**YTM = [C + {(F – P) ÷ n}] ÷ [(F + P) ÷ 2]**

C = Interest payment

F = Face value

P = price

n = years to maturity

YTM formula or yield to maturity equation is utilized to figure the yield on a security bond on the basis of its current market price. The yield to maturity formula takes in to account the viable yield of a bond using compounding technique rather than the basic yield which can be calculated by utilizing dividend yield formula.

The formula used above is commonly used to find the rough yield to maturity. To figure the precise yield to maturity ratio you must have to use experimentation by placing rates into the bond present value formula until Price value equalizes the genuine cost of the bond. One can also use any financial calculator or other related software for yield to maturity calculations.

## Calculating yield to maturity & present value of a bond

We can get the yield to maturity formula by using thepresent value of a bond formula;

**Yield to maturity = [C ÷ (1 + r)] + [C ÷ (1 + r)**^{t}**] … [C ÷ (1 + r)**^{t}**] + [F ÷ (1 + r)**^{t}**]**

The present value of a bond is alreadyknown in the shape of the current price of the bond. While you have to workback the present value formula to calculate the value of ** r** for putting all thevalues in YTM formula for calculations.

### Yield to maturity formula illustration

Let’s suppose that the face value of abond is $1,500 and the price of the bond is $1,280 while the annual coupons are$150 (apparently the rate is 10%) while the maturity period is 10 years. Now ifwe put all the values in the Yield to maturity formula;

**Approx YTM = $150 + [($1,500 – $1280) ÷ 10 ] ÷ [($1500 + $1280) ÷ 2]**

Estimated yield to maturity is 12.667%for solving above equation with example figures.

### YTM with PV of bond illustration

Using the above example the estimated YTM is 12.667%. Now wewill calculate the PV by using the YTM to replace the rate ** r** by using the presentvalue of the bond formula. The present value with this technique is $1320 whichis a bit close to the current price i.e. $1280 and this variance can differwith a case to case.

Noticeably, a higher yield to maturity indicates towards alower present value of a bond. While in this example, YTM gives a present valuea bit higher if compared with the purchasing price of $1280. Thus, the realyield to maturity will be a bit higher than 12.667%.

By using the ‘trial and error’ the yield to maturity will be12.89%, this is found by adjusting the rate each time after calculation untilthe present value equals the purchasing price of the bond.

One can use the yield to maturity calculator below for thatpurpose or can also use the trial and error method within excel and just changethe value or rate in a specific cell to get the required results.