Chapter 7: Interest Rates and Bond Valuation

You purchase a bond with an invoice price of $1,319. The bond has a coupon rate of 6.25 percent, a face value of $1,000, and there are two months to the next semiannual coupon date. What is the clean price of this bond? a. $1,298.17 b. $1,352.17 c. $1,314.14 d. $1,408.12 e. $1,283.50

a. $1,298.17 Accrued interest = (.0625 × $1,000) × 1/2 × 4/6 = $20.83 Clean price = $1,319 - 20.83 = $1,298.17

Global Exporters wants to raise $29.6 million to expand its business. To accomplish this, it plans to sell 20-year, $1,000 face value, zero coupon bonds. The bonds will be priced to yield 7.75 percent. What is the minimum number of bonds it must sell to raise the money it needs? Assume semiannual compounding. a. 110,411 b. 139,800 c. 154,907 d. 126,029 e. 135,436

e. 135,436 ??? Bond price = $1,000 / [1 + (.0775 / 2)]^(20 × 2) = $218.554 Number of bonds = $29,600,000 / $218.544 = 135,436 bonds

A 13-year, 6 percent coupon bond pays interest semiannually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent? a. 1.79 percent decrease b. 1 percent decrease c. 1.6 percent decrease d. 1.97 percent increase e. 1.79 percent increase

A) -1.79 percent N = 13X2=26 I/Y = 5.7/2 PV = ? PMT = (.06x1000)/2 = 30 FV = 1000 Then once more but change I/Y to 5.5/2 = -1027.28 and -1046.01 [(1,027.28-1,046.01)/1,046.01]

A newly issued 20-year, $1,000, zero coupon bond just sold for $311.05. What is the implicit interest, in dollars, for the first year of the bond's life? Assume semiannual compounding. a. $17.72 b. $18.70 c. $18.47 d. $17.63 e. $17.89

B) 18.70 ???? N: 40 PMT: None PV: -311.05 FV: 1000 IY: ?? Find IY: 2.96 x 2 = 5.93 orrr u can use equation below Bond price 0 = $311.05 = $1,000 / [1 + (r / 2)]^(20 × 2); r = 5.925% Bond price 1 = $1,000 / [1 + (.05925 / 2)](19 × 2) = $329.75 Implicit interest = $329.75 - 311.05 = $18.70

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. 8.00 percent b. 8.50 percent c. 9.00 percent d. 10.50 percent e. 12.00 percent

E. 12.00 percent n=14 iy=7.5 pv=-1382.01 pmt=? fv=1000 pmt=120 then divide by 1000(fv) to get coupon rate

A 10-year, 4.5 percent, semiannual coupon bond issued by Tyler Rentals has a $1,000 face value. The bond is currently quoted at 98.7. What is the clean price of this bond if the next interest payment will occur 2 months from today? a. $987.00 b. $994.50 c. $1,002.00 d. $1,011.25 e. $1,022.50

a. $987.00 Clean price is typically the price which is quoted. .987 x 1000 = $987

Redesigned Computers has 6.5 percent coupon bonds outstanding with a current market price of $742. The yield to maturity is 13.2 percent and the face value is $1,000. Interest is paid annually. How many years is it until these bonds mature? a. 5.73 years b. 4.19 years c. 7.41 years d. 6.16 years e. 8.32 years

a. 5.73 years N: ? I/Y: 13.2 PV: -742 FV: 1000 PMT: (6.5% x 1000)

World Travel has 7 percent, semiannual, coupon bonds outstanding with a current market price of $1,023.46, a par value of $1,000, and a yield to maturity of 6.72 percent. How many years is it until these bonds mature? a. 12.26 years b. 12.53 years c. 18.49 years d. 24.37 years e. 25.05 years

b. 12.53 years N: ? I/Y: 6.72 /2 PV: -1023.46 FV: 1000 PMT: (7% x 1000)/2 N = 25.05 Divide by 2 to get the years

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? a. 4.24 percent b. 4.85 percent c. 5.36 percent d. 5.62 percent e. 4.66 percent

b. 4.85 percent Current Yield is equal to the annual interest earned divided by the current price of the bond. 4.75/98.96 = .048 =4.85%

Oil Wells offers 6.5 percent coupon bonds with semiannual payments and a yield to maturity of 6.94 percent. The bonds mature in seven years. What is the market price per bond if the face value is $1,000? a. $989.70 b. $975.93 c. $996.48 d. $902.60 e. $913.48

b. 975.93 Bond price = $32.50 × [(1 − {1 / [1 + (.0694 / 2)](7 × 2)}) / (.0694 / 2)] + $1,000 / [1 + (.0694 / 2)](7 × 2) Bond price = $975.93

Do-Well bonds have a face value of $1,000 and are currently quoted at 86.725. The bonds have a 7 percent coupon rate. What is the current yield on these bonds? a. 7.42 percent b. 7.67 percent c. 8.07 percent d. 9.03 percent e. 8.47 percent

c. 8.07 percent Current Yield is a bond's annual coupon divided by its price. (1000x7%) / 86.725 = .807

A Treasury bond is quoted at a price of 101.6533 with a current yield of 6.276 percent. What is the coupon rate on a $10,000 bond? a. 7.20 percent b. 6.48 percent c. 6.41 percent d. 6.38 percent e. 6.27 percent

d. 6.38 percent Price = 1.016533 × $10,000 = $10,165.33 Annual interest = .06276 × $10,165.33 = $637.98 Coupon rate = $637.98 / $10,000 = 6.38 percent

The 7 percent bonds issued by Modern Kitchens pay interest semiannually, mature in eight years, and have a $1,000 face value. Currently, the bonds sell for $1,032. What is the yield to maturity? a. 6.87 percent b. 6.92 percent c. 6.08 percent d. 6.48 percent e. 7.20 percent

d. 6.48 percent $1,032 = $35 × [(1 − {1 / [1 + (r / 2)](8 × 2)}) / (r / 2)] + $1,000 / [1 + (r / 2)](8 × 2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 16 −1,032 35 1,000N I/Y PV PMT FVSolve for: 3.2405 YTM = 2 × 3.2405% = 6.48%

The yield-to-maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today you buy a 9 percent annual coupon bond for $1,000. The bond has 12 years to maturity. Three years from now, the yield-to-maturity has declined to 7 percent and you decide to sell. What is your holding period yield? a. 8.84 percent b. 9.49 percent c. 10.96 percent d. 13.01 percent e. 12.83 percent

e. 12.83 percent