Question

Question 1

XYZ's corporate bonds mature in 20 years, have a par value of $1,000, and an annual coupon rate of 8% (paid on an annual basis). The market requires an interest rate of 7% (annual) on these bonds. What is the bond's price (report answer as a positive number)?

$1,066.32

$1,118.01

$1,241.89

$1,105.94

None of the above.

Question 2

A corporate bond has a maturity of ten years, face value of $1,000, and an annual coupon rate of 6.75%. Coupon payments are paid on a semi-annual basis. Assume interest rates are currently at 5.5% (annual). What is the current price of this bond (report answer as a positive number)?

$520.38

$1,149.38

$1,095.17

None of the above.

Question 3

Suppose a corporate bond has a maturity of five years, par value of $1,000, and an annual coupon rate of 4.5% (paid on a quarterly basis). Assume interest rates are currently at 8% (annual). What is the current price of this bond (report answer as a positive number)?

$643.93

$856.93

$1,149.38

None of the above.

Question 4

Goldman Corporation’s bonds have a 15-year maturity, a 6% annual coupon rate (paid semi-annually), and a par value of $1,000. If interest rates are currently at 5%, what is the bond’s current yield (defined as: Annual Interest Payment / Bond Price)?

5.43%

6.00%

5.76%

6.37%

None of the above.

Answer 1

Question 1:

Par Value = $1,000

C = Annual coupon payment = $1,000 * 8% = $80

r = market interest rate = 7%

n = 20 years

Bond;s price today = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

= [$80 * [1 - (1+7%)^-20] / 7%] + [$1,000 / (1+7%)^20]

= [$80 * 0.741580997 / 0.07] + [$1,000 / 3.86968446]

= $847.52114 + $258.419003

= $1,105.94014

Therefore, bond's price today is $1,105.94

Question 2:

Face Value = $1,000

C = Semi Annual coupon payment = $1,000 * 6.75%/2 = $33.75

r = semi annual market interest rate = 5.5%/2 = 2.75%

n = 10*2 = 20 semi annual periods

Bond;s price today = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

= [$33.75 * [1 - (1+2.75%)^-20] / 2.75%] + [$1,000 / (1+2.75%)^20]

= [$33.75 * 0.418749434 / 0.0275] + [$1,000 / 1.72042843]

= $513.91976 + $581.250567

= $1,095.17033

Therefore, bond's price today is $1,095.17

Question 3:

Par Value = $1,000

C = Quarterly coupon payment = $1,000 * 4.5%/4 = $11.25

r = Quarterly  interest rate = 8%/4 = 2%

n = 5 * 4 = 20 Quarters

Bond;s price today = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

= [$11.25 * [1 - (1+2%)^-20] / 2%] + [$1,000 / (1+2%)^20]

= [$11.25 * 0.327028667 / 0.02] + [$1,000 / 1.4859474]

= $183.953625 + $672.971331

= $856.924953

Therefore, bond's price today is $856.93

Question 4:

Par Value = $1,000

C = Semi Annual coupon payment = $1,000 * 6% / 2 = $30

r = semi annual market interest rate = 5%/2 = 2.5%

n = 15*2 = 30 semi annual periods

Bond;s price today = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

= [$30 * [1 - (1+2.5%)^-30] / 2.5%] + [$1,000 / (1+2.5%)^30]

= [$30 * 0.523257315 / 0.025] + [$1,000 / 2.09756758 ]

= $627.908776 + $476.742685

= $1,104.65146

bond's price today is $1,104.65

Bonds current yeild = Annual coupon / bond's price

= $60 / $1,104.65

= 0.0543158466

= 5.43%

Therefore, bond's current yeild is 5.43%