Question

A firm plans to raise $94 million by issuing 12 - year, 6.54 percent semiannual coupon bonds with face value of $1,000 and yield to maturity of 5.26 percent. What is the minimum number of these bonds the firm needs to sell to meet its objective

Answer 1

Number of bonds = 84,469 bonds

Step-by-step explanation:

Given:

Face value M = $1000

Time n = 12 x 2 = 24 semi-annual periods

Yield to maturity i = 5.26% / 2 = 2.63% (semi-annually)

Coupon amount C = [6.54%] $1000/2 = $32.70 (semi-annually)

Computation:

`P = [C][(1-(1)/((1+i)^n) )/(i) ]+(M)/((1+i)^n) \\\\ P = [32.70][(1-(1)/((1+0.0263)^(24)) )/(0.0263) ]+(1000)/((1+0.0263)^(24)) \\\\ P = 1112.84`

Number of bonds = $100,000,000/$1,112.84

Number of bonds = 84,469 bonds