A corporate bond with a 7.700 percent coupon has eleven years left to maturity.
ID: 2632325 • Letter: A
Question
A corporate bond with a 7.700 percent coupon has eleven years left to maturity. It has had a credit rating of BB and a yield to maturity of 10.1 percent. The firm has recently become more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 9.0 percent.
What would be the total return of the bond in dollars?
What would be the total return of the bond in percentage?
What would be the total return of the bond in dollars?
What would be the total return of the bond in percentage?
Explanation / Answer
Annual coupon = 7.7%*1000 = 77
Current price of the bond can be calculated in Excel as =PV(10.1%,11,-77,-1000). This is equal to 844.83.
Alternately, the price can also be calculated as 77 * (1-1/(1+10.1%)^11) / 10.1% + 1000/(1+10.1%)^11 which is equal to 844.83.
If the new yield is 9%, then the new bond price can be calculated in Excel as =PV(9%,11,-77,-1000). This is equal to 911.53
Another way of calculating the new bond price is 77 * (1-1/(1+9%)^11) / 9% + 1000/(1+9%)^11 which is equal to 911.53
So as we have just calculated, the old price was 844.83 and the new price (after the re-rating) is 911.53
So total return of the bond in dollars = new price - old price = 911.53 - 844.83 = 66.70
Total return of the bond in % = (new price - old price) / old price = (911.53 - 844.83) / 844.83 = 7.89%
Answer: Total return of the bond in dollars = $ 66.70 and the total return of the bond in % = 7.89%
Hope this helped ! Let me know in case of any queries.
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