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 6.75%.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 bonds.

Question

Quizplus · Accepted Answer

The par bonds have a 10% semiannual coupon rate, so the semiannual coupon payment is $1,000 × 10%/2 = $50.
The par bonds will raise $3,000,000, so the total number of par bonds is $3,000,000 ÷ $1,000 = 3,000 bonds.
Let's denote the face value of an OID bond as PV. The market value of an OID bond can be written as PV × (1 - discount rate), where the discount rate is the rate that equates the present value of the cash flows to the market value. In this case, the semiannual cash flow is $1,000 × 6.75%/2 = $33.75, and the total discounted cash flow over the life of the bond is also $1,000. So we have:
PV × (1 - discount rate) = $1,000
The discount rate can be calculated using the RATE function in Excel, which gives a result of 3.5% per semiannual period or 7% per year. Note that this rate is lower than the coupon rate, which is why the bond is offered at a discount.
The market value of an OID bond is therefore PV × 0.9346, where 0.9346 = 1 - 7%/2. To raise $3,000,000, the number of OID bonds required is:
(3,000,000 ÷ 1,000) ÷ 0.9346 = 4,266.24
Rounding up to the nearest whole number, the answer is 4,266. The correct answer choice is E.