Question

Your firm has a credit rating of A.
You notice that the credit spread for 10-year maturity debt is 90 basis points (0.90%).

Your firm’s ten-year debt has a coupon rate of 5%.

You see that new 10-year Treasury notes are being issued at par with a coupon rate of 4.5%. What should the price of your outstanding 10-year bonds be?

(Assume face value is $100 & interests are paid semi-annually)

Answer good?

Bond Price Formula = Coupon Rate x Face Value of The Bond x {1-(1+R)^-n/R} +
Face Value of The bond/(1+R)^n

where N is the number of years

No. of years = 10 Years
C = Coupon Rate = 5 % (Assumed Annual Coupon)
R = YTM of the Bond
Given that treasury notes are trading at par therefore when a bond trades at par its
Yield to Maturity = Coupon Rate

Therefore YTM of Treasury = 4.5%
Now given the credit rating of A we need to add 90 basis points to arrive at the YTM of the bond issued by the company.
Therefore the YTM of the bond issued by the company = 4.5% +0.90% = 5.4%.

Bond Price Formula =
Coupon Rate * Face Value of The Bond * {1-(1+R)^-n/R} + Face Value of The bond/(1+R)^n

Now Bonds Price = 5% *100 * (1-1.054^-10) / 0.54) + 100/1.054^10
   =5 * 0.75739125285 + 100/1.69202240224
                      Bonds Price       =3.78695626425 + 59.1008723452
Bonds Price = $62.88

Answer 1

Price of the bond = BP and is calculated as:

Where,

F = Facevalue/ParValue = $100

c = Coupon Rate = 5%

n = Coupon rate compounding frequency = 2 (Semi annual)

r = market interest rate = 5.4%(Given YTM of Treasury = 4.5% and for 0.9% is the credit spread. For furture value of bond to $100, the YTM on this bond should = 5.4%)

t = No. of years unitl maturity = 10 years

Substituting, these values the answer is $96.94

you can also solve this using excel PV function.

PV(rate,nper,pmt,FV)*-1

where,

rate = YTM/n = 5.4%/2 = 2.7%

nper = n*t = 20

PMT = $100*5%/2 = $2.5

FV = 100

PV = $96.94 (computed)