By Yuriy Smirnov Ph.D.

A callable bond is a simple financial instrument that can be redeemed by the issuer before the maturity date. The call price is usually higher than the par value, but the call price decreases as it approaches the maturity date.

Please note that call option does not mean that an issuer can redeem a bond at any time. Some terms must usually be met:

- a set period of time, also known as call protection, where the bond cannot be redeemed
- call price
- other terms and conditions

The issuer needs a call option to reduce interest rate risk and avoid damage when interest rates decline. In such a scenario, the issuer can redeem bonds and reissue them at a lower interest rate.

If a bond has a call option, an investor must consider prepayment and reinvestment risk. Thus, yield to call (YTC) can be defined as the internal rate of return (IRR) if a bond is expected to be redeemed before the maturity date. Yield to call can also be defined as the discount rate at which the present value of all coupon payments (left to call date) and the call value are equal to the bond’s current market price.

To calculate the yield to call, the investor must understand that the market price of a bond is equal to future cash flows. To find the exact YTC value, the following equation should be solved:

Market Price = | N | Coupon payment | + | Call Price |

Σ | ||||

(1 + YTC)^{t} |
(1 + YTC)^{N} |
|||

t = 1 |

where “Market Price” is the current market price of a bond, and N is the number of periods to maturity.

To solve the equation above, the financial calculator or MS Excel is needed. For an approximate appraisal of yield to call, the following formula can be used:

Approx YTC = | Coupon Payment + | Call Price - Market Price |

N | ||

Call Price + Market Price | ||

2 |

Please note that coupon payments are usually made semiannually, so the semiannual YTC should be adjusted to the annual YTC as follows:

Annual YTC = (1 + Semiannual YTC)^{2} - 1

For example, a 10-year corporate bond has a $1,000 par value, a fixed annual coupon rate of 9.5%, and a call protection period of 5 years. The issuer has a right to redeem the bond at any time during the fifth year at $1,050. Let’s assume that a bond is currently traded at $985, coupon payments are made semiannually, and two years remain before the end of the call protection period.

Since 2 years remain before the end of the call protection period, the investor will receive four coupon payments of $42.5 each.

Semiannual coupon rate = 9.5% ÷ 2 = 4.75%

Semiannual coupon payment = $1,000 × 4.75% = $47.5

If the bond is to be redeemed in 2 years, the investor will be paid the call price of $1,050. Thus, to find the yield to call of the bond, the following equation should be solved:

$985 = | $47.5 | + | $47.5 | + | $47.5 | + | $47.5 + $1,050 |

(1 + YTC)^{1} |
(1 + YTC)^{2} |
(1 + YTC)^{3} |
(1 + YTC)^{4} |

To solve this equation, you can use the IRR function of MS Excel as in the figure below.

- Select output cell
**B4**. - Click
button, select**fx****All**category, and select**IRR**function from the list. - In field
**Values**, select the data range**B2:F2**, leave empty the field**Guess**, and press the**OK**button.

The calculated semiannual YTC of 6.32% should be adjusted to an annual basis.

Annual YTC = (1 + 0.632)^{2} - 1 = 13.05%

Using the IRR function allows us to get a precise appraisal of the yield to call, but an approximation approach can also be used to get a rough appraisal.

Approx YTC = | $47.5 + | $1,050 - $985 | = 6.27% |

4 | |||

$1,050 + $985 | |||

2 |

YTC is based on three basic assumptions:

- All coupon payments are reinvested at the YTC rate.
- The investor holds the bond until it is redeemed.
- The bond will be redeemed on the exact date.

These assumptions create method vulnerability. The bond is expected to be called if interest rates decrease below the coupon rate, but the call price to be paid partially prevents this from happening. In other words, the call price limits bond price appreciation. If the market price reaches this limit, the issuer most likely will redeem bonds and reissue them at a lower interest rate. The key problem is that nobody can know in advance whether or not this will happen or when. Thus, many investors use the lowest yield to call and yield to maturity as the most realistic appraisal of the expected rate of return.

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