Web Solutions: 5 – 37
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one type of original issue discount bond. Any nonconvertible bond whose coupon rate is
set below the going market rate at the time of its issue will sell at a discount, and its will
be classified (for tax and other purposes) as an OID bond.
5A-2 Shortly after corporations began to issue zeros, investment bankers figured out a way to
department of a bank and used as collateral for “zero coupon U.S. Treasury Trust
Certificates,” which are, in essence, zero coupon Treasury bonds. Treasury zeros are, of
course, safer than corporate zeros, so they are very popular with pension fund managers.
In response to this demand, the Treasury has also created its own “Strips” program,
which allows investors to purchase zeros electronically.
generally are not callable and because there are no coupon payments to reinvest, Treasury
zeros are completely protected against reinvestment risk (the risk of having to invest cash
flows from a bond at a lower rate because of a decline in interest rates).
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Solutions to Problems
5A-1 Year 0 1 2 3 4
Accrued value 708.43 772.19 841.69 917.44 1,000.00
Interest 63.76 69.50 75.75 82.56
Tax savings (40%) 25.50 27.80 30.30 33.02
Interest = Accrued valuet – Accrued valuet – 1.
Tax savings = Interest(T).
5.4%.
Web Solutions: 5 – 39
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5A-2 0 1 2 3 4
Accrued value 708.43 772.19 841.69 917.44 1,000.00
Interest 63.76 69.50 75.75 82.56
Tax savings (35%) 22.32 24.33 26.51 28.90
Cash flow -708.43 -22.32 -24.33 -26.51 +971.10
Enter the following data into your calculator to determine the price of each bond:
N = 4; I/YR = 9; PMT = 0; FV = 1000; PV = ? Solve for PV = $708.43.
Note that in Year 4, the investor receives the maturity value of the bond; however, he
must pay taxes on the interest income in Year 4. Thus, cash flow in Year 4 equals $1,000
– Taxes.
To solve for the IRR of this cash flow stream, using a financial calculator, enter the
individual cash flows into the cash flow register and solve for the IRR. IRR = 5.85%.
5A-4 Step 1: Find out what was paid for the bond:
PV = $1,000/(1.068)7 = $630.959.
Step 2: Determine the Year 1 accrued interest:
Web Solutions: 5 – 40
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5A-5 First find the yields on one-year and two-year zero coupon bonds, so you can find the
2-Year:
Using a financial calculator, enter the following data: N = 2; PV = -873.4387; PMT = 0;
FV = 1000; and then solve for I/YR = 7.0%.
Therefore, if the implied rate = X, then:
Using a financial calculator, enter the following data: N = 1; I/YR = 7.5; PMT = 0; FV =
1000; and then solve for PV = -$930.23.
5A-6 0 10 50
-87.2037 1,000
N = 50; I/YR = 5; PMT = 0; FV = 1000; and then solve for PV = $87.2037.
Step 2: Using a financial calculator, we can find the investor’s effective annual rate of
return by entering the following data:
N = 10; PV = -87.2037; PMT = 0; FV = 156.2503; and then solve for INOM/2 = 6.0055%.
Web Appendix 5D
The Pure Expectations Theory and Estimation of Forward
(1 + rT2)2 = (1.05)(1.06)
(1 + rT2)2 = 1.113
1 + rT2 = 1.055
rT2 = 5.5%.
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5D-4 r* = 2%; MRP = 0%; r1 = 5%; r2 = 7%; X = ?
X represents the one-year rate on a bond one year from now (Year 2).
(1.07)2 = (1.05)(1 + X)
05.1
1449.1
= 1 + X
X = 9%.
9% = r* + I2
9% = 2% + I2
7% = I2.
The average interest rate during the 2-year period differs from the 1-year interest rate
expected for Year 2 because of the inflation rate reflected in the two interest rates. The
inflation rate reflected in the interest rate on any security is the average rate of inflation
expected over the security’s life.