Corporate Finance

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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
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