Econ 340, Fall 2009
Problem Set 2
Chapter 3: Questions 1-2, Quantitative Problems 1-3, 11, 13, 14.
1. $2000 = $100/(1 + i) + $100/(1 + i)2 + . . . + $100/(1 + i)20 + $1000/(1 + i)20.
2. If there is a decline in interest rates, you would rather be holding long-term bonds because
their price would increase more than the price of the short-term bonds, giving them a higher
return. However, long-term bonds have a greater interest-rate risk. And, this answer really
depends on the duration of the bonds, not just there term to maturity. For example, a 5 year
coupon bond might be subject to less interest rate risk than a 4 year zero coupon bond.
Quantitative Problems
1. Calculate the present value of $1,000 zero-coupon bond with 5 years to maturity if the
yield to maturity is 6%.
Solution: PV = FV/(1 + i)n,
where FV = 1000, i = 0.06, n = 5
PV = 747.25
See Durationexamp.xls
3. Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the
following table: What relationship do you observe between yield to maturity and the current
market value?
Solution:
When yield to maturity is above the coupon rate, the bond’s current price is below its face value.
The opposite holds true when yield to maturity is below the coupon rate. For a given maturity,
the bond’s current price falls as yield to maturity rises. For a given yield to maturity, a bond’s
value rises as its maturity increases. When yield to maturity equals the coupon rate, a bond’s
current price equals its face value regardless of years to maturity.
Term
YTM
Current Price
Excel
3
5
$1,054.46
"=PV(5%,3,70,1000,0)"
3
7
$1,000.00
6
7
$1,000.00
9
5
$1,000.00
9
9
$880.10
