HOW MUCH SHOULD YOU PAY FOR THE BOND?
Johnson Company issues a $1000, 3-year 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%.