Question

A 10-year bond of a firm in financial distress has a coupon rate of 12% and is selling at $900 (face value is $1,000). The firm is re-negotiating its debt and the bond-holders have agreed to cut coupon payments in half.

a. What is the stated (promised) yield-to-maturity on the bond? (i.e. what is the YTM at which the bond was trading?)

b. How does it compare to the expected yield on the bond? (i.e. what is the expected yield given the agreement?)

Answer 1

A)

Calculation of stated YTM:

YTM can be calculated using approximation formula or exact formula.

 

Using approximation formula, YTM is:

=[Annual coupon + (Face value-Current price)/Years to maturity]/(Face value-Current price)/2

Annual coupon = Face value*Coupon rate

=($1000*12%)=$120

 

Thus, YTM is:

= [$120+($1000-$900)/10]/($1000+$900)/2

= ($120+$10/$950

= 0.1368 or 13.68%

 

If we use exact formula, then YTM will be 13.91%

 

B)

Calculation of expected YTM:

Revised Annual coupon = ($1000*12%)*50%

                                           = $60

 

Approximation YTM is:

= [$60+($1000-$900)/10]/($1000+$900)/2

= ($60+$10)/$950

= 0.0739 or 7.39%

 

Exact YTM=7.45%

A) If we use exact formula, then YTM will be 13.91%

 

B) Exact YTM = 7.45%