Question

Moon Software Inc. is planning to issue two types of 25-year, noncallable bonds to raise a total of $6 million, $3 million from each type of bond. First, 3,000 bonds with a 10% semiannual coupon will be sold at their $1,000 par value to raise $3,000,000. These are called "par" bonds. Second, Original Issue Discount (OID) bonds, also with a 25-year maturity and a $1,000 par value, will be sold, but these bonds will have a semiannual coupon of only 6.25%. The OID bonds must be offered at below par in order to provide investors with the same effective yield as the par bonds. How many OID bonds must the firm issue to raise $3,000,000? Disregard flotation costs, and round your final answer up to a whole number of bond

Answer 1

Answer:

It will issue 34,407 bonds

Explanation:

The Original Issue Discount state that the interest are accrued during the life of the bond and included in the face value.

This means in 25 years, it will receive 1,000 dollars, how much will it pay for that now ?

we have to find the present value which makes the YTM equal to 10%

$\frac{Face \: Value }{(1 + rate/m)^{time \times m} } = PV$

where m are the times it compound per year

in this case a semiannualy rate is compounding 2 times per year

the rate will be 0,10 percent

the face value will be 1,000

and time equal to 25 years

$\frac{1,000}{(1 + 0.1/2)^{25\times2} } = 87.20$

If it needs to raise 3,000,000 It will issue:

3,000,000/87.20 = 34406.669 = 34,407 OID bonds