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Bond pricing

 

  • Bonds are either zero coupon bonds (having no interest payments) or coupon bonds
  • (with periodic interest payments
  • The price of a bond is the present value of all the coupon payment and the final principal payment received at the end of its life. 

                       

 

  • B-  the bond price
  • C-  coupon payment
  • r-  zero interest rate at time t
  • P-  bond principal
  • T-  time to maturity
  • The yield of a bond is the discount rate (applied to all future cash flows) at which the present value of the bond is equal to its market price
    • Yield to Maturity = Investor’s Required Rate of Return
  • The par yield is the coupon rate at which the present value of the cash flows equal to the par value (principal value) of the bond
  • If we are looking at a semi-annual 5 year coupon bond with a par value of $100 then the coupon payment would be solved using the following equation: 


Question

A 10 year bond has a yield of 12% with a 7% coupon payment annually

What is the bond price?

What will happen if the yield of the bond increases by 1%.


Solution:
Use :

 

Or

 

Years

1

2

3

4

5

6

7

8

9

10

Yield

12%

 

 

 

 

 

 

 

 

 

Coupon payments

7

7

7

7

7

7

7

7

7

7

Principal payment

 

 

 

 

 

 

 

 

 

100

PV factor

0.892857

0.797193878

0.711780248

0.635518078

0.567427

0.506631

0.452349

0.403883

0.36061

0.321973

Total PVs

6.25

5.580357143

4.982461735

4.448626549

3.971988

3.546418

3.166445

2.827183

2.52427

34.45114

Bond price

71.74888

 

 

 

 

 

 

 

 

 

 





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