Consider a $10, 000 par value, 10 year bond which matures at par (redemption val

Question

Consider a $10, 000 par value, 10 year bond which matures at par (redemption value=par value) bearing a 5% nominal coupon rate convertible semiannually. (a) Find the price of the bond in order to earn a nominal yield to maturity convertible semiannually of 7%. Is the bond sold at premium or discount? (b) Calculate the book value of the bond at the end of the 4th coupon period. (c) Calculate the the price and price-plus-accrued of this bond halfway through the 5 th coupon period (that is at t = 4.5).

Explanation / Answer

Given Info:

Par value

$10,000

Maturity (years)

10

Coupon

5%

YTM

7%

a) Finding out the Present Value on a semiannual basis

Face Value

$10,000

Maturity (periods)

20

Coupon (semi-annual)

2.5%

YTM

7%

PMT (Coupon*Face Value)

$250

Present Value (Price)

- 5,232.69

The bond is sold at a discount as the current market discount rate is 7% and we are paid only 5% for coupon on our bond. Therefore the carrying value of the bond will be lesser than the face value

b) Finding out the Present Value on a semiannual basis after 4 periods

Face Value

$10,000

Maturity (periods)

16

Coupon (semi-annual)

2.5%

YTM

7%

PMT

$250

Present Value after 2 years

- 5,749.01

The bond is issued at a discount and as the maturity of the bond has reduced the present value will increase due to the inverse relationship

Note: The present value formulae has been used above

Par value

$10,000

Maturity (years)

10

Coupon

5%

YTM

7%

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