Principles of Managerial Finance

292 PART 2 Important Financial Concepts

(PVIFAkd/2, 2 n)M(PVIFkd/2, 2 n) (6.8a)

EXAMPLE Assuming that the Mills Company bond pays interest semiannually and that the

required stated annual return, kd, is 12% for similar-risk bonds that also pay

semiannual interest, substituting these values into Equation 6.8a yields

B 0 (PVIFA12%/2, 2 10yrs)$1,000(PVIF12%/2, 2 10yrs)

Table Use

B 0 $50 (PVIFA6%,20periods) $1,000 (PVIF6%,20periods)

$50 (11.470) $1,000 (0.312) $



8



8



5



.



5



0



Calculator Use In using a calculator to find bond value when interest is paid

semiannually, we must double the number of periods and divide both the

required stated annual return and the annual interest by 2. For the Mills Com-

pany bond, we would use 20 periods (2 10 years), a required return of 6%

(12%2), and an interest payment of $50 ($1002). Using these inputs, you

should find the bond value with semiannual interest to be $885.30, as shown at

the left. Note that this value is more precise than the value calculated using the

rounded financial-table factors.

Comparing this result with the $887.00 value found earlier for annual com-

pounding (see Table 6.6), we can see that the bond’s value is lower when semian-

nual interest is paid. This will always occur when the bond sells at a discount.For

bonds selling at a premium, the opposite will occur: The value with semiannual

interest will be greater than with annual interest.

Review Questions

6–16 What basic procedure is used to value a bond that pays annual interest?

Semiannual interest?

6–17 What relationship between the required return and the coupon interest

rate will cause a bond to sell at a discount?At apremium?At its par

value?

6–18 If the required return on a bond differs from its coupon interest rate,

describe the behavior of the bond value over time as the bond moves

toward maturity.

6–19 As a risk-averse investor, would you prefer bonds with short or long peri-

ods until maturity? Why?

6–20 What is a bond’s yield to maturity (YTM)?Briefly describe both the trial-

and-error approach and the use of a financial calculator for finding YTM.

$100



2

I



2

885.30

20 N

I

FV

CPT

PV

PMT

6

50

1000

Solution

Input Function