## Bonds yield to maturity calculator

On this page is a bond yield to maturity calculatorto automatically calculate the internal rate of return IRR earned on a certain bond.

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This calculator automatically assumes an investor holds to maturity, reinvests coupons, and all payments and coupons will be paid on time. The page also includes the approximate yield to maturity formulaand includes a discussion on how to find — or approach — the exact yield to maturity. For this particular problem, interestingly, we start with an estimate before building the actual answer.

That's right - the actual formula for internal rate of return requires us to converge onto a solution; it doesn't allow us to isolate a variable and solve. However, that doesn't mean we can't estimate and come close. The formula for the approximate yield to maturity on a bond is:. If you've already tested the calculator, you know the actual yield to maturity on our bond is We calculated the rate an investor would earn reinvesting every coupon payment at the current rate, then determining the present value of those cash flows.

The summation looks like this:. As discussing this geometric series is a little heavy for a quick post here, let us note: for further reading, try Karl Sigman's notes, hosted with Columbia. For most purposes, such as quickly estimating a yield to maturity, the approximation formula should suffice. The calculator internally uses the secant method to converge upon a solution, and uses an adaptation of a method from Github user ndongo.

A zero coupon bond is a bond which doesn't pay periodic payments, instead having only a face value value at maturity and a present value current value.

This makes calculating the yield to maturity of a zero coupon bond straight-forward:. Use the Yield to Maturity as you would use other measures of valuation: a factor in your decision whether to buy or avoid a bond.

You can compare YTM between various debt issues to see which ones would perform best. Note the caveat that YTM though — these calculations assume no missed or delayed payments and reinvesting at the same rate upon coupon payments. Never Miss a Post.

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Don't Quit Your Day Job DQYDJ may be compensated by our advertising and affiliate partners if you make purchases through links. See our disclosures page for more information.Are you a student? Did you know that Amazon is offering 6 months of Amazon Prime - free two-day shipping, free movies, and other benefits - to students?

Click here to learn more. One of the key variables in choosing any investment is the expected rate of return. We try to find assets that have the best combination of risk and return. In this section we will see how to calculate the rate of return on a bond investment.

If you are comfortable using the TVM keys, then this will be a simple task. We will discuss each of these in turn below.

In the bond valuation tutorial, we used an example bond that we will use again here. For the sake of simplicity, we will assume that the current market price of the bond is the same as the value. You should be aware that intrinsic value and market price are two different, though related, concepts. The current yield is a measure of the income provided by the bond as a percentage of the current price:.

## Yield To Maturity (YTM) Calculator

There is no built-in function to calculate the current yield, so you must use this formula. For the example bond, the current yield is 8. Note that the current yield only takes into account the expected interest payments.

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It completely ignores expected price changes capital gains or losses. Therefore, it is a useful return measure primarily for those who are most concerned with earning income from their portfolio. It is not a good measure of return for those looking for capital gains. Furthermore, the current yield is a useless statistic for zero-coupon bonds.

Unlike the current yield, the yield to maturity YTM measures both current income and expected capital gains or losses. The YTM is the internal rate of return of the bond, so it measures the expected compound average annual rate of return if the bond is purchased at the current market price and is held to maturity.

## Bond Yield to Maturity Calculator

In the case of our example bond, the current yield understates the total expected return for the bond. As we saw in the bond valuation tutorialbonds selling at a discount to their face value must increase in price as the maturity date approaches.

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The YTM takes into account both the interest income and this capital gain over the life of the bond. There is no formula that can be used to calculate the exact yield to maturity for a bond except for trivial cases.

Instead, the calculation must be done on a trial-and-error basis. This can be tedious to do by hand. Fortunately, the BAII Plus has the time value of money keys, which can do the calculation quite easily.

Technically, you could also use the IRR function, but there is no need to do that when the TVM keys are easier and will give the same answer. Enter 6 into N But wait a minute! That just doesn't make any sense. You need to remember that the bond pays interest semiannually, and we entered N as the number of semiannual periods 6 and PMT as the semiannual payment amount Since the YTM is always stated as an annual rate, we need to double this answer.

In this case, then, the YTM is 9. Many bonds but certainly not allwhether Treasury bonds, corporate bonds, or municipal bonds are callable. That is, the issuer has the right to force the redemption of the bonds before they mature. This is similar to the way that a homeowner might choose to refinance call a mortgage when interest rates decline.

Given a choice of callable or otherwise equivalent non-callable bonds, investors would choose the non-callable bonds because they offer more certainty and potentially higher returns if interest rates decline.

Therefore, bond issuers usually offer a sweetener, in the form of a call premium, to make callable bonds more attractive to investors.Here we are going to take a look at two different ways to calculate bond yield: current yield and yield to maturity YTM.

We can calculate the yield on a bond investment using the current yield as long as we know the annual cash inflows of the investment and the market price of the security. The formula is shown below:. Current yield is usually calculated for bonds, where the annual income is the coupon paid out, but the yield could also be calculated for stocks, where the annual income is the dividend paid out, or really for any asset that pays out annually. In any case, the current market price is the price someone would be willing to pay for the asset whether that price is at a premium or a discount.

The formula for calculating YTM is shown below:. The yield to maturity is the discount rate that equates the present value of all future cashflows of the bond coupon payments and payment of face value and the current price of the bond.

We must assume that all payments are made on time, and we must assume that the bond is held to maturity. We can recognize that, because all of the coupon payments are the same, we can rewrite the formula by breaking it down into the present value of an annuity and the present value of the face value of the bond. The rewritten formula is shown below:. The left half of the right side of the equation is the present value of all the coupon payments, i.

In either situation, there is not an easy way to calculate YTM. If we want to be smart about our first guess, we can take a look at the current bond price compared to the face value of the bond. If the current market price is less than the face value, then the bond is said to be selling at a discount.

Contrarily, if the current market price is greater than the face value of the bond, then the bond is said to be selling at a premium. Intuitively, if the bond is selling at a discount, then we know that the YTM is going to be greater than the coupon rate, and if the bond is selling at a premium, then the YTM is going to be less than the coupon rate. A third situation is that when the current market price is equal to the face value.

This would imply that the YTM is equal to the coupon rate. To understand these concepts, think about plugging different rates into the first form of the YTM equation.

If the YTM is greater than the coupon rate, then the denominator of each cash flow will increase, so the sum of those cash flows will be less than the face value of the bond and hence will sell at a discount. If the YTM is less than the coupon rate, then the denominator of each cash flow will decrease, so the sum of those cash flows will be greater than the face value of the bond and hence will sell at a premium. This means that twice per year, your bond will pay out 4.

We can start with the current yield calculation, as that will be a much easier task. To calculate current yield, we must know the annual cash inflow of the bond as well as the current market price.

The current market price of the bond is how much the bond is worth in the current market place. Now that we have our two inputs to the equation, we just need to plug the inputs in and solve. The work is shown below:. This means that if you bought the bond at its current market price and held it for one year, your current return you would expect is 4. Remember, this yield assumes that all payments are paid on time and the bond is held to maturity.

We must first determine the cash flows. Now, we must take a shot at a guess for YTM. Remember that, because our coupon payments are paid out semiannually, we must halve the YTM in our equation.Yield to Maturity Calculator is an online tool for investment calculation, programmed to calculate the expected investment return of a bond. This calculator generates the output value of YTM in percentage according to the input values of YTM to select the bonds to invest in, Bond face value, Bond price, Coupon rate and years to maturity.

Definition The term Yield to Maturity also called as Redemption Yield often abbreviated as YTM and used when it comes to bond funds, is defined as the rate of return obtained by buying a bond at the current market price and holding it to maturity.

Yield to Maturity is the index for measuring the attractiveness of bonds. When the price of the bond is low the yield is high and vice versa. YTM is beneficial to the bond buyer because a rising yield would decrease the bond price hence the same amount of interest is paid but for less money. Where the coupon payment refers to the total interest per year on a bond. Yield to maturity can be mathematically derived and calculated from the formula.

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YTM is therefore a good measurement gauge for the expected investment return of a bond. When it comes to online calculation, this Yield to Maturity calculator can help you to determine the expected investment return of a bond according to the respective input values. YTM deals only with the time-value-of-money calculations between the price, coupons and face value of the bond at hand, not with other potential future investments. If the coupons and face value are paid as promised the bond earns its yield-to-maturity.

Yield to Maturity Calculator. Yield to Maturity. Annual Semi-Annual. Bond Face Value. Bond Price. Coupon Rate.

### Bond Yield Calculator

Years to Maturity. Home Finance Investment Yield to Maturity Calculator is an online tool for investment calculation, programmed to calculate the expected investment return of a bond. Close Download. Continue with Facebook Continue with Google. By continuing with ncalculators. You must login to use this feature! Privacy Terms Disclaimer Feedback.On this page is a bond yield calculator to calculate the current yield of a bond. Enter the bond's trading price, face or par value, time to maturity, and coupon or stated interest rate to compute a current yield.

The tool will also compute yield to maturity, but see the YTM calculator for a better explanation plus the yield to maturity formula.

The current yield of a bond is the annual payout of a bond divided by its current trading price. That is, you sum up all coupon payments over one year and divide by what a bond is paying today. A bond's yield to maturity is the annual percentage gain you'll make on a bond if you hold it until maturity assuming it doesn't miss payments.

It's expressed in an annual percentage, just like the current yield. However, YTM is not current yield — yield to maturity is the discount rate which would set all bond cash flows to the current price of the bond. You can find more information including an estimated formula to calculate YTM on the yield to maturity calculator page.

Let's work through an example and compute the current yield for an example bond. We'll use the example in the tool's defaults. Current yield gives you a quick read of how a bond compares in the market. It is inferior to yield to maturity, although YTM does come with the risk that a bond may stop paying out while your next year of payments is more certain.

In almost all cases you should compute both, though. Yield to Maturity. Never Miss a Post. Don't Quit Your Day Job DQYDJ may be compensated by our advertising and affiliate partners if you make purchases through links. See our disclosures page for more information.We are home to the Center for Mathematical Finance and Actuarial Research, an interdisciplinary research center providing leadership in quantitative finance.

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