# Understanding Bond Calculations

Many investors allocate part of their capital to investments that are intended to maintain a relatively stable principal amount and to generate returns mainly in the form of interest or dividend income. This is good practice. Having part of your capital in this type of investment, as opposed to growth-oriented assets like common stocks, could help a portfolio withstand the inevitable down periods in the stock market.

Banks and financial institutions offer fixed-rate depository accounts – savings accounts, certificates of deposit and others, which we covered in detail in past articles. These accounts have zero or near-zero probability of losing any of their principal. The trade-off is that in exchange for near-zero risk, they also offer very low returns.

**Doing Better Than Cash Based Investments**

There are other types of instruments that offer higher returns than cash. Two main types are bonds, which pay a fixed rate of interest; and preferred stocks, which pay a fixed dividend amount. Bonds and preferred stocks can pay substantially more than cash. It is important to understand what to expect as the returns for these income-generating investments. This goes a bit beyond just the stated interest or dividend rate, because the value of the investment principal itself can fluctuate, affecting the overall yield. Here we will discuss bonds.

**What is a Bond?**

A bond is a loan or I.O.U. with a fixed principal amount, interest rate, and repayment date. An investor who owns a bond has indirectly lent money to the government or corporation that issued the bond.

Every bond has a face value or ** Par Value**, usually $1,000 per bond.

It has a stated interest rate, or ** Coupon Rate**. For an example, let’s say 4%.

These two pieces of information tell us that we could expect an income of $40 per year on each $1,000 bond.

(Almost) every bond has a Maturity Date. This tells us at what future date the bond issuer will repay the principal to the investor.

Simple so far. A bond with a maturity one year in the future, with a 4% coupon rate, will pay $40 a year for one year, and then repay the $1,000 principal.

If we paid exactly $1,000 for the bond originally, then that is all there is to it – very much like a $1,000 1-year CD.

**Bond Premiums and Discounts**

But here’s the rub – we almost never pay exactly the face amount for bonds. Investors generally buy bonds at some time after they are issued, through stockbrokers in what is called the secondary market. The bonds trade freely, and their prices fluctuate from day to day. The prices of the bonds drop when interest rates rise and rise when rates drop. Our eventual net return on the bonds depends both on the income we collect while we hold them, and also on how much we make or lose on the bond price.

The price at which we purchase a bond – its market value at that time – might be above the par value, in which case the difference is called a ** premium**; or below the par value, in which case the difference is called a

**. Since we will eventually be paid an amount equal to the par value, a premium paid today will result in a known loss on the bond price, while a discount is a sure gain. These must be figured into our yield. This gain or loss, amortized over the bond’s remaining lifetime, must be added or deducted from the interest income each year to determine the net yield, which is called**

*discount***. We’ll get to that calculation in a moment.**

*yield to maturity (YTM)*In our 1-year 4% example, let’s say that today, with one year until maturity, we can buy the bond for $990, or 99% of its par value.

Over the next year, we collect interest equal to 4% of the $1,000 par value, or $40. (The interest amount is always calculated based on the par value, not our purchase price).

**Current Yield/Distribution Yield**

First, let’s consider just the interest payments. Since we paid only $990, our actual cash-on-cash return, called ** current yield**, is $40 / $990, or 4.04%.

Current yield is related to another term used by mutual funds or ETFs that contain bonds. These funds refer to the amount of the fund’s annual payouts, which usually equal the combined current yield of all the bonds in the fund, as the **Distribution Yield** of the fund.

**Yield to Maturity (YTM)**

At the maturity date, we are repaid the full $1,000 par value. Since we originally paid $990 (we bought the bond at a $10 discount), we have a $10 gain on the principal. This amounts to $10/$990, or an additional 1.01% return.

Adding together the ** current yield** of 4.04% and the

**of 1.01%, our net yield is 5.05%. This is called the**

*discount***.**

*yield to maturity*We can show this another way as follows:

Original Investment: | $990 |

Interest Income | $40 |

Gain at maturity | $10 |

Total Yield, dollars |
$50 |

Total Yield, percent |
$50 / 990 = 5.05% YTM |

If instead of $990, we had originally paid $1010 for the same bond (paid a $10 **premium**), then we would have a different result:

Original Investment: | $1010 |

Interest Income | $40 |

Gain (loss) at maturity | ($10) |

Net Yield, dollars |
$30 |

Net Yield, percent |
$30 / 1010 = 2.97% YTM |

If the bond matured in two years instead of one, then the $10 premium or discount would have to be divided over the two years, so that it would have just half as much effect on the *annual* yield to maturity; if ten years, then 1/10 as much effect each year, etc.

Both the current yield and yield to maturity figures are always quoted for every bond. Of the two, the ** current yield** tells you what your annual cash-on-cash return will be; and the

**tells you what your real, all-in yield will be in the end. The yield to maturity is the more important measure.**

*yield to maturity***Yield to Call (YTC)**

Finally, let’s assume that the bond was *callable*. Some bonds, not all, are callable. If so, the issuer has reserved the right to pay off the bond early and, of course, stop paying interest when they repay the bond.

A bond shortened by yield to call gives a different figure than yield to maturity because the premium or discount on the bond (difference between original purchase price and eventual repayment at par) is spread over a different number of months.

If a $1000 bond had a 12-month term, and I paid $1010 for it, the $10 premium I paid (1% of par) would be spread over 1 years, reducing my yield by 1% / 1 = 1% per year on average, so YTM would be roughly 1% lower than current yield.

But if that bond was called after 9 months, the $10 premium would have been incurred in 3/4 years, not a full year, reducing my yield by 1%/.75 = 1.33% instead of 1%.

The quote for yield to call will always be less than yield to maturity on callable bonds if they are purchased at a premium; and YTC will be greater than YTM if purchased at a discount. This is true whether both figures are quoted *raw* (un-annualized) or annualized.

Say the interest was scheduled as four quarterly payments of $10 each. The call date is 3 months before maturity. This calls for a different calculation, referred to as ** yield to call**, which takes into account two additional factors:

Original Investment:$990, $1010

Bond bought at: |
$10 Discount |
$10 Premium |

Original Investment | $990 | $1010 |

Interest Income (3 qtrs) | $30 | $30 |

Gain (Loss) at maturity | $10 | ($10) |

Total Yield, dollars | $40 | $20 |

strong>YTC raw (9 mo) | $40 / 990 = 4.04% | $20 / 1010 = 1.98% |

YTC annualized (X12/9) |
5.38% |
2.64% |

YTM if not called: |
5.05% |
2.97% |

As we can see here, any effect of the amortization of the premium/discount is magnified if the bond is called early. This is true whether the bond was purchased at a premium or a discount.

**Yield to Worst (YTW)**

Finally, there is the measure called ** yield to worst**. This is the same as yield to maturity if the bond is not callable; or the lower of yield to maturity or yield to call if the bond is callable.

**Which Measure to Use**

When choosing among bond investment alternatives, *where the plan is to hold the bonds to maturity*, the best yield number to use is the lowest one, which will be yield to call for callable bonds, or yield to maturity for non-callable bonds. This figure will give the best idea of the true long-term result and the most comparable measure among different bonds. Focusing on current yield alone would severely distort your expectations.

If bonds are purchased with any plan other than holding them to maturity, then the expected yield cannot be calculated accurately since the bond prices will fluctuate. Where neither the eventual sale price nor the term over which the premium/discount are to be amortized are known in advance, then no yield calculation (except current yield during the holding period) is possible. Buying bonds with the intention of selling them before maturity amounts to trading bonds, not investing in them. People can and do trade bonds, some of them profitably, but that’s requires a more detailed discussion.

Knowing which yield measure to use is a key tool for selecting interest-bearing investments. I hope this information helps with those choices.