CHAPTER 5
ANSWERS TO "DO YOU UNDERSTAND" TEXT QUESTIONS
1. Why is a dollar today worth more to most people than a dollar received at a future date?
Solution: Investing means deferring consumption. Deferred consumption has an opportunity cost. In the
absence of risk, the minimum return must at least compensate the investor for this opportunity cost. Thus
a future dollar should be discounted by at least this rate, and a present dollar invested for at least this rate.
2. If you were to invest $100 in a savings account offering 6 percent interest compounded quarterly, how
much money would be in the account after three years?
Solution: ($100)(1+(.06/4))12 = $119.56
3. Your rich uncle promises you $10,000 when you graduate from college. What is the value of this gift if
you plan to graduate in 5 years and interest rates are 10%?
Solution:
PV 
$10,000
 $6209.21
1.105
1. When a bond’s coupon rate is less than the prevailing market rate on interest on similar bonds, will the
bond sell at par, a discount, or a premium? Explain.
Solution: The bond will sell at a discount because buyers in the secondary market will bid the price down
until the bond yields the market rate.
2. Under what conditions will the total return on a bond equal the promised yield?
Solution: If the investor receives all cash flows as and when promised by the issuer and reinvests them
consistently at the bond’s promised yield (yield to maturity at time of purchase), total return will equal
promised yield. If the issuer defaults on payments of interest or principal, if the investor consumes the
coupon payments rather than reinvesting them, or if the market interest rate at which coupon payments can
be reinvested deviates from promised yield, total return will not necessarily equal promised yield.
3. Using trial-and-error, find the yield to maturity of a bond with 5 years to maturity, par value of $1,000,
and a coupon rate of 8% (annual payments). The bond currently sells at 98.5% of par value.
Solution: The price of the bond is $985 = 0.985($1,000). Set up the known information in the bond
pricing formula and try different interest rates until the right side equals the left side:
5 $80
$1,000
$985  

t
(1  i )5
t 1 (1  i )
The yield to maturity is 8.38%.
4. An investor purchases a $1,000 par value bond with 15 years to maturity at $985. The bond pays $80
of interest annually. The investor plans to hold the bond for 5 years and expects to sell it at the end of the
holding period for 94% of its face value. What is this investor’s expected yield? Use the trial-and-error
method.
Solution: The current price is $985. The investor expects to sell after 5 years for $940. Thus the investor
expects $80/year for each of the next 4 years and $1020 in year 5. The rate that discounts these cash flows
to $985 is 7.95% (to 2 decimal places).
5. Suppose the investor in the previous question actually sells the bond for 102 percent of its face value.
What is her realized yield?
Solution: If she invests $985 in the bond, reinvests the annual $80 coupons, and sells the bond for $1020,
the rate necessary to discount the indicated cash flows back to $985 is 8.25%.
6. Suppose the investor in question 4 actually sells the bond for 102 percent of its face value and is able to
reinvest the coupon payments she receives at 7 percent annually. What is her total return?
Solution: If she invests $985 in the bond, reinvests the annual $80 coupons at 7% annually, and sells the
bond for $1020, she will accumulate $1480.06=terminal value of the bond plus $460.06 future value of the
interest payments. 1480.06/(1+i)5 = 985. Solving for i, total return (to 2 decimal places) is 8.48%.
1. Consider a 4-year bond selling at par with a 7% annual coupon. Suppose yields on similar bonds
increase by 50 basis points. Use duration (Equation 5.8) to estimate the percent change in the bond price.
Check your answer by calculating the new bond price.
Solution: 4 year, 7% annual coupon bond selling at par. Duration = 3624.32/1000 = 3.62. Per equation
5.8, (-3.62)(0.005/1.07)(100) = -1.69%. The increase in interest rates would actually decrease the bond’s
price by 1.67 % to $983.25, assuming a par value of $1000.
2. Define price risk and reinvestment risk. Explain how the two risks offset each other.
Solution: Price risk is the variability of the market price of the bond caused by its inverse movement with
interest rates, while reinvestment risk is the variability in return caused by varying reinvestment rates as
payments are received. As interest rates fall, bond prices rise but reinvestment yields decline. As interest
rates rise, bond prices fall but reinvestment yields increase.
3. What is the duration of a bond portfolio made up of two bonds: 37 percent of a bond with duration of
7.7 years and 63 percent of a bond with duration of 16.4 years?
Solution: The portfolio duration is the weighted-average duration of the component bonds:
7.7(.37) + 16.4(.63) = 13.18 years
4. How can duration be used as a way to rank bonds on their interest rate risk?
Solution: Duration is a measure of price variability, given a change in interest rates. The price risk varies
directly with the duration of the bond.
5. To eliminate interest rate risk, should you match the maturity or the duration of your bond investment to
your holding period? Explain.
Solution: Duration matching is a technique that eliminates interest rate risk. Duration matching matches the
duration of the bond to the investor’s holding period. When a bond’s duration matches the holding period, the
bond’s price risk directly offsets the bond’s reinvestment rate risk, thus eliminating interest rate risk.