Kenneth R. Szulczyk

You can become confused by the terms used throughout this book. We use yield to
maturity, discount rate, and interest rate interchangeably, and you can interpret these terms to
mean an interest rate. However, a rate of return differs because investors could sell their
securities before they matured. Thus, the rate or return includes the interest rate and capital gains
or losses. A capital gain is an investor sells a financial security for greater price, while a capital
loss is an investor sells a financial security for a lower price. Investors do not want capital
losses, but they can occur. For instance, an investor must sell an asset whose market price has
dropped because he or she needs cash quickly. Thus, the present value still works for capital
gains and losses. Finally, if the investor holds onto the security onto the maturity date, then the
rate of return equals the yield to maturity.
A bond, for example, has a face value of $2,000 with a coupon interest rate of 5% and a 10-
year maturity. You bought this bond for $2,000 and then resold it two years later for $2,400.
Thus, you collected two years of interest. Consequently, your rate of return equals the two years
of interest plus the capital gain of 14.33%. We calculated the capital gain in Equation 10, and r
equals the rate of return. The author used a computer program to solve for r.

   

   

0. 1433

1

100 2,400

1

100

2,000

1 1

2

1 2

r=

+r

$ +$

+

+r

$

$ =

+r

FV

+

+r

FV

PV 0 =^12

( 10 )

A capital loss is similar. As an illustration, you bought a financial security for $2,000 with a
coupon interest rate of 5% and held it for two years. Although you earned two years of interest,
this company reported financial trouble, and the bond price dropped to $1,000. Unfortunately,
we calculated your return from the investment as a huge loss of - 23.3% in Equation 11.

   

0. 233

1

100 1,000

1

100

2,000 2

r=

+r

$ +$

+

+r

$

$ =

( 11 )

The Valuation of Stocks

Value of a stock equals the present value of an asset's future cash flows. Thus, the present
value of all future cash flows is the asset’s market price in Equation 12. Market price of stock
per share equals P 0. Market price in the time period 1 is P 1 while D 1 indicates the dividends.
Finally, the rate of return is r, and the subscripts indicate the time period.

  +r

P

+

+r

D

P=

1 1

1 1

0 (^12 )^