**Yield to maturity** is the term used to describe the anticipated return of investment at the end of the bond’s life (i.e maturity). Yield to maturity is similar to the current yield and is computed the same way (including the difference between current bond price and its face value).

## Yield to Maturity by example:

Take Andrew, who is buying a bond with a face value of $1,000 which expires in 30 years. Assume the annual coupon payment is 5%. What is the value of the bond after it expires (maturity)?

There are two ways to value this bond: simple interest and compound interest.

### Yield to Maturity by Simple Interest(SI)

Simple interest is calculated by adding up all the coupon payments until the bond is matured or sold.

In our example, the annual coupon payment is $50 (5% of $1,000). Remember, coupon payments in the US is paid every 6 months, the first 6 months payment is $25 and the last 6 months payment is $25 amounting to $50.

In the period of 30 years, the number of coupon payments is 60. What is the total simple interest earned?

One coupon payment (6 months) is $25 and for 60 payments it is $25 x 60 amounting to $1500.

So the simple interest amounts to $1,500 given the fact that the **coupon payments were not reinvested**.

#### Coupon yield under simple interest

Coupon yield is the coupon payment divided by the face or par or original value of the bond.

Coupon: $50; Face value: $1,000

Coupon yield = $50 / $1,000 which is **5%**

#### Current yield under simple interest

Current yield is the coupon payment divided by the current price of the bond.

Let’s look at three cases:

**Case 1:** Coupon of $50 and the price is $1200. Current yield is 4.2% ($50/$1200)

**Case 2:** Coupon of $50 and the price is $1000. Current yield is 5% ($50/$1000)

**Case 3:** Coupon of 50 and the price is $800. Current yield is 6.3% ($50/$800)

*Note: Remeber the original value of the bond will be paid at maturity (in our bond example, the original value of $1,000 will be paid at the end of 30 years)*

What current yield fails to take into account is the difference between the price and the par value. If the price is greater than par value then the bond is premium (Case 1, there is loss of $200 dollars) and the price is lower than part value then the bond is discount(Case 3, there is a profit of $200 dollars)

### Compound Interest(CI)

Compound interest is the sum of all the** coupon payment when its reinvested**.

Let’s say the coupon payments are reinvested at 5%. By the end of 30 years, the compound interest will be $3,400

#### Yield to maturity under compound interest

Yield to maturity takes into account the difference between the current price and par value of the bond.

The formula for Yield to Maturity is express as follows:

Let’s look at three cases:

**Case 1:** Coupon is $3,400 annual, price is $1200. The price value difference is $2,200. Yield to Maturity is **3.87%**

**Case 2:** Coupon is $3,400 annual, price is $1000. The price value difference is $2,400. Yield to Maturity is **5.00%**

**Case 3:** Coupon is $3,400 annual, price is $800. The price value difference is $2,600. Yield to Maturity is **6.53%**

In summary, we can compare coupon yield, current yield and yield to maturity as different ways to value a bond.

Type |
Market price with the maturity of 30 years |
||

$800 | $1000 | $1200 | |

Coupon Yield | 5% | 5% | 5% |

Current Yield | 6.3% | 5% | 4.2% |

Yield to Maturity | 6.53% | 5% | 3.87% |

Yield to maturity aides investor in the investment analysis by valuation of the bond.

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