You are a corporate finance analyst at Globe motors which is looking to repurcha

Question

You are a corporate finance analyst at Globe motors which is looking to repurchase some of its outstanding debt. The bond issue pays an annual coupon of 6%, and has a par value = $1,000. The yield-to-maturity of 15 year US Government Treasury bonds is 4.5%, Global motors is a BBB+ company and the spread of BBB+ credit cover over 15-year US Government bonds is 1.25%  

What is the appropriate yield-to-maturity or discount rate to value Global Motor’s bond issue?

What is the fair market price of the bond?

Explanation / Answer

First we will summarize given information

Coupon rate                             = 6%
Par value                                  = 6%
Maturity                                    = 15 years
YTM of 15 years
US Government Treasury       = 4.5%
bonds
BBB+ bond spread over
15-year US Government         = 1.25%
bonds


Answer 1

Answer 2

Now to find fair market price of the bond we will use market rate of BBB+ bond which we just calculated above

Now to calculate fair market value we will find present value of all cash flow which bond will give us till maturity
It will give 15 coupon i.e. $60 (6% of $1000) and par value i.e. $1000

To find present value of cash flow we divide (nth) cash flow by yield to maturity factor (n) number of time
this is basic time value money concept.
So formula goes like this

Fair value = coupon 1   +   coupon 2 + coupon 3 + ………….   Coupon nth + Par value
                     (1+ r)                 (1+ r)2        (1+ r)3                                     (1+ r)nth

Fair value =      $60    . +      $60     .   +      $60     .   + …………………….. +   $60 + $1000
                     (1+.0575)       (1+.0575)2     (1+.0575)3                                            (1+.0575)15

= $1024.68

One way to check your answer is in the right direction is that fair value is greater than par value because interest in market (i.e. YTM) is lower than the interest provided by your bond so automatically bond will be costly as it is given more interest than market.
Similarly fair value will be lower if market rate (i.e. YTM) is more than your bond’s interest rate as market is given more interest than your bond so it will be available in cheap price.

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