# How The Yield to Maturity (Ytm) Method Works

Yield to maturity (YTM) is a method for calculating the return on a bond. It is assumed that the bearer holds it till the expiry date, and that the interim cash flows (coupon) can and will reinvest up to the end date at the same yield to maturity.

In theory, this calculation method allows investors to estimate the fair value of various financial instruments. Yield to maturity is usually in terms of an effective annual interest rate.

Bond investors need to realize its potential effects, especially in a situation of high interest rates. It is often not realistic to assume that the coupons will be reinvested at that high rate throughout a term: the market rate might very well decline.

This phenomenon is called “yield illusion”. (It may, in a situation of a constant rate and a normal yield curve, highlight the fact that reinvestment of coupons is made for an increasingly shorter period, and thus at lower returns).

YTM is a good method for different bonds on their relative merits. When referring to the return on a bond without reference to a certain time period, the yield to maturity is normally cited. And when it pertains to the return over a given period, the total return will generally be provided.

The calculation takes place through an iterative process, where the discount factor is found in instances where the present value of all revenue is equal to the desired price (exchange rate plus accrued interest).

The yield to maturity is calculated in the same way as the internal rate of return. Whenever the value of a coupon bond is sold at a premium, and the value equals the coupon’s yield to maturity – the instrument is sold at the specified value.

When a certificate is issued the rate reflects the performance that the market guarantees a long-term loan and it determines the encounter of supply and demand for savings.

There are different types of yield to maturity. For example, the first outstanding yield (yield to call): Unlike the yield to maturity, there is the assumption that outstanding debentures are not maintained until the original call.

Algebraically it corresponds to internal performance (IRR), or the value for which the present value of cash flows (NPV) is 0. NPV =- P + \ frac (1 + CF_1) (i) + \ frac (CF_2) ((1 + i) ^ 2) + \ cdots + \ frac (CF_n) ((1 + i) ^ n) = 0. Meaning: NPV =-P + \ sum_ (t = 1) ^ n \ frac (CF_t) ((1 + i) ^ t) = 0

Where: T – time constraints; P: the market price of securities subject to assessment: CFt: cash flow of the coupons and redemption of the capital of the stock at time t;

In a sense, the rate is the financial rate of return (debt and equity) that the company may take in relation to a particular project. The internal rate of return can not be calculated directly, but as the answer to the aforementioned polynomial equation.

The rates are extremely volatile and vary continuously reflecting the flow of purchase orders and sales of securities by varying the prices of those securities if they are resold on the secondary market.

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