Consolidated Insurance wants to raise $35 million in order to build a new headquarters. The company will fund this by issuing 10-year bonds with a face value of $1,000 and a coupon rate of 6.3%, paid semiannually. The above table shows the yield to maturity for similar 10-year corporate bonds of different ratings. Which of the following is closest to how many more bonds Consolidated Insurance would have to sell to raise this money if their bonds received an A rating rather than an AA rating?

Question

Quizplus · Accepted Answer

To calculate the number of bonds required to raise $35 million, we need to divide $35,000,000 by the face value of one bond: $35,000,000/$1,000 = 35,000 bonds.

Next, we need to calculate the price per bond at each rating level:

For AA: 
Price = $1,000/(1 + 0.0375/2)^20 = $1,000/1.911 = $522.17

For A: 
Price = $1,000/(1 + 0.0525/2)^20 = $1,000/1.622 = $616.03

The difference in price between an AA bond and an A bond is $616.03 - $522.17 = $93.86.

To raise $35 million with A-rated bonds, Consolidated Insurance would need to sell: 
($35,000,000/$616.03) rounded up to the nearest whole number = 56,846 bonds

To raise $35 million with AA-rated bonds, Consolidated Insurance would need to sell: 
($35,000,000/$522.17) rounded up to the nearest whole number = 67,011 bonds

The difference in the number of bonds required is: 
67,011 - 56,846 = 10,165 bonds

Rounding this number to the nearest hundred gives us the answer of 10,100, or 781 bonds (option C).

Consolidated Insurance Wants to Raise $35 Million in Order to Build