This

**preview**shows pages 1-2. to view the full**6 pages of the document.**CHAPTER 3

MEASURING YIELD

COMPUTING THE YIELD OR INTERNAL RATE OF RETURN ON

ANY INVESTMENT

The yield on any investment is the interest rate that will make the present

value of the cash flows from the investment equal to the price (or cost) of the

investment.

Mathematically, the yield on any investment, y, is the interest rate that

satisfies the equation.

)

y + (1

C

+. . . +

)

y + (1

C

+

)

y + (1

C

+

)

y + (1

C

= P N

N

2

2

1

1

3

3

where CFt = cash flow in year t, P = price of the investment, N = number of

years. The yield calculated from this relationship is also called the internal

rate of return.

Solving for the yield (y) requires a trial-and-error (iterative) procedure. The

objective is to find the yield that will make the present value of the cash

flows equal to the price. Keep in mind that the yield computed is the yield

for the period. That is, if the cash flows are semiannual, the yield is a

semiannual yield. If the cash flows are monthly, the yield is a monthly yield.

To compute the simple annual interest rate (i.e., the APR), the yield for the

period is multiplied by the number of periods in the year.

Special Case; Investment with Only One Future Cash Flow

When the case where there is only one future cash flow, it is not necessary to

go through the time-consuming trial-and-error procedure to determine the

yield. We can solve for yield, y, using the following equation:

1 =

/1

P

CF

yn

n

.

1

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Annualizing Yields

To obtain an effective annual yield associated with a periodic interest rate,

the following formula is used: effective annual yield = (1 + periodic interest

rate)m – 1 where m is the frequency of payments per year. To illustrate, if

interest is paid quarterly and the periodic interest rate is 8% / 4 = 2%, then

we have: the effective annual yield = (1.02)4 – 1 = 1.0824 – 1 = 0.0824 or

8.24%.

We can also determine the periodic interest rate that will produce a given

annual interest rate by solving the effective annual yield equation for the

periodic interest rate. Solving, we find that: periodic interest rate = (1 +

effective annual yield)1/m – 1. To illustrate, if the periodic quarterly interest

rate that would produce an effective annual yield of 12%, then we have:

periodic interest rate = (1.12)1/4 – 1 = 1.0287 – 1 = 0.0287 or 2.87%.

CONVENTIONAL YIELD MEASURES

Yield to Maturity

The yield to maturity is the interest rate that will make the present value of

the cash flows equal to the price (or initial investment). For a semiannual

pay bond, the yield to maturity is found by first computing the periodic

interest rate, y, which satisfies the relationship:

)

y + (1

F

+

)

y + (1

C

+. . . +

)

y + (1

C

+

)

y + (1

C

+

y + (1

C

= P nn2 3

)

where P = price of the bond, C = semiannual coupon interest (in dollars), F

= maturity value (in dollars), and n = number of periods (number of years x

2).

For a semiannual pay bond, doubling the periodic interest rate or discount

rate (y) gives the yield to maturity, which understates the effective annual

yield. The yield to maturity computed on the basis of this market convention

is called the bond-equivalent yield (BEY).

It is much easier to compute the yield to maturity for a zero-coupon bond

because we can use:

1 =

/1

P

F

y

n

. Remember that n should be counted as the

2

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