Corporate
Finance FIN 622

**VU**

**Lesson
04**

**DISCOUNTED
CASH FLOW & EFFECTIVE ANNUAL
INTEREST**

We
shall discuss the following in this hand
out.

**Discounted
Cash Flow**

**Effective
Annual Interest**

**Bond
Valuation - introduction**

**Discounted
Cash Flows:**

So far
we assumed cash flow of same
rupee level over a period of time.
Like the way bond
interest

occurs
cash flow of interest
remains at a constant level through to
maturity. Often this is not
the

case
when we move to other areas of
valuation. The cash flow at
the end of every period
is

different
from the other and therefore, we
need to calculate the present
value of each cash flow
by

discount
factor depending upon the time. For
example, an investment opportunity yields
cash flow

of Rs.
100 after first year, Rs.
200 and Rs. 300 at the
end of second and third
year respectively
shall

be
discounted at 10% rate with
first year factor of 0.9090,
second year 0.8264 and
third year 0.7513.

This
means that we can't work
out present value here
like we did in case of
annuities.

**Effective
Annual Rate
EAR**

The
Effective Annual Rate (EAR)
is the interest rate that is
annualized using compound
interest.

The
EAR is the annualized equivalent of
interest with shorter compounding
periods. It can be

calculated
from the following
formula:

EAR =
[1 + i/n) n - 1

Where
n is the number of times (or periods)
interest is compounded during the year
and i is the

interest
rate per period.

Explanation:

The
effective annual rate is a value
used to compare different
interest plans. If two plans
were being

compared,
the interest plan with the higher
effective annual rate would be
considered the better

plan.
The interest plan with the
higher effective annual rate would be the
better earning plan.

For
every compounding interest plan
there is an effective annual rate. This
effective annual rate is

an
imagined rate of simple
interest that would yield
the same final value as the
compounding plan

over
one year.

When
interest is compounded more than
once in a year, EAR will be
greater than the stated
or

quoted
interest rate.

Bank A
pays 15% interest on deposit, compounded
monthly.

Bank B
pays 15% interest on deposit, compounded
quarterly.

Bank C
pays 15% interest on deposit, compounded
half yearly.

Bank A = 1 +
.15/12 12 - 1

=1.16075
1

=
16.075%

Bank B = 1 +
.15/4 4 - 1

=(1.0375) 4
1

=
1.15865 1

=
15.865%

Bank C = (1 +
.15/2) 2 - 1

=
(1.075) 2 - 1

=
1.155625 1

=
15.5625%

**Example:**

A bank offers 12%
compounded quarterly. If you place 1000
in an account

today,
how much you have at the
end of two years? What is
EAR?

**Solution:**

EAR =
(1 + .12/4)4 1= 12.55%

=
(1.1255)2 X 1000 =
1266.75

OR

Quarterly
interest is 12/4 = 3%

15

Corporate
Finance FIN 622

**VU**

=(1.03)8 X
1000 = 1.2667 X 1000
=1266.77

**BOND
VALUATION:**

A bond
is a financial instrument or a debt security
issued by a company to raise
money. It is offered to

general
public or to institutions.

Equity
& Debt (Bonds)

Equity
represents ownership and is a residual
claim

Features
on Bond

Coupon
Interest: stated interest payments
per period

Face
value: Also Par value.
The principal amount

Coupon
rate: interest payments
stated in annualized
term.

Maturity:
specified future date on
which principal will be
repaid.

Yield
to Maturity (YTM): Interest
rate required in market on a
bond.

Current
yield= Annual coupon
payment(s) divided by bond
price.

Discount
Bond: A bond which is sold
less than the face or par
value is discount bond.

Premium
Bond: A bond which is sold
more than the face or par
value is premium bond

16