Page 27 - DMGT405_FINANCIAL%20MANAGEMENT

Unit 2: Time Value of Money

The general formula for the present value of 1 is Notes

pv = 1/(1+i)n
The present value on the tables can be constructed from this formula.

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Caution To find out the present value of any future amount, the appropriate factor from
the table is multiplied by the amount.

Example: Alpha company can invest at 16 per cent compounded annually. Beta company
can invest at 16 per cent compounded semi-annually. Each company will need 2,00,000 four
years from now. How much must each invest today?
Solution: With annual compounding n=4 and I =16 per cent. With semi-annual compounding
n=8 and i=8 per cent. Using the above formula we find the present value
= 1/(1.16) 4 = 0.55229 × 2,00,000 = 110,458

For Beta Company present value = 2,00,000 × 1/(1.08)4 = 200,000 × 0.54027 = 108,054
Beta company needs to invest less than Alpha Company because its investment grows faster due
to more frequent compounding.

Did u know? The more frequent the compounding the smaller the present value.
Self Assessment

Fill in the blanks:
4. Discounting is the opposite of ………………
5. Finding the present value of future receipts involves ……………the future value to the
present.
6. The more frequent the compounding the …………..the present value.

2.3 Present and Future Value of Annuities

An annuity is a series of equal payments made at equal time intervals, with compounding or
discounting taking place at the time of each payment. Each annuity payment is called a rent.
There are several types of annuities, out of which in an ordinary annuity each rent is paid or
received at the end of each period.

Notes
 There are as many rents as there are periods.

 Installment purchases, long-term bonds, pension plans, and capital budgeting all
involve annuities.

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