# Finding the yield on individual corporate bonds

I'm looking at an individual corporate bond (20341WAD7) with a 8.25 coupon trading at a last price of around 88 cents on the dollar (88/100). By my simple math the yield should be 8.25%/.88 = 9.375%. And yet the yield is listed by my broker as 12.08%. (Yield to Worst and Yield to Maturity are both listed as about 11.82) How can this be?

9.375% would be the current yield, meaning the yield you'd get from the next coupon payment. The yield to maturity is the annualized return you'll receive if you hold the bond until maturity and reinvest the coupons at the same rate. It's essentially the IRR of the bond if you hold it to maturity. IRR generally can't be computed directly - it is typically calculated with an iterative process, changing the rate of return until the present value of the bond's cash flows equals the market price. However, one formula to estimate it is

``````YTM = Int + (Par - MV)/TTM
--------------------
(Par + MV)/2

= 8.25 + (100-88)/4
-----------------
(100+88)/2

= 11.97%
``````
• Why would you be reinvesting the coupons at the same rate? There's no guarantee you'll get that rate in the future based on market fluctuations and most people I know use the interest payments to live off, not reinvest. – public wireless Oct 15 at 4:27

Here's the simple math for four years but without a compounding logic:

100 - 88 = 12

12 / 4 = 3

8.25 + 3 = 11.25

11.25 / 88 = 0.1278 as 12.78% .

• I have a math degree and I can barely follow what you're doing. Could you add an explanation of each of these steps, and what the end result represents? – Tanner Swett Oct 11 at 10:22
• @TannerSwett -- that 12 is the capital gain when the bond matures. It was bought for 88, and at maturity it will pay 100, for a gain of 12. – Pete Becker Oct 11 at 13:11
• The primary fundamental, in addition to the most simple calculation, is that the bond returns to par progressively across the four years as it approaches redemption. Returning to par must be included in a simple calculation. A compounding of the dividends is not the primary fundamental but included in the other post as current practice. Here is a link to valuing bonds without the compounding of dividends: kbhscape.com/bond.htm . – S Spring Oct 11 at 13:36
• But returning to par is a one-time event that only happens at maturity (and isn't guaranteed). Most people investing in income securities use the income to pay yearly living expenses and so in the example above they could only plan on receiving ~\$94/year for every \$1000 invested. It seems this 9.375% value is most useful and yet my broker doesn't include it. – public wireless Oct 15 at 4:32
• The yield-to-maturity includes progressively moving to the bond's redemption value. – S Spring Oct 19 at 1:09