 1000 Sumeet Natwani EXIM BANK 86.00 9.04% 10% 5yrs 1000
  15. 15. <ul><li>Present Value:- </li></ul><ul><li>P O = I (PVIFA kd,n ) + F (PVIF kd,n ) </li></ul><ul><li>= I {(1+k) n – 1/k(1+k) n } + F {1/(1+k) n } </li></ul><ul><li>= 89.5{(1+0.10) 10 - 1/0.10(1+0.10) 10 } </li></ul><ul><li>+1000{(1/(1+0.10) 10 } </li></ul><ul><li>= 3737. 50 </li></ul>21/10/2008 PRESENT VALUE AND YTM
  16. 16. <ul><li>  Yield to Maturity:- </li></ul><ul><li>  </li></ul><ul><li>YTM = {I+ (F-P)/n} / (F+P)/2 </li></ul><ul><li>= {89.5 + (1000-101)/10} / </li></ul><ul><li>(1000+101)/2 </li></ul><ul><li>= 179.4/550.5 </li></ul><ul><li>= 0.32 </li></ul>21/10/2008 PRESENT VALUE AND YTM
  17. 17. 21/10/2008 PRESENT VALUE AND YTM