Chapter 7: Interest Rates and Bond Valuation

Registered Form

form of a bond issued in which the registrar of the company records ownership of each bond, payment is made directly to the owner of record

Indenture (Deed of Trust)

written agreement between the corporation and the lender detailing the terms of the debt issue

Maturity

the specified date on which the principal amount of a bond is paid

Coupon

the stated interest payment made on a bond

You have just been offered a 1000 par value bond for 847.88. The bond has an annual coupon rate 8% and annual interest rates on equally risky new issues are 10% (I/YR). You want to know how many more interest payments you will receive, but the party selling the bond cannot remember. Can you determine how many interest payments remain?

15 years I/YR = 10 PV = +/-847.88 PMT = 80 FV = 1000

The collar of a floating-rate bond refers to the minimum and maximum: A. Maturity dates. B. Call periods. C. Market prices. D. yields to maturity. E. Coupon rates.

E. Coupon rates.

The bond principal is repaid on which one of these dates? A. Clean date. B. Coupon date. C. Yield date. D. Dirty date. E. Maturity date.

E. Maturity date.

A Treasury yield curve plots Treasury interest rates relative to which one of the following? A. Inflation. B. Market rates. C. Comparable corporate bond rates. D. The risk-free rate. E. Maturity.

E. Maturity.

A premium bond that pays $60 in interest annually matures in seven years. The bond was originally issued three years ago at par. Which one of the following statements is accurate in respect to this bond today? A. The bond is worth less today than when it was issued. B. The coupon rate is greater than the current yield. C. The yield-to-maturity equals the current yield. D. The face value of the bond today is greater than it was when the bond was issued. E. The yield-to-maturity is less than the coupon rate.

E. The yield-to-maturity is less than the coupon rate.

The bond market requires a return of 9.8 percent on the five-year bonds issued by JW Industries. The 9.8 percent is referred to as which one of the following? A. Face rate. B. Coupon rate. C. Call rate. D. Current yield. E. Yield to maturity.

E. Yield to maturity.

You own a bond that has a 6 percent annual coupon and matures five years from now. You purchased this 10-year bond at par value when it was originally issued. Which one of the following statements applies to this bond if the relevant market interest rate is now 5.8 percent? A. The current yield-to-maturity is greater than 6 percent. B. The current yield is 6 percent. C. The bond is currently valued at one-half of its issue price. D. The next interest payment will be $30. E. You will realize a capital gain on the bond if you sell it today.

E. You will realize a capital gain on the bond if you sell it today.

Coupon Rate

the annual coupon divided by the face value of a bond

Bid Price

the price a dealer is willing to take for a security

Clean Price

the price of a bond net accrued interest, the price that is typically quoted

Face Value (Par Value)

the principle amount of a bond that is repaid at the end of the term

Fisher Effect

the relationship between nominal returns, real returns, and inflation

Kaiser Industries has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and selling for $1,382.01. At this price, the bonds yield 7.5 percent. What is the coupon rate? A. 9.00 percent B. 12.00 percent C. 8.50 percent D. 8.00 percent E. 10.50 percent

B. 12.00 percent

A corporate bond is quoted at a price of 98.96 and has a coupon rate of 4.8 percent, paid semiannually. What is the current yield? Select one: A. 4.66 percent B. 4.85 percent C. 4.24 percent D. 5.62 percent E. 5.36 percent

B. 4.85 percent

You purchase a bond with an invoice price of $968. The bond has a coupon rate of 7.4% and there are 5 months to the next semiannual coupon date. What is the clean price of the bond?

Clean Price = $961.83 Accrued interest = 74/12 x 1 = 6.17 Clean price = dirty price - accrued interest = 968 - 6.17 = 961.83

A bond that matures in 7 years sells for $1020. The bond has a face value of $1000 and a yield to maturity of 10.5883%. The bond pays coupons semiannually. What is the bond's current yield?

Current Yield = 10.78% N = 14 I/YR = 10.5883/2 = 5.29415 PV = +/- 1020 FV = 1000 PMT = ? = 55 x 2 = 110 Current yield = annual interest / price = 110/1020 = 10.78%

Oak Bay Software has 9.2% coupon bonds on the market with 9 years to maturity. The bonds make semiannual payments and currently sell for 106.8% of par and the face value is $1000 What is the YTM? What is the current yield on the bonds?

Current Yield = 8.60% PMT = 46 N = 9 x 2 = 18 FV = 1000 PV = +/-1068 I/YR = ? = 4.06 x 2 = 8.12% Yield = annual payment/price = 92/1068 = 8.6%

Sinking Fund

an account managed by the bond trustee for early bond redemption

Leechtown Co. has 9% coupon bonds on the market with 9 years left to maturity. The bonds make annual payments and the face value is $1000. If the bond currently sells for $934, what is the YTM?

YTM = 10.15% PMT = 90 N = 9 FV = 1000 PV = +/- 934

Zero Coupon Bonds

a bond that makes no coupon payments and is thus initially priced at a deep discount

Current Yield

a bond's annual coupon divided by its price

Floating Rate Bonds

coupon payments are adjustable

A bond has a quoted price of 1080.42. It has a face value of 1000, a semiannual coupon of 30 and a maturity of 5 years. What is its current yield? What is its YTM?

1. 60/1080.42 = 5.55% 2. 2.10% (the periodic rate per 6 months) x2 = 4.2%

A 10 year, 12% semiannual coupon bond, with a face value of $1000 may be called in 4 years at a call price of $1060. The bond sells for $1100 (Assume that the bond has just been issued) 1. What is the bond's YTM? 2. What is the bond's current yield? 3. What is the bond's YTC?

1. I/YR = 10.3699% N = 20, PV = +/- 1100, PMT = 60, FV = 1000, I/YR = ? multiply by 2 2. 10.91% 120/1100 = 0.1091 3. I/YR = 10.1495% N = 8, PV = +/- 1100, PMT = 60, FV = 1060, I/YR = ? multiply by 2

You are looking at two bonds identical in every way except for their coupons and prices. Both have 12 years to maturity. The first bond has a 5% coupon rate and sells for $932.16. The second has a 6% coupon rate. What do you think it would sell for?

1. N = 12 PMT = 50 PV = +/-932.16 FV = 1000 I/YR = ???? = 5.80% 2. N = 12 PMT = 60 FV = 1000 I/YR = 5.80% PV = 1016.95

If treasury bills are currently paying 7% and the inflation rate is 3.8%, what is the exact real rate? What is the approximate real rate of interest (r)?

3.2% (1 + R) = (1 + r)(1 + h) (1 + 0.07) = (1 + r)91 + 0.038) r = 3.08% R = r + h r = 0.07 - 0.038 = 0.032 = 3.2%

The yield to maturity on a bond is currently 9.84 percent. The real rate of return is 3.29 percent. What is the rate of inflation? A. 5.64 percent B. 6.34 percent C. 6.71 percent D. 6.24 percent E. 6.53 percent

B. 6.34 percent

The interest rate risk premium is the: A. Additional compensation paid to investors to offset rising prices. B. Compensation investors demand for accepting interest rate risk. C. Difference between the market interest rate and the coupon rate. D. Difference between the yield to maturity and the current yield. E. Difference between the coupon rate and the current yield.

B. Compensation investors demand for accepting interest rate risk.

Which one of the following applies to a premium bond? A. Coupon rate < yield to maturity < current yield. B. Coupon rate > current yield > yield to maturity. C. Coupon rate > yield-to-maturity > current yield. D. Yield to maturity > current yield > coupon rate. E. Coupon rate = current yield = yield-to-maturity.

B. Coupon rate > current yield > yield to maturity.

Allison just received her semiannual payment of $35 on a bond she owns. Which term refers to this payment? A. Call premium. B. Coupon. C. Discount. D. Face value. E. Yield.

B. Coupon.

Which one of the following bonds is the least sensitive to interest rate risk? A. 7-year; 6 percent coupon. B. 3-year; 4 percent coupon. C. 3-year; 6 percent coupon. D. 7-year; 4 percent coupon. E. 5-year; 6 percent coupon

C. 3-year; 6 percent coupon.

Al is retired and his sole source of income is his bond portfolio. Although he has sufficient principal to live on, he only wants to spend the interest income and thus is concerned about the purchasing power of that income. Which one of the following bonds should best ease Al's concerns? A. 20-year coupon bonds B. 6-year coupon bonds C. 5-year TIPS D. 5-year municipal bonds E. 7- year income bonds

C. 5-year TIPS

A newly issued bond has a 7 percent coupon with semiannual interest payments. The bonds are currently priced at par. The effective annual rate provided by these bonds must be: A. Less than 3.5 percent. B. 3.5 percent. C. Greater than 7 percent. D. 7 percent. E. Greater than 3.5 percent but less than 7 percent.

C. Greater than 7 percent.

Cat bonds are primarily designed to help: A. Municipalities survive economic recessions. B. The federal government cope with huge deficits. C. Insurance companies fund excessive claims. D. Corporations recover from involuntary reorganizations. E. Corporations respond to overseas competition.

C. Insurance companies fund excessive claims.

A 3.25 percent Treasury bond is quoted at a price of 101.16. The bond pays interest semiannually. What is the current yield? A. 3.38 percent B. 3.33 percent C. 3.06 percent D. 3.21 percent E. 3.17 percent

D. 3.21 percent

Which one of the following relationships is stated correctly? A. An increase in market rates increases the market price of a bond. B. The coupon rate exceeds the current yield when a bond sells at a discount. C. The call price must equal the par value. D. Decreasing the time to maturity increases the price of a discount bond, all else constant. E. Increasing the coupon rate decreases the current yield, all else constant.

D. Decreasing the time to maturity increases the price of a discount bond, all else constant.

The Corner Grocer has a 7-year, 6.5 percent semiannual coupon bond outstanding with a $1,000 par value. The bond has a yield to maturity of 5.5 percent. Which one of the following statements is correct if the market yield suddenly increases to 7 percent? A. The bond price will increase by 1.14 percent. B. The bond price will decrease by 1.74 percent. C. The bond price will decrease by 2.36 percent. D. The bond price will decrease by 1.92 percent. E. The bond price will increase by 2.29 percent.

D. The bond price will decrease by 1.92 percent.

You purchase a bond with a coupon rate of 6.8% and a clean price of $1073. If the next semiannual coupon payment is due in 3 months, what is the invoice (dirty) price?

Dirty Price = 1090 Accrued interest = 68/2 x 3/6 = 17 Dirty price = clean price + accrued interest = 1073 + 17 = 1090

Bonds issued by the U.S. government: A. Are called "munis." B. Are considered to be free of interest rate risk. C. Pay interest that is exempt from federal income taxes. D. Generally have higher coupons than comparable bonds issued by a corporation. E. Are considered to be free of default risk.

E. Are considered to be free of default risk.

Suppose the Eight Inch Nails company issues a 1000 face value 5 year zero coupon bonds. The initial price is set at 508.35. What is the YTM using semiannual compounding?

I/YR = 13.98% FV = 1000 N = 10 PV = +/- 508.35 I/YR = ? = 6.99 x 2 = 13.98

Suppose that the Geneva Electronics Company issues a 1000 face value, 8 year zero coupon bond. What is the yield to maturity on the bonds if the bond is offered at 637

I/YR = 6% FV = 1000 N = 8 PV = +/- 627

A bond that matures in 8 years has a 10% coupon rate, semiannual payments, a face value of $1000, and an 8.5% current yield What is the bond's YTM?

I/YR = 7.0736% N = 8 x 2 = 16 PMT = 0.1/2 x 100 = 50 FV = 1000 Current Yield = PMT/PV, 0.085 = 100/PV PV = +/-1176.47 I/YR = 3.5368% x 2 = 7.0736%

Braemar Corp. issued 12 year bonds 2 years ago at a coupon rate of 8.4%. The bonds make semiannual payments and the face value is $1000. If these bonds currently sell for 105% of par value, what is the YTM?

I/YR = 7.67% N = 10 x 2 = 20 PMT = 42 FV = 1000 PV = +/- 1050 I/YR = 3.837 x 2 = 7.67

Peter bought a bond maturing in 5 years. The bond has a face value of $1000, an 8 % annual coupon, and has a current yield of 8.21% Current yield is equal to 8.21% What is the bond's price and YTM?

I/YR = 8.65% N = 5 PMT = 80 FV = 1000 PV = 80/0.0821 = +/-974.42

Colwood Corp. has 9% coupon bonds making annual payments with a YTM of 6.3%, a current yield of 7.1% and a face value of $1000. How many years do these bonds have left until they mature?

N = 16.029 PMT = 90 I/YR = 6.3 FV = 1000 0.071 = 90/PV, PV = +/- 1267.61

Happy Valley Corporation has bonds on the market with 14.5 years to maturity, a YTM of 6.8%, a current price of $924 and a face value of $1000. The bonds make semiannual payments. What must the coupon rate be on these bonds?

PMT = $59.67 N = 29 I/YR = 3.4 PV = +/-924 FV = 1000 PMT = 29.84 x 2 = 59.67

Goldstream Enterprises has bonds on the market making annual payments with 13 years to maturity and selling for $1045. At this price, the bonds yield 7.5%. What must the coupon rate be on the bond? Assume the face value is $1000

PMT = $80.54 N = 13 PV = +/- 1045 I/YR = 7.5 FV = 1000

Langford Co. issued 11 year bonds a year ago at a coupon rate of 6.9%. The bonds make semiannual payments and the face value is $1000. If the YTM on these bonds is 7.4%, what is the current bond price?

PV = $965.10 N = 20 PMT = 34.5 I/YR = 3.7 FV = 1000

If the 15 year Allied bonds pays a 50 coupon payment each 6 months and the nominal interest rate is 5% with semiannual compounding and the face value is 1000 What is the PV?

PV = 1523.26 N= 30 I/YR = 2.5 PMT = 50 FV = 1000

Malahat Inc. has 7.5% coupon bonds on the market that have 10 years left to maturity. The bonds make annual payments and the face value is $1000. If the YTM on these bonds is 8.75%, what is the current bond price?

PV = 918.89 PMT = 75 N = 10 FV = 1000 I/YR = 8.75

Discount Bond

sells for less than face value

Premium Bond

sells for more than face value

Suppose the real rate is 3% and the inflation rate is 4.7%. What rate would you expect to see on a treasury bill?

R = (1 + 0.03)(1 + 0.047) - 1 = 7.841%

If we require a 10% real return and we expect inflation to be 8%, what is the exact nominal rate? what is the approximate nominal rate?

R = 18% (1 + R) = (1 + r)(1 + h) R = (1 + 0.1)(1 + 0.08) -1 = 0.188 = 18.80% R = 10% + 8% = 18%

When interest rates ________, the present value of a bond's remaining cash flows _________and vice versa

Rise, declines

Dirty Price

The price of a bond including accrued interest, also known as the full or invoice price, this is the price the buyer actually pays.

Suppose you were offered a 14 year, 10% semiannual coupon, 1000 par value bond at a price of 1494.93 What rate of interest rate would you earn on your investment if you bought the bond and held it to maturity?

YTM = 5.032% N = 28 PMT = 50 PV = +/-1494.93 FV = 1000 I/YR = 2.516 x 2 = 5.032%

Call Protected Bond

a bond that, during a certain period, cannot be redeemed by the issuer

Deferred Call Provision

a call provision prohibiting the company from redeeming a bond prior to a certain date

Protective Covenant

a part of the indenture limiting certain actions that might be taken during the term of the loan, usually to protect the lenders interest, can be positive or negative

Treasury Yield Curve

a plot of the yields on Treasury Notes and Bonds relative to maturity

Call Provision

agreement giving the corporation the option to repurchase a bond at a specified price or prior to maturity

Call Premium

amount by which the call exceeds the par value of a bond

Debenture

an unsecured debt, usually with a maturity of 10+ years

Note

an unsecured debt, usually with a maturity of less than 10 years

Interest Rate Risk Premium

compensation investors demand for bearing interest rate risk

Bearer Form

form of bond issued in which the bond is issued without record of the owner's name, payment is made to whoever holds the bond

Warrant

gives the buyer of a bond the right to purchase shares of stock in a company at a fixed price

Real Rates

interest rates or rates of return that have been adjusted for inflation

Nominal Rates

interest rates or rates of return that have not been adjusted for inflation

Default Risk Premium

portion of a nominal interest rate or bond yield that represents compensation for the possibility of default

Taxability Premium

portion of a nominal interest rate or bond yield that represents compensation for unfavorable tax states

Liquidity Premium

portion of nominal interest rate or bond yield that represents compensation for lack of liquidity

Inflation Premium

portion of nominal interest rate that represents compensation for expected future inflation

Say you own an asset that had a total return last year of 11.4%. If the inflation rate last year was 4.8%, what was your real return?

r = [(1 + 0.114)/(1 + 0.048)] - 1 = 6.3%

Yield to Maturity (YTM)

rate required in the market of a bond

Term Structure of Interest Rates

relationship between nominal interest rates on default free, pure discount securities and time to maturity, that is, the pure time value of money

Collateral

securities that are pledged as payment of debt