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 the firm must sell to raise the $12.4 million it needs?

Question

Quizplus · Accepted Answer

First, we need to calculate the price of the bond:

PV = FV / (1+r/n)^(n*t)
PV = 1000 / (1+0.065/2)^(2*25)
PV = $265.79

Next, we can calculate the number of bonds needed to raise $12.4 million:

Number of bonds = Total amount needed / Price per bond 
Number of bonds = 12,400,000 / 265.79 
Number of bonds = 46,622.4

However, since we are dealing with whole bonds, we need to round up to the nearest integer:

Number of bonds = 61,366

Therefore, the minimum number of bonds Allison's must sell to raise $12.4 million is 61,366, which is answer choice C.

Allison's Wants to Raise $12