Page 30 - DMGT405_FINANCIAL%20MANAGEMENT

Financial Management

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

Self Assessment
Fill in the blanks:

7. …………..is a series of equal payments made at equal time intervals, with compounding
or discounting taking place at the time of each payment.
8. The …………….of an annuity is the sum that must be invested today at compound interest
in order to obtain periodic rents over some future time.
9. The ……………..of an annuity or amount of annuity is the sum accumulated in the future
from all the rents paid and the interest earned by the rents.

2.4 Perpetuities
An annuity that goes on for ever is called a perpetuity. The present value of a perpetuity of C
amount is given by the simple formula: C/i where i is the rate of interest.
This is because as the length of time for which the annuity is received increases, the annuity
discount factor increases but as length gets very long, this increase in the annuity factor slows
down.

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Caution as annuity life becomes infinitely long the annuity discount factor approaches an
upper limit. Such a limit is 1/i.

Example: Mr. X wishes to find out the present value of investments which yield 500 in
perpetuity, discounted at 5%. The appropriate factor can be calculated by dividing 1 by 0.05. The
resulting factor is 20. This is to be multiplied by the annual cash inflow of 500 to get the present
value of the perpetuity i.e., 10,000.

Managerial Problems

Many business problems are solved by use of compound interest and present value tables. For
example, B Corporation is investigating two possible investments. Project A is the purchase of
a mine for 20,00,000 which will give an expected income from sale of ore of 480,000 per year
for 10 years, after which the property will be sold at an estimated price of 600,000. Project B is
the purchase of an office building that is leased for 15 years. The lease provides annual receipts
of 4,00,000 at the end of the each of the next 4 years, and annual receipts of 4,50,000 for the
remaining life of the lease. The purchase price is 20,00,000. B Corporation requires a 20 per cent
return on its investments. Which investment is preferable?

Solution: To evaluate Project A we need to find the present value of the future income stream of
4,80,000 per year for 10 years plus the present value of the future sales price of 6,00,000, both
discounted to the present at the company’s required rate of return of 20 per cent.

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