Question

Barnstaple Corporation is aiming to raise $113 million to acquire another business. This amount will be through an issue of 3-year corporate bonds with a face value of $1 000 paying quarterly coupons with a yield of 6.4% p.a. These bonds will mature at par and the market is expected to require a yield of 88% p a. Barnstaple Corporation has sought an underwriter to assist them with this capital raising. The underwriter requires 3.5% fees for the issue. 6. a.) Calculate the expected price of the corporate bond, giving your answer correct to the nearest cent. (3 marks) b.) How much will Barnstaple Corporation need to sell for this issue, giving your answer to the nearest dollar? (2 marks) c.) How many corporate bonds will Barnstaple Corporation need to sell? (Hint: Be careful you are not using rounded figures from a.) and b.) in your answer here) (2 marks) Prior to the corporate bonds being sold, the central bank announced that the interest rate would rise by 0.5%, without performing any calculations, how would you answers in a), b.) and c.) change? Give a brief explanation in your answer. (2 marks) d.)

Answer 1

Given Information:
Amount to be raised = $ 113 million
3 year corporate bond
Term = 3 years
Face value = $ 1000
Quarterly coupons with yield of 6.4% p a
maturity value = at par
expected market yield = 8.8%pa
Underwriting fees = 3.5%

Assumption: It is assumed that the underwriting commission expense will be paid out of the proceeds received from sale of bonds. Calculations are made on this assumption.

If we do not take this assumpotion then, the no of bonds to be sold will be 120557 (113000000 / 937.32 ).

1. Calculation of expected price of the bond :

Price of the Bond =  c × F × [1 − (1 + r)^-t / r] + [ F /(1 + r)^t ]

   ⁼ 0.064 * 1000 * [ 1 - (1+ 0.088)^-3 / 0.088] + [1000/ (1+0.088)³]

= 937.32

Note: r is the interest rate prevailing in the market, c is the coupon rate on the bond, t is the time periods occurring over the term of the bond and F is the face value of the bond.

2. How much will Barnstaple need to sell the issue:

They will need to sell bonds worth :

Amount to be raised + underwriting commission

= 113 million + (113 million * 3.5% )

= $ 113.565 million

3. Number of bonds required to be sold to raise $ 113 million:

Amount to be raised = Number of bonds sold * Price of the bond

113565000 = Number of bonds sold * 937.32

Therefore, No. of bonds to be sold = 113000000 / 937.32

= 121160 bonds

4. Effect of rise in rate of interest on price of bond :

There exists an inverse relationship between interest rates and bond prices. Hence on an increase in the interest rates by the government, the price of the bond will decrease as interest rate increase by 0.5%.

This is so because interest rate and bond prices share an inverse relationship with each other.