Appendix 7A Zero Coupon Bonds
Answers and Solutions
7A–1
Web Appendix 7A
Zero Coupon Bonds
Answers to Questions
7A-1 No, not all original issue discount bonds have zero coupons. Zero coupon bonds are just one type
of original issue discount bond. Any nonconvertible bond whose coupon rate is set below the going
7A-2 Shortly after corporations began to issue zeros, investment bankers figured out a way to create
zeros from U.S. Treasury bonds, which at the time were issued only in coupon form. In 1982,
Salomon Brothers bought $1 billion of 12%, 30-year Treasuries. Each bond had 60 coupons worth
$60 each, which represented the interest payments due every 6 months. Salomon then in effect
clipped the coupons and placed them in 60 piles: the last pile also contained the now “stripped”
7A-3 Treasury zeros are not protected from price risk, because the principal is totally susceptible to
interest rate movements. You can see this by changing interest rates and seeing what happens to
7A–2
Answers and Solutions
Appendix 7A Zero Coupon Bonds
Solutions to Problems
7A-1 0 1 2 3 4
| | | | |
Accrued value 708.43 772.19 841.69 917.44 1,000.00
Interest expense 63.76 69.50 75.75 82.56
Tax savings (25%) 15.94 17.375 18.9375 20.64
7A-2 0 1 2 3 4
| | | | |
Accrued value 708.43 772.19 841.69 917.44 1,000.00
Interest income 63.76 69.50 75.75 82.56
Tax (35%) 22.32 24.33 26.51 28.90
I/YR = 9%
I/YR = ?
Appendix 7A Zero Coupon Bonds
Answers and Solutions
7A–3
7A-3 0 1 2 3 4 5
| | | | | |
PV = ? FV = 6,000,000
7A-4 Step 1: Find out what was paid for the bond:
PV = $1,000/(1.068)7 = $630.959.
7A-5 First find the yields on one-year and two-year zero-coupon bonds, so you can find the implied
rate on a one-year bond, one year from now. Then use this implied rate to find its price.
1-Year:
Using a financial calculator, enter the following data: N = 1; PV = -938.9671; PMT = 0; FV = 1000;
and then solve for I/YR = 6.5%.
7A-6 0 10 50
| • • • | • • • |
-87.2037
I/YR = 10%
7A–4
Answers and Solutions
Appendix 7A Zero Coupon Bonds
Step 1: Using a financial calculator, we find the PV of the zeros at Time 0 by entering the
following data:
Step 3: Now add the call premium:
1.10 × $142.0457 = $156.2503.
Step 4: Using a financial calculator, we can find the investor’s effective annual rate of return by
entering the following data: