Introduction to Corporate Finance

4: Valuing Bonds

To calculate this value in Excel, once again we use the PV function, entering 0.08 for the rate, 11 for the
number of periods, –91.25 for the payments, and –1,000 for the future value. (In this Excel function, the ‘future
value’ argument simply refers to any payment, above and beyond the regular annuity cash flow, coming at the
very end of the final period.) By entering the coupon payments and the principal repayment as negative values,
we will obtain a positive value for the bond’s price.

=PV(0.08,11, –91.25, –1,000) = 1,080.31

Figure 4.1 also illustrates the keystrokes one might use when solving this problem using a financial
calculator.

Notice that this bond sells above face value because the price, $1,080.31, is greater than the $1,000

face or par value. When a bond sells for more than its face value, we say that the bond trades at a

premium. Why are Platypus’s bonds trading at a premium? By assumption, the market’s required return

on an investment like this is just 8%, but Platypus’s bonds offer a coupon rate of 9.125%. Therefore, if

Platypus’s bonds sold at their face value, they would offer investors a particularly attractive return, and

investors would rush to buy them. As more and more investors purchase Platypus bonds, the market

price of those bonds rises.

Think about the return that an investor earns if she purchases Platypus bonds today for $1,080.31

and holds them to maturity. Every year, the investor receives a $91.25 cash payment. At the current

market price, this represents a coupon yield of about 8.4% ($91.25 ÷ $1,080.31), noticeably above the

8% required return in the market. However, when the bonds mature, the investor receives a final interest

payment plus the $1,000 face value. In a sense, this bond has a built-in loss of $80.31 ($1,000 face value

• $1,080.31 purchase price) at maturity, because the bond’s principal is less than the current price of

the bond. The net effect of receiving an above-market return on the coupon payment and realising a loss

at maturity is that the investor’s overall return on this bond is exactly 8%, equal to the market’s required

return.

In the example above, 8% is the required rate of return on the bond in the market, also called the

bond’s yield to maturity (YTM). The yield to maturity (YTM) is simply the discount rate that equates the

present value of a bond’s future cash flows to its current market price.^3 As a general rule, when a bond’s

coupon rate exceeds its YTM, the bond will trade at a premium, as Platypus’s bonds do. Conversely, if

the coupon rate falls short of the YTM, the bond will sell at a discount to face value.

example

Suppose the market’s required return on Platypus bonds is 10% rather than 8%. In that case, the price of the
bonds would be determined using this equation:

=

+

+

+

+

+

+...+

+

+

+

P

$91.25

(1 0.10 )

$91.25

(1 0.10 )

$91.25

(1 0.10 )

$91.25

(1 0.10 )

$1, 000

(1 0.10 )

(^01231111)
3 The holding period yield is a similar measure of return used by investors to measure the realised return on a bond that is sold before its
maturity date. It represents the compound annual return earned by the investor over the holding period for the bond. The calculation of
the holding period yield is the same as that for yield to maturity, except that the actual holding period and sale price are substituted into
Equation 4.2 for years to maturity (n) and the maturity value (M), respectively.
premium
A bond trades at a premium
when its market price exceeds
its face or par value
yield to maturity (YTM)
The discount rate that equates
the present value of the bond’s
cash flows to its market price
discount
A bond trades at a discount
when its market price is less
than its face value

example