Cost of Capital-After tax cost of debt?

CFA Level I
#1

Having a hard time understanding the following problem, any help would be much appreciated.

Dot.Com has determined that it could issue $1,000 face value bonds with an 8% Coupon paid semi-annually and a five year-maturity at $900 per bond. If Dot.Com’s marginal tax rate is 38%, its after-tax cost of debt is closest to?

Solution:

Fv=$1,000

PMT=$40

N=10

PV=-$900

YTM=5.3149% * 2= 10.62985%…10.62985%(1-.38)=6.5905%

Question: How did we come up with a PMT of $40? (The rest I understand)

S2000Magician-Thanks in advanced.

#2

You have a semi-annual coupon payment, so you need to divide the coupon payment by 2.

In this case you have PMT=100*8%/2=40

1 Like
#3

THREE key concepts to remember when solving most bond problems are:

  1. Bonds problem are (almost) always expressed on an ANNUAL basis, but they’re solved on a PERIODIC basis. So yields, coupons, and maturities are expressed annually (i.e the coupon rate is the percentage of par paid PER YEAR, the maturity is the number OF YEARS, and so on).
  2. However, you solve these problems on a PERIODIC basis (i.e. if it’s a semiannual coupon bond, “N” is the number of 6-MONTH periods, PMT is the SEMIANNUAL coupon payment , and so on).
  3. Finally, if it’s a rate (Coupon Rate, Yield To Maturity) or Number of periods you’re solving for, you express your answer on an ANNUAL basis.