HOW MUCH SHOULD YOU PAY FOR THE BOND? 








Johnson
Company issues a $1000, 3year bond with annual interest 


at 8%. Can you sketch out the cash flows for this
situation? 









0 
1 
2 
3 
INTEREST 

80 
80 
80 
FACE AMOUNT 



1,000 





Because a bond
is a contract, we know exactly how much money 



will be paid
to the investor. The cash flows
consist of interest each 


year plus the
return of face value at the end of three years. Note that 


these cash
flows are determined by the contractual interest rate
(8%) 


and the face value of the bond. 









As we have
discussed in class, the investor might pay more or less 


than $1000 for
this bond. If the investor pays less
than $1,000 



for this bond,
the investor will earn a yield of more than 8%. 








Example 1: The 8% bond shown
above is issued in a market that 


demands an 8%
return. In other words, the
prevailing market rate is 


8%. Our 8% bond goes into a market where
competing bonds 



are also
offering 8%.
How much would our bond sell for 



assuming that the market
rate is also 8%? 









Strategy: discount the cash flows of our bond at the
market rate 



of interest (8%). 









PV of the $80 annuity 
$206.17 
This is $80 * IF 3 years @ 8% 
PV of the $1,000 face
amount 
$793.83 
This is $1,000 * IF 3 years @ 8% 
The 8% bond sold to yield
8% sells for 
$1,000.00 
Add the two figures. 






Conclusion: in an 8% market, our 8% bond will sell for 




$1000 









Example 2: The 8% bond is sold
in a 




market that demands
10%. How much will our bond 




sell for, assuming
investors wish to earn 10%? 









Strategy: discount the cash flows of our bond 




at the market rate of
interest, which is 10%. 









PV of the $80 annuity 
$198.95 
This is $80 * IF 3yrs @ 10% 
PV of the $1,000 face
amount 
$751.31 
This is $1,000 * IF 3 yrs @ 10% 
The 8% bond sold to yield
10% sells for 
$950.26 
Add the two figures. 






Conclusion: the bond must sell for 950.26 in order to 




yield 10%. 









Can you PROVE
that $950.26 will result in a 10% yield? 








Example 3: The 8% bond is sold
in a market that demands 



only 6%. Our bond should sell at a premium, right? 




How much will the bond
sell for in a 6% market? 









PV of the $80 annuity 
$213.84 
Use $80 * IF 3 yrs @ 6% 
PV of the $1,000 face
amount 
$839.62 
Use $1000 * IF 3 yrs @ 6% 
The 8% bond sold to yield
6% sells for 
$1,053.46 
Add the two figures. 






Conclusion: if the bond sells for 1053.46, the buyer
of 




that bond earns a 6%
yield. 









Prove that this is the
correct amount to pay for this 




8% bond to earn only 6%. 








