Question

Clements Marshall Ltd plans to raise $2 million to build a new onion-processing factory near Devonport in Tasmania. It will issue bonds with a term to maturity of 12 years. The face value per bond will be $1,000 and the coupon rate will be 7% per annum, paid semi-annually. Similar corporate bonds are trading at a yield to maturity of 8% per annum, compounded semi-annually. It is expected that these new bonds will trade at this rate. How many bonds will Clements Marshall need to issue?

Answer 1

Face Value of bond = $1,000

Coupon rate = 7%

C = Semi annual Coupon payment = $1,000 * 7%/2 = $35

r = Semi annual yeild to maturity = 8%/2 = 4%

n = 12*2 = 24 semi annuals

Market Value of bond today = [C * [1 - (1+r)^-n] / r] + [Face Value / (1+r)^n]

= [$35 * [1 - (1+4%)^-24] / 4%] + [$1,000 / (1+4%)^24]

= [$35 * 0.609878526 / 0.04] + [$1,000 / 2.88336858]

= $533.64371 + $390.121475

= $923.765185

Market Value of bond today is $923.77

Amount needed = $2,000,000

Bonds need to be issued = Amount needed / Market Value of bond

= $2,000,000 / $923.77

= 2,165.041018

= 2,166

Therefore, Clements marshal need to issue 2,166 bonds