Question

Yoyo company issued a 33-year non-callable bond, 3 years ago. It pays semi-annual coupons with a coupon rate of 10% and has a current market price of $1,989.86 now. If the firm’s tax rate is 40%, what is the component cost of debt that is used in the WACC calculation?

SHOW WORK

Answer 1

Taking $1000 par value, we have -

Semi - annual interest payment = $1000 x 10% x 6 / 12 = $50

Total semi - annual periods till maturity = (33 - 3) x 2 = 60

First, compute approximate YTM using the following formula -

where, I = interest payment, RV = redeemable value, MV = market value, n = no. of time periods

or, Approx YTM = 2.241%

Now, YTM is close to this rate. We need to choose two rates close to approximate YTM and compute the market value of the bond at those rates. The rate at which market value is equal to the offered value will be the YTM. Remember, the closer the rates to YTM, the closer will be your answer.
?

Let's Try 2.00% and 2.20%

At 2.20%, Bond price = $50 x PVIFA (2.20%, 60) + $1000 x PVIF (2.20%, 60) = $50 x 33.1370170818 + $1000 x 0.2709856242 = $1927.83647825

At 2.00%, Bond price = $50 x PVIFA (2.00%, 60) + $1000 x PVIF (2.00%, 60) = $50 x 34.760886675 + $1000 x 0.3047822665 = $2042.82660021

Now, we need to interpolate -

Difference required = $2042.82660021 - $1989.86 = $52.96660021

Total difference = $2042.82660021 - $1927.83647825 = $114.99012196

YTM = Lower rate + Difference in rates x (Difference required / Total difference)

or, YTM = 2.00% + 0.20% x (52.96660021 / $114.99012196) = 2.092%

Now, this is the semi - annual YTM, Therefore Annual YTM or pre - tax cost of debt = 2.092% x 2 = 4.184%

Post tax debt or cost of debt to be used in WACC calculation = ?4.184% x (1 - 0.40) = 2.5104% or 2.51%

NOTE : PVIFA = [ 1 - { 1 / (1 + r)ⁿ? } ] / r

PVIF = 1 / (1 + r)ⁿ