I have the explanation to the question below, however I still have some question
ID: 2763343 • Letter: I
Question
I have the explanation to the question below, however I still have some question about the calculations
How was the face value of $1,000 calculated?
How was the PMT of $46.25 calculated?
I also need help understanding what numbers were used in the explanations to get the answer.
Also what does rd = ? (and how is it calculated)
What does t = ? (and how is calculated or is it already given?)
Thanks and I really appreciate the help.
Chemical Company sold a non-callable bond several years ago that now has 20 years to maturity. It has a 9.25% coupon rate, sells at a price of $875 now. If the firm's tax rate is 40%, what is the component cost of debt for use in the WACC calculation?
a.5.95%
b.5.63%
c.6.47% (Answer)
d.6.15%
e.5.31%
Answer c
Explanation
m=2 semiannual coupon payments and face value is $1000.
Calculator inputs:
N = 2 x 20 40
PV = Bond's price -$875.00
PMT = Coupon rate Par / 2 $46.25 (how was this calculated?)
FV = Par = Maturity value $1,000 (how was this calculated?)
CPT I/Y, yields semiannual rate i/2= 5.39%(what numbers were used to get this answer?)
Annual rate = 2 x (I/Y) = Before-tax cost of debt is 10.79%(what numbers were used to get this answer?)
After-tax cost of debt = rd(1 –T)= 6.47 (what numbers were used to get this answer?)
Explanation / Answer
Face Value 1000 Current Price of Bonds 875 Maturity Period N= 40 Coupon Rate = 0.04625 Coupon amount or PMT= 46.25 Yield to Maturity= 6.47% Semi Annual Payment Means we pay interest in two times in the year, interest rate given for whole year so we divide it by 2 Maturity Period which is given as 20 years, when we pay the interst in two times a year N means nuber of times we paid the interest, obviously it is 2*20=40 times Face Value=A Bond selling at par is priced at 100% of face value.Par is also used to refer to its original issue value or its value upon redemption at maturity. This amount is typically $1000 per Bond. Yield to Maturity=(Coupon Payment+(Maturity Value+Current Price)/n)/(Coupon Payment+Current Market Price)/2 Yield to Maturity=($46.25+(1000-875)/40)/(1000+875)/2 Yield to Maturity= ($46.25+$3.125)/975.5 Yield to Maturity= 0.054 5.39 (Approx) (Half Yearly) Yearly Yield to Maturity= 10.78 After Tax Cost of debt= 6.468 40% is tax rate so cost of debt is calculated after tax i.e 6.468