Page 29 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes Solution: The investment today is the present value of an annuity of 5,00,000 per year, with
n = 32 and i = 9 per cent compounded annually. From the cumulative present value table we find
the factor 10.40624 which is the present value if the rents were 1.
PV = Rent × f (n = 32, i = 9%)
= 5,00,000 × 10.40624 = 52,03,120

Effective Interest Rate

In the real world, interest rates are often compounded more often than once per year. By
convention, interest rates are quoted on an annual basis. An interest rate, quoted on an annual
basis, which is compounded more often than once per year is called a nominal rate, stated rate,
quoted rate, or Annual Percentage Rate (APR). For example, mortgages typically require monthly
payments and, therefore, the interest rates quoted on mortgages are compounded monthly.
Thus, the nominal interest rate on a mortgage might be 12% compounded monthly. However,
the relevant rate for valuations is the periodic rate. The periodic rate is computed by dividing
the nominal rate by the number of compounding periods per year.
r
r  nom
m
where
 r = the rate per period,

 r = the nominal rate, and
nom
 m = the number of compounding periods per year.
Thus a 12% nominal rate compounded monthly is equivalent to a periodic rate of 1% per month.

The Effective or Equivalent Annual Rate (EAR) is the interest rate compounded annually that is
equivalent to a nominal rate compounded more than once per year. In other words, present and
future values computed using the EAR will be the same as those computed using the nominal
rate. The EAR is computed as follows:

 r nom  m
EAR  1    1

 m 
 EAR = the Equivalent or Effective Annual Rate,
 r = the nominal interest rate,
nom
 m = the number of compounding periods per year

Moreover, it is not proper to directly compare interest rates which have a particular compounding
frequency with those that have a different compounding frequency, e.g., comparing 10.1%
compounded semiannually with 10% compounded quarterly. This problem can be overcome by
finding the EAR for each of the rates and then comparing the EARs.
First, let's find the EAR for 10.1% compounded semiannually. Here, m equals 2.

EAR for 10.1% compounded semiannually

 0.101  2
EAR  1    1  0.1036  10.36%

 2 
Now, let's find the EAR for 10% compounded quarterly. Here m = 4.

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