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 rating of 6.5%,paid semi-annually.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 determine the number of bonds Consolidated Insurance would have to sell to raise $35 million, we divide the total amount by the face value of one bond:

$35,000,000 ÷ $1,000 = 35,000

Now, to find out how many more bonds they would have to sell if they receive an A rating rather than an AA rating, we need to find the yield to maturity for these two ratings.

For an AA rating, the yield to maturity is 3.63%, so the semi-annual coupon payment would be:

($1,000 × 6.5%) ÷ 2 = $32.50

To raise $35 million at this yield, Consolidated Insurance would need to sell:

$35,000,000 ÷ [$1,000 × (6.5%/2)] = 1,076.92 ≈ 1,077 bonds

For an A rating, the yield to maturity is 4.25%, so the semi-annual coupon payment would be:

($1,000 × 6.5%) ÷ 2 = $32.50

To raise $35 million at this yield, Consolidated Insurance would need to sell:

$35,000,000 ÷ [$1,000 × (4.25%/2)] = 1,647.06 ≈ 1,647 bonds

The difference between the number of bonds they would have to sell at these two ratings is:

1,647 – 1,077 = 570

However, we need to round to the closest answer choice, which is 765 (C).

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