Allison's wants to raise $12.4 million to expand its business. To accomplish this, it plans to sell 25-year, $1,000 face value, zero-coupon bonds. The bonds will be priced to yield 6.5 percent, with semiannual compounding. What is the minimum number of bonds Allison's must sell to raise the $12.4 million it needs?

Question

Tia Clayton

Business

6 May, 05:02

Allison's wants to raise $12.4 million to expand its business. To accomplish this, it plans to sell 25-year, $1,000 face value, zero-coupon bonds. The bonds will be priced to yield 6.5 percent, with semiannual compounding. What is the minimum number of bonds Allison's must sell to raise the $12.4 million it needs?

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Micah · Answer 1

= 55,780.5 units

Explanation:

A bond is a financial instrument used by a company or government to borrow money.

Zero-coupon bond: Most bonds pay a fixed percentage of their face value - coupon - as interest payment at requalr intervals.

A zero - coupon bond pays no coupon. However, the return on it is the difference between its face value and price.

The Price of a bond is determined using the discounted flow method. Here the present value is calculated using its the face value and the yield. The face value is the amount promised by borrower to pay back. And the yield is the return on the bond expressed in %.

This can be captioned as follows:

P * (1+r) ^n = FV,

P - price, FV - Face value, r = yield

P-?, FV - 1000, r = 6.5%/2 = 3.25% (semi-annual interest rate)

P * (1.0325) ^ (25 * 2) = 1000

P * 4.9488 = 1000

P = 1000/4.4988

P = $222.28

P = $222.3

If the bond sells for $222.3, then to raise $12.4 million, Allison will have to sell:

= 12,400,000/222.3

= 55,780.5 units