test 3 chap 6

There is a bond that has a quoted price of 93.105 and a par value of $2,000. The coupon rate is 6.48 percent and the bond matures in 12 years. If the bond makes semiannual coupon payments, what is the YTM of the bond?

$1,862.10 = $64.80{[1 − 1/(1 + r)24]/r} + $2,000/(1 + r)24r = .0368, or 3.68% YTM = 3.68% × 2 = 7.35%

Crossfade Corp. has a bond with a par value of $2,000 that sells for $1,902.14. The bond has a coupon rate of 6.48 percent and matures in 12 years. If the bond makes semiannual coupon payments, what is the YTM of the bond?

$1,902.14 = $64.80{[1 − 1/(1 + r)24]/r} + $2,000/(1 + r)24r = .0355, or 3.55% YTM = 3.55% × 2 = 7.09%

There is a zero coupon bond that sells for $398.72 and has a par value of $1,000. If the bond has 22 years to maturity, what is the yield to maturity? Assume semiannual compounding.

$399.00 = $2/(1 + r)44r = .0211, or 2.11% YTM = 2.11% × 2 = 4.22%

Footsteps Co. has a bond outstanding with a coupon rate of 5.9 percent and annual payments. The bond currently sells for $935.93, matures in 15 years, and has a par value of $1,000. What is the YTM of the bond?

$935.93 = $59{[1 − 1/(1 + YTM)15]/YTM} + $1,000/(1 + YTM)15YTM = .0659, or 6.59%

A 25-year, semiannual coupon bond sells for $975.11. The bond has a par value of $1,000 and a yield to maturity of 6.87 percent. What is the bond's coupon rate?

$975.11 = C{[1 − 1/(1 + .0687/2)50]/(.0687/2)} + $1,000/(1 + .0687/2)50C = $33.30 Coupon rate = ($33.30 × 2)/ $1,000 = .0666, or 6.66%

You purchase a bond with an invoice price of $1,005. The bond has a coupon rate of 5.36 percent, it makes semiannual payments, and there are 4 months to the next coupon payment. The par value is $1,000. What is the clean price of the bond?

Coupon payment = .0536($1,000)/2 = $26.80 Accrued interest = $26.80[(6 − 4)/6] = $8.93 Clean price = $1,005 − 8.93 = $996.07

A bond that pays interest semiannually has a coupon rate of 5.41 percent and a current yield of 4.89 percent. The par value is $1,000. What is the bond's price?

Coupon payment = .0541 × $1,000 = $54.10 Price = $54.10/.0489 = $1,106.34

A bond with 16 years to maturity and a semiannual coupon rate of 6.04 percent has a current yield of 5.67 percent. The bond's par value is $2,000. What is the bond's price?

Coupon payment = .0604 × $2,000 = $120.80 Price = $120.80/.0567 = $2,130.51

A bond has a par value of $1,000, a current yield of 6.45 percent, and semiannual coupon payments. The bond is quoted at 95.32. What is the amount of each coupon payment?

Coupon payment = [.0645 × (.9532 × $1,000)/2] = $30.74

A municipal bond has a YTM of 5.19 percent while the YTM of a comparable taxable bond is 7.78 percent. What is the tax rate that will make an investor indifferent between the municipal bond and the taxable bond?

Critical tax rate = 1 − .0519/.0778 = .3329, or 33.29%

A bond that pays interest semiannually has a price of $941.35 and a semiannual coupon payment of $26.00. If the par value is $1,000, what is the current yield?

Current yield = ($26.00 × 2)/$941.35 = .0552, or 5.52%

A bond with a coupon rate of 5.88 percent and semiannual coupon payments matures in 20 years. The YTM is 6.91 percent. What is the effective annual yield?

Effective rate = (1 + .0691/2)2 − 1 = 7.03%

Navarro, Inc., plans to issue new zero coupon bonds with a par value of $1,000 to fund a new project. The bonds will have a YTM of 5.31 percent and mature in 30 years. If we assume semiannual compounding, at what price will the bonds sell?

PV = $1,000/(1 + .0531/2)60PV = $207.58

You purchase a zero coupon bond with 17 years to maturity and a yield to maturity of 5.69 percent. The bond has a par value of $1,000. What is the implicit interest for the first year? Assume semiannual compounding.

PV = $1,000/(1 + .0569/2)34 = $385.28PV = $1,000/(1 + .0569/2)32 = $407.51 Implicit interest = $407.51 − 385.28 = $22.23

Whatever, Inc., has a bond outstanding with a coupon rate of 5.56 percent and semiannual payments. The yield to maturity is 6.7 percent and the bond matures in 11 years. What is the market price if the bond has a par value of $1,000?

PV = $27.80{[1 − (1/1.033522)]/.0335} + $1,000/1.033522PV = $912.26

Setrakian Industries needs to raise $76.4 million to fund a new project. The company will sell bonds that have a coupon rate of 5.82 percent paid semiannually and that mature in 15 years. The bonds will be sold at an initial YTM of 6.52 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds? (Round your intermediate calculations to two decimal places and final answer to the nearest whole number.)

PV = $58.20{1 − [1/(1 + .0652/2)30]}/(.0652/2) + $2,000/(1 + .0652/2)30PV = $1,867.30 Bonds to sell = $76,400,000/$1,867.30 = 40,915

Lincoln Park Co. has a bond outstanding with a coupon rate of 5.82 percent and semiannual payments. The yield to maturity is 6.9 percent and the bond matures in 24 years. What is the market price if the bond has a par value of $2,000?

PV = $58.20{[1 − (1/1.034548)]/.0345} + $2,000/1.034548PV = $1,748.41

Harpeth Valley Water District has a bond outstanding with a coupon rate of 3.15 percent and semiannual payments. The bond matures in 17 years, with a yield to maturity of 3.81 percent, and a par value of $5,000. What is the market price of the bond?

PV = $78.75{[1 − (1/1.0190534)]/.01905} + $5,000/1.0190534PV = $4,589.83

Wine and Roses, Inc., offers a bond with a coupon of 10.0 percent with semiannual payments and a yield to maturity of 11.00 percent. The bonds mature in 9 years. What is the market price of a $1,000 face value bond?

PV=[(0.100×$1,000)/2]×1−(1/[1+(0.1100/2)]2×9)0.1100/2+$1,000/[1+(0.1100/2)]2×9=$562.30+$381.47=$943.77

A municipal bond has a coupon rate of 6.07 percent and a YTM of 5.69 percent. If an investor has a marginal tax rate of 28 percent, what is the equivalent pretax yield on a taxable bond?

Pretax yield = 5.69%/(1 − .28) = 7.90%

A bond with a par value of $5,000 is quoted at 95.326. What is the dollar price of the bond?

Price = 95.326/100 × $5,000 = $4,766.30

The inflation rate over the past year was 1.9 percent. If an investment had a real return of 7.1 percent, what was the nominal return on the investment?

R = [(1 + .071) × (1 + .019)] − 1 = .0913, or 9.13%

The Lo Sun Corporation offers a 5.5 percent bond with a current market price of $844.50. The yield to maturity is 9.17 percent. The face value is $1,000. Interest is paid semiannually. How many years until this bond matures?

Semi-annual interest rate = 0.0917/2 = 0.04585 PV=$844.50=[(0.055×$1,000)/2]×1−[1/(1+0.04585)t]0.04585+$1,000/(1+0.04585)tPV=$844.50=[(0.055×$1,000)/2]×1−[1/(1+0.04585)t]0.04585+$1,000/(1+0.04585)t (Note: t is the number of semi-annual periods) $844.50=$27.50×1−[1/(1.04585)t]0.04585+$1,000/(1.04585)t$844.50=$27.50×1−[1/(1.04585)t]0.04585+$1,000/(1.04585)t Dividing by $27.50, you get:30.7091 = {[1 - 1/1.0458t]/0.0459} + 36.3636/1.0458t Multiplying by 0.0459, you get:1.4080 = 1 - 1/1.0458t + 1.6673/1.0458t0.4080 = 0.6673/1.0458t1.0458t = 1.6354t = ln1.6354/ln1.0458 = 0.4919/0.0448 = 10.97 semi-annual periods = 5.49 years

An investment had a nominal return of 11.4 percent last year. The inflation rate was 3.8 percent. What was the real return on the investment?

r = [(1 + .114)/(1 + .038)] − 1 = .0732, or 7.32%