Chapter 8 Recommended End-of-Chapter Problems and Solutions
3.
If a corporate bond paid 9% interest, and you are in the 28% income tax bracket,
what rate would you have to earn on a municipal bond of equivalent risk and
maturity in order to be equally well off? Given that municipal bonds are often not
easily marketable, would you want to earn a higher or lower rate than the rate you
just calculated?
The after-tax yield on the taxable corporate bond is 6.48% = 9%(1 - 0.28) and is the
comparable rate of a tax-free municipal bond. If the muni were less marketable, investors
would pay less or require a higher rate of return (i.e., above 6.48%).
a.
Suppose that when issued, a dealer buys $500 million in face value of 5% coupon 20year U.S. Treasury bonds for the purposes of stripping into zero coupon bonds.
(a) How many new CUSIP numbers would the dealer request?
(b) How many $1,000 zero coupon bonds with 7.5 years to maturity would be
formed?
(c) How many $1,000 zero coupon bonds with 20.0 years to maturity would be
formed?
(d) In total, how many $1,000 zero coupon bonds are formed?
(e) What is the total in face value of all zero coupon bonds?
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b.
41 (because STRIP securities formed from last coupon payment and payment of par
take different CUSIP numbers)
coupon income each 6 months = (500 million)(.025) = $12.5 million or 12,500
$1,000 bonds
$500 million + $12.5 million = $512.5 million or 512,500 $1,000 bonds.
40(12,500) + 500,000 = 1,000,000
$1 billion
With reference to the CPI slide, (a) how much inflation occurred over the period
6/30/09 and 6/30/13, and (b) how much inflation was there over the first 10 months
of 2008?
(a) (233.504 - 215.693) / 215.693 = 8.2576%
(b) (216.573 - 210.0) / 210.0
= 3.1300%
c.
How much inflation was there between the end of September 2008 and the end of
September 2012?
(231.407 – 218.783)/218.783 = 5.7701%
d.
Consider a 1.6% coupon rate TIPS issued on the last day of March 2007. What was
its adjusted principal on the last day of September 2011?
1000 + 1000*(226.889 – 205.352)/205.352 = 1104.88
e.
The National Debt Held by the Public on 9/30/15 was $13.1 trillion. Roughly, how
much of this would be in the form of T-bills, T-notes, T-bonds, and TIPS?
T-bills: 13.1 (.10) = $1.31 trillion
T-notes: 13.1 (.60) = $7.86 trillion
T-bonds: 13.1 (.15) = $1.97trillion
TIPS:
13.1 (.10) = $1.31 trillion
f.
If the Total National Debt is $18.13 trillion and the interest on this debt currently
averages 2.35%, what is the total annual interest on this debt? Since 1% of $1
trillion is $10 billion,
annual interest = 18.13(10)2.35 = $426.06 billion
g.
At what marginal tax rate would a 5.9% taxable bond be comparable to a similar
4.7% municipal bond?
Rearranging the expression on the Municipal Bonds slide, we have
(ibt – iat)/ibt = (5.9 – 4.7)/4.7 = 1.2/4.7 = 25.5%
h.
Let us divide municipal debt into state and local. With regard to municipal debt at
the state level, Georgia is the 2nd least debt-ridden state. Georgia state debt is only
about $15 billion. Given that the population of Georgia is 9.8 million, (a) how much
state debt is that per citizen of Georgia? (b) If the average interest rate on this debt
is 2.7%/year, how much must be collected in state taxes each year per citizen of
Georgia to pay the interest on this debt?
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$15 billion/9.8 million = $1,530.62 per person
.027($1,530.62)= $41.33 per person per year
However, this is only part of the picture because we have not included municipal debt at
the local level.
i.
In 2014 Social Security receipts were $769 billion and administrative expenses were
$3.1 billion. Suppose that in 2014 the average balance in the Social Security Trust
Fund was $2.7 trillion. Then, in 2014, administrative expenses were what
percentage of: (a) the average balance in the Social Security Trust Fund, and (b)
Social Security receipts? Express in basis points.
(a) 0.0031/2.7000 = 0.001148 = 0.1148% = 11.48 basis points
(b) 0.0031/0.7690 = 0.004031 = 0.4031% = 40.31 basis points