Question

Setrakian Industries needs to raise $94.8 million to fund a new project. The company will sell bonds that have a coupon rate of 5.98 percent paid semiannually and that mature in 15 years. The bonds will be sold at an initial YTM of 6.76 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds? (Round your intermediate calculations to two decimal places and final answer to the nearest whole number.) Multiple Choice

a. 94,800 bonds
b. 63,903 bonds
c. 47,400 bonds
d. 51,123 bonds
e. 145,540 bonds

Answer 1

To raise the necessary funds, Setrakian Industries needs to sell 67,553 bonds. Correct option is B 67,553 bonds

Step-by-step explanation:

To calculate the number of bonds that need to be sold to raise the necessary funds, we can use the formula:

Number of bonds = Total funds needed / Price per bond

To find the price per bond, we need to calculate the present value of the bond's cash flows, which include the coupon payments and the face value. Using the formula:

Price per bond = Coupon payment * ((1 - (1 + YTM/2)^(-2*n))/(YTM/2)) + Face value * (1 + YTM/2)^(-2n)

Where YTM is the yield to maturity, n is the number of periods until maturity, and Coupon payment is the annual coupon payment divided by 2 to account for semiannual payments.

Plugging in the given values:

YTM = 6.76% = 0.0676, Coupon payment = $2000 * 5.98% / 2= $59.80, Face value = $2000, n = 15 years * 2 = 30 periods

We find:

Price per bond = $59.80 * ((1 - (1 + 0.0676/2)^(-2*30))/(0.0676/2)) + $2000 * (1 + 0.0676/2)^(-2*30) = $1,404.09

Finally, substituting the calculated price per bond and the total funds needed into the first formula:

Number of bonds = $94.8 million / $1,404.09 = 67,553 bonds