A corporate bond shows a trading price of $124.65; a coupon rate of 6.245; a maturity date of February 15, 2034; and a par value of $1,000.
What will you pay, and what will the yield be?
a) You will pay $1,246.50, and the yield will be 6.245 percent.
b) You will pay $124.65, and the zero-coupon rate will be 4.09 percent.
c) You will pay $1,000, and the yield will be 4.09 percent.
d) You will pay $1,246.50, and the yield will be 4.09 percent.
The correct answer is D.
I did the manual calculation to get the bond value of $1,236.50, but I am not sure how to use the PV function to get the same answer since I am missing the yield.
For the yield, i used RATE function and got a YTM of approximately 3.3094%, which doesnt tie to that 4.09% in the answer.
Can anyone provide clarification?
1 Like
The market price is $124.65 per $100 of face amount, so the price of the bond is 10 x $124.65 = $1,246.50, so the answer can’t be B or C.
Since this is a premium bond, you know YTM< coupon, so the answer can’t be A or C. The only answer left is D. If you know the purchase date of the bond, you could use the TVM worksheet in whatever official calculator you use to calculate the YTM.
right. that’s exactly how I solved it. I was looking to see why the Excel functions approaches are wrong.
Yeah, @breadmaker is correct that the yield must be lower than the coupon since this is a premium bond.
As for how to get exactly 4.09%, we would need to first know exactly what N (time period) is. It gives us a maturity date, but we don’t know what “today” is supposed to be in this question. Is it February 15, 2024? Is it February 14, 2034? Without this crucial piece of information, we are going to have to make some assumptions.
At first I assumed it’s a ten-year bond, and I got the same YTM of 3.3094% that you did.
Using Excel’s Goal Seek feature, you can find out what N should be in order to get a yield of 4.09%.
I tried it out, and it looks like N should be around 15 years, after rounding.
1 Like