Business Economics 271
John W. Sell

BOND YIELD PROBLEM SET

There are several ways of measuring the yield on bonds. Two of the most common are current yield and yield to maturity (YTM). These values are not always equal. Sometimes, current yield exceeds YTM and sometimes the reverse is true. Verify this relationship by completing the following chart:

AshO 8.8s08.

Use annual interest payments.  Assume a bond rating of “A”.  Let the purchase (settlement) date be today’s date and let the maturity date be the same month and day of the year indicated.

Bond Price

YTM

CYield

 

$1,109.00

 

?

 

?

 

$1,049.375

?

?

 

Par

?

?

 

$966.875

?

?

 

$910.50

?

?

 

$881.50

11.65%

9.98%

You can create an EXCEL spreadsheet to do the calculations for you.  For at least one of the calculations, however, you should use the approximation formula to confirm the result.

To create the spreadsheet:

·       Type the labels, “Settlement,” “Maturity”, “Coupon”, and “Price” in cells A5 through A8 respectively.

·       Type the labels, “YTM” and “CYield” in cells D4 and E4 Respecively.

·       In cell D5, enter the formula, “=YIELD(B5,B6,B7,B8,100,1,0)”

·       In cell E5, enter the formula, “=(B7/B8)x100”

·       Note that the coupon rate that you enter in cell B7 should be expressed as a decimal.  That is, 5.4% should be entered as 0.054.

·       Note that the price that you enter in cell B8, should be expressed as price per $100 of par value.  Thus, a price of 98% of par should be entered as 98.

·       To check your spreadsheet, the values for the last two calculations are shown in the table.

Plot these points on graph paper. But bond price on the horizontal axis and Yield (%) on the vertical axis. Connect the current yield points with one line and the YTM points with another. Label each.

Problem: Are there any points where current yield and YTM are the same? Are the prices given in the chart unusual in this regard or will your answer always hold true? Would it make any difference if the bond rating were changed (to, say, "A")? Why or why not?

Problem: Can you identify the pattern of when YTM is greater than current yield and vice versa? Can you explain why this pattern exists?