Question

Russell Container Corporation has a $1000 par value bond outstanding with 20 years to maturity. The bond carriers an annual interest payment of $126 and is currently selling for $980 per bond. Russell Corp. is in a 30 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.

a. Compute the yield to maturity on the old issue and use this as the yield for the new issue

b. Make the appropriate tax adjustment to determine the aftertax cost of debt

Answer 1

Usually, exact value of YTM cannot be calculated without using the Excel or calculator which has rate calcuation option.

There are two ways of doing of calculating YTM. Using the approximate method or using excel.

We will calculate using approximate method first:

Here: Face Value = $1000

Coupon value = $126, hence coupon rate = 12.6%

Price = $980

Maturity = 20 years

Approximate YTM = (Coupon Value + (Face Value - Price) / Maturity) / ((Face Value + Price)/2)

Hence approximate YTM = (126+ (1000-980)/20) / ((1000+980)/2) = 12.82%

Now using excel

In excel, we will use the formula of RATE

YTM = Rate (nper, pmt, pv, -fv, type, guess)

where nper is the maturity, pmt is the coupon (interest payment), pv = face value of bond, fv = price or market value of bond and type =0 for end of period payment and =1 for beginning of period payment. Guess, we can enter as 0

YTM = Rate(20, 126, 1000,-980,0,0)

YTM = 12.87% which is very close to approximate method

B.

Calculating cost of debt using YTM

Cost of debt after tax = YTM * (1-tax rate)

Cost of debt after tax = 12.87% * (1-30%) = 9.01%