Homework answers / question archive /   SCHOOL OF MATHEMATICAL SCIENCES                     Question 1 (Example 1)   A 15-year 100 par value bond bearing a 8% coupon rate payable semiannually, and redeemable at 110, is bought to yield 6% convertible semiannually

  SCHOOL OF MATHEMATICAL SCIENCES                     Question 1 (Example 1)   A 15-year 100 par value bond bearing a 8% coupon rate payable semiannually, and redeemable at 110, is bought to yield 6% convertible semiannually

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SCHOOL OF MATHEMATICAL SCIENCES                  

 

Question 1 (Example 1) 

 A 15-year 100 par value bond bearing a 8% coupon rate payable semiannually, and redeemable at 110, is bought to yield 6% convertible semiannually. Find the price. Verify that all four formulas produce the same answer.
 

Question 2 (Example 2)

  

A 10-year bond with coupons at 6% convertible quarterly will be redeemed at 1,500. The bond is bought to yield 8% convertible quarterly. The purchase price is 900.40. Calculate the par value.
 

Question 3 (Example 3)

 

John buys a 10-year, 1,000 par value bond with coupons at 10% convertible semiannually. The price of the bond to earn a yield of 8% convertible semiannually is 1,432.45. The redemption value is more than the par value. Calculate the price John would have to pay for the same bond to yield 10% convertible semiannually.
 

Question 4 (Example 4)

 

A 5-year, 800 par value bond with coupons at 8% convertible semiannually is purchased for 770.60. The present value of the redemption value is 555.88. Calculate the redemption value.

Question 5

 

A 4% RM100 bond matures in 25 years. It bears semi-annual coupons and is purchased for RM117.50 to yield i⁽²⁾ . A 5% RM100 bond maturing in 25 years also bears semi-annual coupons but is purchased for RM135 to yield i⁽²⁾ . Determine i⁽²⁾ .

 

Question 6 (Example 5)

 

A 100 par value 8% bond with semiannual coupons is purchased at 110 to yield a nominal rate of interest of 6% convertible semiannually. A similar 4% bond with semiannual coupons is purchased at P to provide with the buyer the same yield. Calculate P.
 

Question 7 (Example 6)

 

A 1,000 par value bond with 8% coupons payable semiannually is purchased for 1,200. The yield to the purchaser is 5% convertible semiannually. If the same bond were redeemable at 130% of par, what price would have been paid to obtain the same yield?

Question 8 

 

A bond with coupons equal to 40 sells for P. A second bond with the same maturity value and term has coupons equal to 30 and sells for Q. A third bond with the same maturity value and term has coupons equal to 80 and sells for R. All prices are based on the same yield rate, and all coupons are paid at the same frequency. Show that R ?5P?4Q .

Question 9 (Example 8a)

 

A 1,000 bond, redeemable at par on 1 December 2018, has 10% coupons paid semiannually. The bond is bought on 1 June 2016. Find the purchase price and construct a bond amortization schedule if the desired yield is 9% compounded semiannually.

Question 10 (Example 8b)

 

A 1,000 bond, redeemable at par on December 1, 2018, with 10% coupons paid semiannually. The bond is bought on June 1, 2016. Find the purchase price and construct a bond amortization schedule if the desired yield is 12% compounded semiannually.

 

The purchase price on 1 June 2016 is

Question 11 (Example 10a)

 

A 10,000 par value 10-year bond with 9% annual coupons is bought at a premium to yield an annual effective rate of 7%. Calculate the interest portion of the 8^th coupon.

Question 12 (Example 10b)

 

A 1,000 par value 5-year bond with 9% semiannual coupons was bought to yield 8% convertible semiannually. Determine the amount of premium amortized in the 7^th coupon payment.

Question 13 (Example 12)

 

Consider a 1,000 par value two-year 9% bond with semiannual coupons bought to yield 7% convertible semiannually. The price of the bond is computed to be 1,078.23. Compute the flat price, accrued coupon, and market price four months after purchase of the bond. Use all three methods. 

Question 14 (Example 13)

 

A 100 par value 5% bond with semi-annual coupons is callable at the following times.

 

• 108.00, 5 to 9.5 years after issue
• 103.50, 10 to 14.5 years after issue
• 100.00, 15 years after issue (maturity date).

 

What price should an investor pay for the callable bond if they wish to realize a yield rate of (a) 6% payable semi-annually and (b) 4% payable semi-annually?

Question 15

 

The first call date of a callable 100 par value 5% bond with annual coupons is the date immediately after the 10th coupon payment with C, is given by

 

? 100,     10 ? n ?17

C ??      ₂                      .

_?100?10(n?17) ,          17 ? n ? 20

 

What price should an investor pay for the callable bond if she realises a yield rate of 4% payable annually? 

Question 15

 

The first call date of a callable 100 par value 5% bond with annual coupons is the date immediately after the 10th coupon payment with C, is given by

 

? 100,     10 ? n ?17

C ??      ₂                      .

_?100?10(n?17) ,          17 ? n ? 20

 

What price should an investor pay for the callable bond if she realises a yield rate of 4% payable annually? 

Question 16

 

Prove that when a bond is purchased at a

 

(a) premium if r > i; and          (b) discount if r < i.

where the following assumptions are necessary: P, F = C > 0; n ≥ 1; and 0 < r, i < 1.