Corporate Finance –
LECTURE 03
DISCOUNTED CASH FLOW & EFFECTIVE ANNUAL INTEREST
We shall discuss the following in this hand out.
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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 Ksh. 100 after first year,
Ksh. 200 and Ksh. 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%
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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) - 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 +2 .12/4)4 – 1= 12.55%
= (1.1255) X 1000 =
1266.75 OR
Quarterly interest is 12/4 = 3%
=(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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