Yield to Maturity Formula – Approximation

**Yield to Maturity Formula – Published on Jul 5, 2016**

In this tutorial, you’ll learn how to approximate the Yield to Maturity (YTM) of a bond, including how you might modify it to cover Yield to Call and Yield to Put as well as real-life scenarios with debt investing.

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Table of Contents:

1:14 Part 1: The Yield to Maturity (YTM) and What It Means

5:27 Part 2: How to Quickly Approximate YTM

10:19 Part 3: How to Extend the Formula to Yield to Call and Yield to Put

13:32 Part 4: How to Use This Approximation in Real Life

16:27 Recap and Summary

Part 1: The Yield to Maturity (YTM) and What It Means

Yield to Maturity is the internal rate of return (IRR) from buying the bond at its current market price and holding it to maturity.

Assumption #1: You hold the bond until maturity.

Assumption #2: The issuer pays all the coupon and principal payments, in full, on the scheduled dates.

Assumption #3: You reinvest the coupons at the same rate.

Intuition: What’s the *average* annual interest rate % + capital gain or loss % you earn from the bond?

You can use the YIELD function to calculate this in Excel:

=YIELD(Settlement Date, Maturity Date, Coupon Rate, Bond Price % Par Value Out of the Number 100, 100, Coupon Frequency)

For example, if you buy a 5% bond for 96.23% of its par value on December 31, 2014, and hold it until its maturity on December 31, 2024, you could enter:

=YIELD(“12/31/2014”, “12/31/2024”, 5%, 96.23, 100.00, 1) = 5.500%

You could also project the cash flows from the bond and use the IRR function to calculate YTM, but this will work only for annual periods and annual coupons.

Part 2: How to Quickly Approximate YTM

Approximate YTM = (Annual Interest + (Par Value – Bond Price) / # Years to Maturity) / (Par Value + Bond Price) / 2

Intuition: Each year, you earn interest PLUS an annualized gain on the bond price if it’s purchased at a discount (or a loss if it’s purchased at a premium).

And you earn that amount on the “average” between the initial bond price and the amount you get back upon maturity.

For example, on a 10-year $1,000 bond with a price of $900 and coupon of 5%:

Annual Interest = 5% * $1,000 = $50

Par Value – Bond Price = $1,000 – $900 = $100

(Par Value + Bond Price) / 2 = ($1,000 + $900) / 2 = $950

Approximate YTM = ($50 + $100 / 10) / $950 = $60 / $950 = ~6.3%

There are a few limitations: the approximation doesn’t work as well with big discounts or premiums to par value, nor does it work as well with different settlement and maturity days. It also will not handle floating interest rates since it assumes a fixed coupon.

Part 3: How to Extend the Formula to Yield to Call and Yield to Put

Call options on bonds let companies redeem a bond early when interest rates have fallen, or its credit rating has improved, meaning it can refinance at a lower rate.

Usually, the company has to pay a premium to par value to call the bond early.

Put options are the opposite, and let investors force early redemption (usually when interest rates have risen, or the company’s credit rating has fallen).

Approximate Yield to Call or Yield to Put = (Annual Interest + (Redemption Price – Bond Price) / # Years to Maturity) / ((Redemption Price + Bond Price) / 2)

For example, to calculate the Yield to Call on a 10-year $1,000 bond with a price of $900, coupon of 5%, and a call date 3 years from now at a redemption price of 103:

Approximate YTC = ($50 + ($1,030 – $900) / 3) / (($1,030 + $900) / 2)

Approximate YTC = ($50 + $43) / $965 = $93 /$965 = ~9.7%, which you can estimate as “just under 10%”

Part 4: How to Use This Approximation in Real Life

Example: You’re at a credit fund that targets a 10% IRR on investments in high-yield debt.

JC Penney has a 4-year 7.950% bond that’s currently trading at 91.75 (as in, 91.75% of par value).

This seems like an easy “yes”: you get around 8% interest per year + an 8% discount / 4, and ~10% / average price of 96% results in a yield just above 10%.

BUT will a distressed company be able to repay the bond principal upon maturity? What if its financial situation worsens?

You estimate that in the best-case scenario, you’ll get 65% of the principal back upon maturity (65% “recovery percentage”). The recovery percentage will be 47% and 13% in more pessimistic cases.

Scenario 1 Approximate YTM: (8% – 27% / 4) / 78.5% = 1.6%

Scenario 2 Approximate YTM: (8% – 45% / 4) / 69.5% = -4.7%

So this is almost certainly a “No Invest” decision if these recovery percentages are accurate – even in the Upside Case, we’re far below 10%.

Yield to Maturity Formula – RESOURCES:

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