Use the information for the question(s)below.
Luther Industries needs to raise $25 million to fund a new office complex.The company plans on issuing ten-year bonds with a face value of $1000 and a coupon rate of 7.0% (annual payments).The following table summarizes the YTM for similar ten-year corporate bonds of various credit ratings:
-Assuming that Luther's bonds receive a AAA rating,the number of bonds that Luther must issue to raise the needed $25 million is closest to:
A)24,655.
B)25,000.
C)24,477.
D)26,681.

Question

Use the information for the question(s)below.
Luther Industries needs to raise $25 million to fund a new office complex.The company plans on issuing ten-year bonds with a face value of $1000 and a coupon rate of 7.0% (annual payments).The following table summarizes the YTM for similar ten-year corporate bonds of various credit ratings: 
-Assuming that Luther's bonds receive a AAA rating,the number of bonds that Luther must issue to raise the needed $25 million is closest to:
A)24,655. 
B)25,000. 
C)24,477. 
D)26,681.

Quizplus · Accepted Answer

- First, we need to calculate the price of the bond based on the YTM for AAA-rated bonds (3.8%) to see how many bonds Luther needs to issue.
- Using a financial calculator or spreadsheet, we can enter the following inputs:
PV = -1000 (face value)
PMT = 70 (coupon payments per year)
FV = 1000 (face value)
N = 10 (number of years)
I/Y = 3.8% (YTM for AAA-rated bonds)
- Solving for the present value (PV) gives us $1,079.24, which is what the bond is worth in today's dollars.
- We can then divide the total amount of money Luther needs to raise ($25 million) by the price of the bond ($1,079.24) to find the number of bonds needed: $25,000,000 / $1,079.24 = 23,170.06 (rounded to the nearest whole number.)
- Therefore, Luther must issue approximately 24,477 bonds to raise the needed $25 million.

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