Investments, tenth edition

 Spreadsheet 14.2 

 Finding yield to maturity in Excel 

A

B

C

D

E

The formula entered here is: 

=YIELD(B3,B4,B5,B6,B7,B8)

Annual coupons

Semiannual coupons

1

2

3

4

5

6

7

8

9

10

12

11

Settlement date

Maturity date

Annual coupon rate

Bond price (flat)

Redemption value (% of face value)

Coupon payments per year

Yield to maturity (decimal)

1/1/2000

1/1/2030

0.08

127.676

100

2

0.0600

1/1/2000

1/1/2030

0.08

127.676

100

1

0.0599

e

X

c e l

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 If the reinvestment rate does not equal the bond’s yield to maturity, the compound rate of return will differ from 

YTM. This is demonstrated below in Examples 14.6 and 14.7.  

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460

P A R T   I V

 Fixed-Income 

Securities

to maturity. For    discount  bonds    (bonds selling below par value), these relationships are 

reversed (see Concept Check 3). 

 It is common to hear people talking loosely about the yield on a bond. In these cases, 

they almost always are referring to the yield to maturity. 

 

 

  Yield to Call 

 Yield to maturity is calculated on the assumption that the bond will be held until maturity. 

What if the bond is callable, however, and may be retired prior to the maturity date? How 

should we measure average rate of return for bonds subject to a call provision? 

  Figure 14.4  illustrates the risk of call to the bondholder. The top line is the value of a 

“straight” (i.e., noncallable) bond with par value $1,000, an 8% coupon rate, and a 30-year 

time to maturity as a function of the market interest rate. If interest rates fall, the bond 

price, which equals the present value of the promised payments, can rise substantially.  

 Now consider a bond that has the same coupon rate and maturity date but is callable 

at 110% of par value, or $1,100. When interest rates fall, the present value of the bond’s 

scheduled  payments rises, but the call provision allows the issuer to repurchase the bond at 

the call price. If the call price is less than the present value of the scheduled payments, the 

issuer may call the bond back from the bondholder. 

 The bottom line in  Figure 14.4  is the value of the callable bond. At high interest rates, 

the risk of call is negligible because the present value of scheduled payments is less than 

the call price; therefore the values of the 

straight and callable bonds converge. At 

lower rates, however, the values of the bonds 

begin to diverge, with the difference reflect-

ing the value of the firm’s option to reclaim 

the callable bond at the call price. At very 

low rates, the present value of scheduled pay-

ments exceeds the call price, so the bond is 

called. Its value at this point is simply the call 

price, $1,100. 

 

This analysis suggests that bond market 

analysts might be more interested in a bond’s 

yield to call rather than yield to maturity, 

especially if the bond is likely to be called. 

The yield to call is calculated just like the 

yield to maturity except that the time until 

call replaces time until maturity, and the call 

price replaces the par value. This computa-

tion is sometimes called “yield to first call,” 

as it assumes the issuer will call the bond as 

soon as it may do so. 

 What will be the relationship among coupon rate, current yield, and yield to maturity for bonds selling at 

discounts from par? Illustrate using the 8% (semiannual payment) coupon bond, assuming it is selling at a 

yield to maturity of 10%. 

 CONCEPT CHECK 

14.3 

2,000

5

6

7

8

9

10

11

12

13

3

4

Interest Rate (%)

Prices ($)

Callable

Bond

Straight Bond

0

200

400

600

800

1,000

1,100

1,200

1,400

1,600

1,800

 Figure 14.4 

Bond prices: Callable and straight debt. 

Coupon  5  8%; maturity  5  30 years; semiannual 

payments.  

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  C H A P T E R  

1 4

  Bond Prices and Yields 

461

 Suppose the 8% coupon, 30-year maturity bond sells for $1,150 and is callable in 

10 years at a call price of $1,100. Its yield to maturity and yield to call would be calcu-

lated using the following inputs: