Interest Rates and Bond
Valuation
Chapter
Seven
Problem Set - Bonds
1. You want to purchase a 182 day Treasury Bill with a $500,000 face
value. If the Bond Equivalent Yield (BEY) is 4.5%, how much
would you pay for the T Bill? ($489,027.04)
2. How much interest will you earn if you hold the T Bill in Problem 1
until the T Bill matures? ($10,972.96)
3. Now assume that you need to sell the T Bill from Problem 1 after
holding it for 50 days. At the date of sale, the BEY has fallen to
4.25%. What is the sale price of the T Bill? ($492,431.40)
4. How much interest did you earn, if you held the T Bill in Problem 1
for 50 days and sold it when the BEY had fallen to 4.25%?
($3,404.36)
Problem Set - Bonds
5. A little algebra will show us that the BEY yield on a T Bill is equal to
 FaceValue  PV  B
BEYT Bill  

PV

n
Based on this, what is the BEY for a 91 day T Bill with a $100,000
face value and a current market price of $98,526.16? (6%)
6. A 5 year bond has a $50,000 face value, an 8% coupon paid
annually and a YTM of 10%:
1. What is the market price of the bond? ($46,209.21)
2. If you hold the bond for one year and then sell it, what price will
you receive, assuming no other change? ($46,830.13)
3. Decompose the YTM of 10% into its two components of
1. Current Yield (8.66%)
2. Capital gain or loss (1.34%)
4. What will happen to the market price of the bond if the YTM
rises by 1% shortly after you purchase it? ($44,456.15)
Problem Set - Bonds
7. We know that the price of long bonds with low coupons is more
affected by a change in YTM than is the price of short bonds with
high coupons. The reason for this is that cash flows that are further
away from today are more affected by a change in the discount rate
than are cash flows that are close to today. To make this concept
more concrete, in this problem we want to focus just on the effect of
the coupon as a stabilizing device. We do it by analyzing two
bonds. Bond A is a $1,000 bond with a 15% coupon and three
years to maturity. Bond B is a $1,000 bond with a 5% coupon and
three years to maturity. For each bond, calculate the percentage of
the bond’s total cash flows that occur prior to the bond’s maturity
date. Bond A – 20.69% Bond B – 8.70%
Problem Set - Bonds
8. You purchased a ten year, $20,000 bond at a price of
$19,060. If the bond has a coupon of 7%, what is the
bond’s YTM? (7.69%)
9. Assume that you purchase a three year, $10,000 bond
with a 7% coupon at a price of $9,742.29. You intend to
hold the bond till its maturity. One day after you
purchase the bond, market yields fall to 6%. Calculate
the yield that you actually earn, if you hold the bond to
maturity. (7.87%)
Problem Set – Bonds
10. You want to purchase a ten year, $5,000 Government of
Canada bond carrying a 9.25% coupon, paid twice a
year. If the YTM on similar bonds is 8%, what is the fair
market price of the bond? ($5,424.70)