Page 25 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes Using this formula, future values can be calculated for any interest rate and any number of time
periods. To obtain the future value of any principal other than 1, we multiply the principal by
the factor for the future value of 1.
fv = (1 + i) n
or fv = Pf

where f is the factor in the future value of 1, with interest rate i and number of periods n.

Example: XYZ Company invests 40,00,000 in certificates of deposit that earn 16%
interest per year, compounded semi-annually. What will be the future value of this investment
at the end of 5 years when the company plans to use it to build a new plant?

Solution: Compounding is semi-annual and there are 5 years, so the number of half-year periods
is 10. The semi-annual interest rate is half of the 16% annual rate or 8%. With i = 8% and n = 10,
the factor in the table is 2.15892. Multiplying this factor by the principal investment, we get:
fv = P × f (n = 10, i = 8%)
= 40,00,000 × 2.15892

= 86,35,680

Self Assessment

Fill in the blanks:
1. The compensation for waiting is the time value of money, called ………………. .

2. The future value includes the original principal and the ………………. .
3. The future value varies with the interest rate, the ………………. frequency and the number
of periods.
2.2 Present Value of Single Amount

If 1 can be invested at 8% today to become 1.08 in the future, then 1 is the present value of
the future amount of 1.08. The present value of future receipts of money is important in
business decision-making. It is necessary to decide how much future receipts are worth today in
order to determine whether an investment should be made or how much should be invested.
Finding the present value of future receipts involves discounting the future value to the present.
Discounting is the opposite of compounding. It involves finding the present value of some
future amount of money that is assumed to include interest accumulations.

Present Value of 1

Knowing the present value of 1 is useful because it enables us to find the present value of
any future payment. Assuming 8% interest per period, a table of present values of 1 can be
constructed as follows:
Present value of 1 discounted for 1 period at 8% = 1.0/1.08 = 0.92593
Present value of 1 discounted for 2 periods at 8% = 0.92593/1.08 = 0.85734

Present value of 1 discounted for 3 periods at 8% = 0.85734/1.08 = 0.79383

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