1A) A $10,000, 8% annual coupon bond will mature in 10 years. What is the price

Question

1A) A $10,000, 8% annual coupon bond will mature in 10 years. What is the price of this bond if the current yield to maturity on bonds of similar risk and maturity is 7.2%?

$10,956

$9,463

$10,557

$10,000

1B) What is the intrinsic value of a $10,000, 8% annual coupon bond with a current yield to maturity of 7.2% and which will mature in 10 years if the coupon payments are made semi-annually?

$6,662

$10,563

$10,834

$10,557

1C) If the price of a $10,000, 8% semiannual coupon bond maturing in 10 years is $9,350, what is its yield to maturity?

7.20%

9.00%

9.35%

4.50%

1D) A 10%, $1,000, 15-year bond is callable in 10 years at 110% par. It is currently selling for $980. What is its yield to call? (we didn't discuss this in class, but it is in the reading)

10.61%

10.27%

10.57%

10.94%

$10,956

$9,463

$10,557

$10,000

Explanation / Answer

Answer to Question 1A:

Face Value = $10,000

Annual Coupon Rate = 8%
Annual Coupon = 8% * $10,000
Annual Coupon = $800

Time to Maturity = 10 years
Annual YTM = 7.2%

Price of Bond = $800 * PVIFA(7.20%, 10) + $10,000 * PVIF(7.20%, 10)
Price of Bond = $800 * (1 - (1/1.072)^10) / 0.072 + $10,000 / 1.072^10
Price of Bond = $10,557

Answer to Question 1B:

Face Value = $10,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $10,000
Semiannual Coupon = $400

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Annual YTM = 7.2%
Semiannual YTM = 3.60%

Price of Bond = $400 * PVIFA(3.60%, 20) + $10,000 * PVIF(3.60%, 20)
Price of Bond = $400 * (1 - (1/1.036)^20) / 0.036 + $10,000 / 1.036^20
Price of Bond = $10,563

Answer to Question 1C:

Face Value = $10,000
Current Price = $9,350

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $10,000
Semiannual Coupon = $400

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$9,350 = $400 * PVIFA(i%, 20) + $10,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -9350
PMT = 400
FV = 10000

I = 4.50%

Semiannual YTM = 4.50%
Annual YTM = 2 * 4.50%
Annual YTM = 9.00%

Answer to Question 1D:

Face Value = $1,000
Current Price = $980
Call Price = 110%*$1,000 = $1,100

Annual Coupon Rate = 10%
Semiannual Coupon Rate = 5%
Semiannual Coupon = 5% * $1,000
Semiannual Coupon = $50

Time to Call = 10 years
Semiannual Period to Call = 20

Let semiannual YTC be i%

$980 = $50 * PVIFA(i%, 20) + $1,100 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -980
PMT = 50
FV = 1100

I = 5.455%

Semiannual YTC = 5.455%
Annual YTC = 2 * 5.455%
Annual YTC = 10.91%

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.