978-1259289903 Chapter 5 Solution Manual Part 1

CHAPTER 5

INTEREST RATES AND BOND

VALUATION

Answers to Concept Questions

1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury

2. All else the same, the Treasury security will have lower coupons because of its lower default risk, so

5. There are two benefits. First, the company can take advantage of interest rate declines by calling in an

6. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used

to establish the coupon rate necessary for a particular issue to initially sell for par value. Bond issuers

are equal only if the bond sells for exactly at par.

example, often must plan for pension payments many years in the future. If those payments are fixed

in dollar terms, then it is the nominal return on an investment that is important.

8. Companies pay to have their bonds rated because unrated bonds can be difficult to sell; many large

9. Junk bonds often are not rated because there would be no point in an issuer paying a rating agency to

assign its bonds a low rating (it’s like paying someone to kick you!).

10. The term structure is based on pure discount bonds. The yield curve is based on coupon-bearing issues.

11. Bond ratings have a subjective factor to them. Split ratings reflect a difference of opinion among credit

agencies.

if doing so would interfere with state government functions. At one time, this principle was thought

to provide for the tax-exempt status of municipal interest payments. However, modern court rulings

make it clear that Congress can revoke the municipal exemption, so the only basis now appears to be

historical precedent. The fact that the states and the federal government do not tax each other’s

13. Lack of transparency means that a buyer or seller can’t see recent transactions, so it is much harder to

determine what the best bid and ask prices are at any point in time.

The wide range coupon of coupon rates shows the interest rate when the bond was issued. Notice that

interest rates have evidently declined. Why?

company pays for a rating, it has the opportunity to make its case for a particular rating. With an

unsolicited rating, the company has no input.

16. A 100-year bond looks like a share of preferred stock. In particular, it is a loan with a life that almost

certainly exceeds the life of the lender, assuming that the lender is an individual. With a junk bond,

the credit risk can be so high that the borrower is almost certain to default, meaning that the creditors

are very likely to end up as part owners of the business. In both cases, the “equity in disguise” has a

used in valuing the cash flows from a bond.

since it provides periodic income in the form of coupon payments in excess of that required by

investors on other similar bonds. If the coupon rate is lower than the required return on a bond,

the bond will sell at a discount since it provides insufficient coupon payments compared to that

required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the

premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less

than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all

cases, the current yield plus the expected one-period capital gains yield of the bond must be equal

18. A long-term bond has more interest rate risk compared to a short-term bond, all else the same. A low

coupon bond has more interest rate risk than a high coupon bond, all else the same. When comparing

a high coupon, long-term bond to a low coupon, short-term bond, we are unsure which has more

interest rate risk. Generally, the maturity of a bond is a more important determinant of the interest rate

Solutions to Questions and Problems

1. The price of a pure discount (zero coupon) bond is the present value of the par. Remember, even

though there are no coupon payments, the periods are semiannual to stay consistent with coupon bond

payments. So, the price of the bond for each YTM is:

2. The price of any bond is the PV of the interest payments, plus the PV of the par value. Notice this

problem assumes a semiannual coupon. The price of the bond at each YTM will be:

a. P = $35({1 – [1/(1 + .035)]46 }/.035) + $1,000[1/(1 + .035)46]

P = $1,000.00

b. P = $35({1 – [1/(1 + .045)]46 }/.045) + $1,000[1/(1 + .045)46]

P = $807.12

c. P = $35({1 – [1/(1 + .025)]46 }/.025) + $1,000[1/(1 + .025)46]

P = $1,271.54

We would like to introduce shorthand notation here. Rather than write (or type, as the case may be)

the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the

equations as:

3. Here we are finding the YTM of a semiannual coupon bond. The bond price equation is:

P = $1,050 = $25.50(PVIFAR%,26) + $1,000(PVIFR%,26)

Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial

and error, we find:

4. Here we need to find the coupon rate of the bond. We need to set up the bond pricing equation and

solve for the coupon payment as follows:

P = $1,040 = C(PVIFA3.2%,25) + $1,000(PVIF3.2%,25)

Solving for the coupon payment, we get:

And the coupon rate is the annual coupon payment divided by par value, so:

5. The price of any bond is the PV of the interest payment, plus the PV of the par value. The fact that the

bond is denominated in euros is irrelevant. Notice this problem assumes an annual coupon. The price

of the bond will be:

6. Here we are finding the YTM of an annual coupon bond. The fact that the bond is denominated in yen

is irrelevant. The bond price equation is:

P = ¥103,250 = ¥4,900(PVIFAR%,18) + ¥100,000(PVIFR%,18)

Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial

and error, we find:

R = 4.63%

(h) is:

R = r + h

Approximate r = .048 – .027

rates, and inflation, is:

(1 + R) = (1 + r)(1 + h)

R = (1 + .018)(1 + .034) – 1

rates, and inflation, is:

(1 + R) = (1 + r)(1 + h)

h = [(1 + .121)/(1 + .076)] – 1

10. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest

rates, and inflation, is:

(1 + R) = (1 + r)(1 + h)

r = [(1 + .114)/(1 + .039)] – 1

With a zero coupon bond, the only cash flow is the par value at maturity. We find the present

value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent

to the YTM of a coupon bond, so:

P = $4,391.30

the price of the bond is:

P = $49(PVIFA1.90%,26) + $2,000(PVIF1.90%,26)

the price of the bond is:

P = $92.50(PVIFA1.95%,32) + $5,000(PVIF1.95%,32)

Bid price = (139.5156/100)



$1,000

Bid price = $1,395.156

The previous day’s ask price is found by:

Previous day’s asked price = Today’s asked price – Change

Previous day’s asked price = 139.5781 – .1406

Previous day’s dollar price = (139.4375/100)



$1,000

Previous day’s dollar price = $1,394.375

based on the asked price, so the current yield is:

Current yield = Annual coupon payment/Price

Current yield = $45/$1,381.250

Current yield = .0326, or 3.26%

price equation is:

P = C(PVIFAR%,t) + $1,000(PVIFR%,t)

P3 = $41(PVIFA3.1%,20) + $1,000(PVIF3.1%,20) = $1,147.41

P8 = $41(PVIFA3.1%,10) + $1,000(PVIF3.1%,10) = $1,084.87

P12 = $41(PVIFA3.1%,2) + $1,000(PVIF3.1%,2) = $1,019.11

P1 = $31(PVIFA4.1%,24) + $1,000(PVIF4.1%,24) = $849.08

P3 = $31(PVIFA4.1%,20) + $1,000(PVIF4.1%,20) = $865.29

P8 = $31(PVIFA4.1%,10) + $1,000(PVIF4.1%,10) = $919.29

P12 = $31(PVIFA4.1%,2) + $1,000(PVIF4.1%,2) = $981.17

is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity

lengths.

17. Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial

YTM on both bonds is the coupon rate, 6.5 percent. If the YTM suddenly rises to 8.5 percent:

PLaurel = $32.50(PVIFA4.25%,8) + $1,000(PVIF4.25%,8) = $933.36

PHardy = $32.50(PVIFA4.25%,46) + $1,000(PVIF4.25%,46) = $799.39

The percentage change in price is calculated as:

$700

$800

$900

$1,000

$1,100

$1,200

$1,300

13 12 11 10 9876543210

Bond Price

Maturity (Years)

Maturity and Bond Price

Miller Bond

Modigliani Bond

18. Initially, at a YTM of 9 percent, the prices of the two bonds are:

PFaulk = $28.50(PVIFA4.5%,28) + $1,000(PVIF4.5%,28) = $740.24

PGonas = $61.50(PVIFA4.5%,28) + $1,000(PVIF4.5%,28) = $1,259.76

PFaulk = $28.50(PVIFA5.5%,28) + $1,000(PVIF5.5%,28) = $625.78

PGonas = $61.50(PVIFA5.5%,28) + $1,000(PVIF5.5%,28) = $1,091.79

$500

$700

$900

$1,100

$1,300

$1,500

$1,700

$1,900

$2,100

$2,300

$2,500

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

Bond Price

Yield to Maturity

YTM and Bond Price

Bond Laurel

Bond Hardy

The percentage change in price is calculated as:

Percentage change in price = (New price – Original price)/Original price

19. The current yield is:

Current yield = Annual coupon payment/Price

Current yield = $64/$1,080

Current yield = .0593, or 5.93%

The bond price equation for this bond is:

This is the semiannual interest rate, so the YTM is: