Chapter 8 Solutions
1.
The price of a pure discount (zero coupon) bond is the present value of the par. Remember,
even though there are no coupon payments, the periods are semiannual to stay consistent
with coupon bond payments. So, the price of the bond for each YTM is:
a.
P = $1,000/(1 + .05/2)
20
= $610.27
b.
P = $1,000/(1 + .10/2)
20
= $376.89
c.
P = $1,000/(1 + .15/2)
20
= $235.41
2.
The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice
this problem assumes a semiannual coupon. The price of the bond at each YTM will be:
a.
P = $35({1 – [1/(1 + .035)]
50
} / .035) + $1,000[1 / (1 + .035)
50
]
P = $1,000.00
When the YTM and the coupon rate are equal, the bond will sell at par.
b.
P = $35({1 – [1/(1 + .045)]
50
} / .045) + $1,000[1 / (1 + .045)
50
]
P = $802.38
When the YTM is greater than the coupon rate, the bond will sell at a discount.
c.
P = $35({1 – [1/(1 + .025)]
50
} / .025) + $1,000[1 / (1 + .025)
50
]
P = $1,283.62
When the YTM is less than the coupon rate, the bond will sell at a premium.
We would like to introduce shorthand notation here. Rather than write (or type, as the case
may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to
abbreviate the equations as:
PVIF
R,t
= 1 / (1 +
r)
t
which stands for P
resent V
alue I
nterest F
actor
PVIFA
R,t
= ({1 – [1/(1 +
r)
]
t
} /
r
)
which stands for P
resent V
alue I
nterest F
actor of an A
nnuity
These abbreviations are short hand notation for the equations in which the interest rate and
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 Fall '08
 STAFF
 Interest Rates, Corporate Finance

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