Time Value of Money

Concept of time value of money

Time value of money is the basic fundamental in all of finance. It is the idea that a rupee in hand today is worth more than the same rupee to be received in the future. Three reasons explain this:

• Inflation: prices rise over time, so a rupee buys less in the future than it does today.
• Investment opportunity: money in hand today can be invested to earn a return, giving it a potential earning capacity.
• Preference for consumption: people generally prefer to consume now rather than later.

Compounding and discounting

These are the two methods of calculating the value of money at different points of time.

• Compounding is the process of finding the future value of a present sum of money (present value moves forward to future value).
• Discounting is the process of finding the present value of a future sum of money (future value moves back to present value).

Compounding carries a present value forward through time to arrive at its future value, while discounting works in the reverse direction, bringing a future value back to its present value.

Concept of cash flow

Cash flow refers to the amount of cash produced by an investment alternative. For example, if you invest Rs 10,000 today that promises to pay you Rs 2,000 in return every year for 10 years, the annual cash flow from your investment is Rs 2,000.

Types of cash flow

1. Single cash flow: an investment that offers only one lump sum cash flow in the future.
2. Even cash flow or annuity: an investment that offers an equal amount of cash flow every period for a certain number of years.
3. Uneven cash flow: the cash flows from one investment differ from one period to another.
4. Perpetuity: a series of equal cash flows that occur over an indefinite period of time.

Present value and future value

Present value (PV) is also known as the initial value, discounted value, current value or value in hand today. It depends upon the future cash flow, the time period and the interest rate.

Future value (FV) is the compounded value of a present sum of money. It depends upon the present cash flow, the time period and the interest rate.

Single cash flow

Future value (compounding):

$$FV = PV(1+k)^n$$

Table method: $FV = PV \times FVIF_{k,n}$

Present value (discounting):

$$PV = \frac{FV}{(1+k)^n}$$

Table method: $PV = FV \times PVIF_{k,n}$

where $PV$ = present value, $FV$ = future value, $k$ = interest rate and $n$ = time period.

Worked examples: future value

Rs 1,000 compounded for 1 year at 14%:

$$ \begin{aligned} FV &= 1000(1+0.14)^1 \ &= 1000 \times 1.14 \ &= Rs\ 1{,}140 \end{aligned} $$

Rs 1,000 compounded for 2 years at 14%:

$$ \begin{aligned} FV &= 1000(1+0.14)^2 \ &= 1000 \times 1.2996 \ &= Rs\ 1{,}299.60 \end{aligned} $$

Rs 500 compounded for 10 years at 6%:

$$ \begin{aligned} FV &= 500(1+0.06)^{10} \ &= 500 \times 1.7908 \ &= Rs\ 895.42 \end{aligned} $$

Rs 1,000 compounded for 3 years at 8%:

$$ \begin{aligned} FV &= 1000(1+0.08)^3 \ &= 1000 \times 1.2597 \ &= Rs\ 1{,}259.71 \end{aligned} $$

Rs 2,250 compounded for 30 years at 12%:

$$ \begin{aligned} FV &= 2{,}250(1+0.12)^{30} \ &= 2{,}250 \times 29.9594 \ &= Rs\ 67{,}403.82 \end{aligned} $$