# Bond Yield to Put (YTP) Calculator

Written by:
PK

On this page is a bond yield to put calculator. It automatically calculates the annual yield earned on a puttable bond assuming you put it back to the issuer at the first possible time. Importantly, it assumes all payments and coupons are on time (no defaults).

Also, find the approximate yield to put formula. Like with Yield to Maturity (YTM), Yield to Put is calculated iteratively.

## Bond Yield to Put Calculator

#### Yield to Put Calculator Inputs

• Current Bond Trading Price ($) - Today's bond trading price. • Bond Face Value/Par Value ($) - The par or face value of the bond.
• Price to Put ($) - Usually, bonds trading with a put option have some discount to the current price. Enter the price here. • Years to Put - The numbers of years until the bond can be putted back to the issuer. • Annual Coupon Rate (%) - The annual interest paid on the bond based on the par value. • Coupon Payment Frequency - Frequency the bond makes coupon payments. #### Bond YTP Calculator Outputs • Yield to Put (%): The converged upon solution for the yield to put of the current bond (the internal rate of return assuming you put the bond). • Current Yield (%): The simple calculated yield which uses the current trading price and face value of the bond. See the bond yield calculator for explanation. ## Bond Yield to Put Formula The calculation for Yield to Put is very similar to Yield to Maturity – and equal to the Yield to Call calculation (just with the incentives flipped). The calculator assumes you will put the bond back to the issuer at your first chance – although, of course, you only want to do that if you would make money on the trade (and assuming all payments are made). And just like how callable bonds usually have a call price higher than par value, puttable bonds generally have a put value below face value. ### Estimated Yield to Put Formula However, that doesn't mean we can't estimate and come close. The formula for the approximate yield to put on a bond is: \frac{(Annual\ Interest)+((Price\ to\ Put-Current\ Price)/(Years\ to\ Put))}{(Price\ to\ Put+Current\ Price ) / 2} ### Estimating Yield to Put for the Calculator Scenario Let's solve the default yield to put calculation inside the tool: • Current Price:$920
• Par Value: $1000 • Price if Put:$970
• Years to Put: 5
• Annual Coupon Rate: 10%
• Coupon Frequency: 2x a Year
\frac{(100)+((970-920)/5)}{(970+920 ) / 2}=\\~\\\frac{100+10}{945}=11.640\%

### Exact Yield to Put Formula

If you actually run the scenario in the tool, you'll find that yield to put is actually 11.700% – what's going on there?

As mentioned, the above formula is just an estimate. A real calculation would sum the present value of all future cash flows in almost the same way you calculate yield to maturity.

Here is the summation:

Price = Coupon\ Payment/(1+rate)^{-1} + Coupon\ Payment/(1+rate)^{-2} +\\ ... +  Coupon\ Payment/(1+rate)^{-n}+Price\ to\ Put/(1+rate)^{-n}

Internally, the tool adapts the method from Github user ndongo. See the yield to maturity calculator's methodology discussion for more.

## Why Does Yield to Put Matter?

As mentioned, bonds with options (calls and puts) introduce a wrinkle into price calculations. Depending on who is able to exercise, it gives that party an option to either call back the bond or put it back to the issuer for a set price.

In this case, a bond with a put option means at some time in the future you can put it back to the issuer if the price is right (and assuming all other incentives are aligned).

Read more in the yield to call discussion (just flip the incentives!).

## Other Financial Basics Calculators

Use the Yield to Put as you would use other measures of bond valuation: a factor in your decision to buy or avoid. Bonds with put options usually have the deck stacked against them in terms of face value vs. put price, but sometimes when bonds trade at a discount the put option can be worth it for you to exercise.

Here are some other bond calculators:

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