Question

A firm has a bond with 12 years to maturity, and pays an annual coupon payment of 8%. The bond is currently selling for $1,122.40. When the company issues a new bond, there will be administrative costs and flotation costs estimated at $25 per bond. If the firm decides to issue new 10-year bonds today, what would be the effective cost of the new bonds, assuming a 35% marginal tax rate?

A. 6.85 percent B. 6.94 percent C. 7.19 percent D. 7.47 percent E. 7.92 percent

Please show work

Answer 1

Life of the new bond = 10 Years

Coupon amount = 1000 * 8% = 80. But there is 25 flotation cost per bond, thus per year it will be 25/10 = 2.5

Thus total coupon amount = 80 + 2.5 = 82.5

Amount realised by sale of bond at current price = 1122.4 - 25 = 1097.4

Therefore ............ 82.5 [ PVIFA] + 1000 * [ PV] = 1097.4

82.5 * [ 1 - (1+r)^-10 ] / r + 1000 * (1+r)^-10 = 1097.4

Let us put ....... r = 6.7 %

82.5 * [ 1 - (1.067)^-10 ] / 0.067 + 1000 * (1.067)^-10 = 587.57 + 522.82 = 1110.39

Let us put ....... r = 6.9 %

82.5 * [ 1 - (1.069)^-10 ] / 0.069 + 1000 * (1.069)^-10 = 582.13 + 513.12 = 1095.25

Use the following simple Interpolation to compute correct effective cost of bonds.

6.7 ............. 1110.39

x ............ 1097.4

6.9 ............ 1095.25

(x - 6.7) / (6.90 - 6.70) = (1097.4 - 1110.39) / (1095.25 - 1110.39)

x - 6.7 / 0.20 = 12.99 / 15.14

x - 6.7 = 0.17

X = 6.87 ................ so among the available Options ............. Option - A 6.85% is to be choosen.