Question

(Bonds) A company has an outstanding issue of $1000 face value bonds with 8.75% annual coupon and 10 years remaining until maturity. The bonds are currently selling at a price of 82.50 (82.50% of face value). The company wishes to sell a new a bond issue with a 30-year maturity. Their investment bank has advised that (1) the new 30-year issue could be sold for a flotation cost of 3% of face value, and (2) current yield curves indicate that 30-year maturity bonds yield a nominal 75 basis points (0.75%) more than 10 year maturity bonds on average. The company is in the 35% tax bracket.

a. Calculate investors' required rate of return today.

b. What annual coupon would have to be placed on the new issue in order for it to sell at par?

c. Calculate the flotation cost and tax savings from the proposed new issue.

d. Calculate the cost of the new bond financing.

Answer 1

Part (a)

Yield of 10 year maturity bonds = RATE (period, PMT, PV, FV) = RATE (10, 8.75% x 1000, - 82.50% x 1000, 100) = 11.83%

Investors' required rate of return today = a nominal 75 basis points (0.75%) more than 10 year maturity bonds on average = 0.75% + 11.83% = 12.58%

Part (b)

Annual coupon = annual yield = 12.58%

Part (c)

Flotation cost per bond = 3% x 1,000 = $ 30

Tax savings per bond per year = Tax savings due to annual interest per bond + Tax savings due to flotation cost per year per bond

Annual interest = Annual coupon x Face value =12.58% x 1000 = $ 125.75

Tax rate, T = 35%

Hence, tax savings due to annual interest per bond = Annual interest x tax rate = 125.75 x 35% = $ 44.01

Flotation cost per bond per year = Flotation cost / life = 30 / 30 = 1

Tax savings due to flotation cost per year per bond = Flotation cost per bond per year x tax rate= 1 x 35% = $ 0.35

Tax savings per bond per year = Tax savings due to annual interest per bond + Tax savings due to flotation cost per year per bond = 44.01 + 0.35 = $ 44.36

Part (d)

Price net of flotation cost = 1,000 - 30 = 970

Hence PV = - 970

Period = 30 years

PMT = Interest - tax shields =  125.75 - 44.36 = 81.39

Cost of new financing = RATE (Period, PMT, PV, FV) = RATE (30, 81.39, -970, 1000) = 8.42%