Time Value of Money- Fundamentals of Finance

Today, I am going to discuss something very basic: Time value of money. As you know, elements in the financial statements have both words and numbers. For example, while reading a balance sheet of XYZ company, you will see- Inventory | $50,000 or Payables | $25,000 etc.

While words help us to name the elements, numbers do two things- they help us to count & measure. These two qualities of quantity are known as multitude & magnitude respectively.

When discussing about the numbers in the financial statements, we are more concerned about their quality to measure than the quality to count. This is because we want to ‘how much’ our assets & liabilities worth rather than ‘how many’ of them we got. Though there is a place for counts in the notes to accounts, it is the measurement we care for while evaluating the financial position of our company.

When it comes to measuring things, money can be considered as the greatest innovation of human history. Its ability to measure is universal. From apple i phones to apple juice, everything that has a value, can be measured with money. Money and accounting are so intimately related that one of its definitions says it is a unit of account. It converts everything, that is accounted (or recorded), into a single unit of measure.

Coming to IFRS, financial elements can be measured or valued or, written in financial statements either on the basis of historical cost (money paid or received in past to acquire an asset or debt), or current cost ( how much they worth now). The current cost can be arrived from three angles based the requirements of IFRS- fair value ( how much we can get if we sell an asset or settle a liability in an orderly transaction), current cost ( how much we need to pay if we buy an equivalent asset or incur an equivalent liability) and value in use ( the present value of future cash flows related to an asset or liability). It is for determining the value in use, we need to understand time value of money. As we will see in the future articles, TVM has applications in various IFRS.

What is time value of money ?

We all know money has value. However, it has an enemy that continuously devours its purchasing power. Time erodes the money’s worth as a persistent stream of water erodes mighty stones. This is why, the value of a $ today is not same as the value of a $ after a year or so. Tomorrow’s dollar is worth less than today’s.

If we have to compare the value of both, we need to measure the value of time. The worth of money now plus value of time should give us the worth money in future and vice versa.

So what is value of time (in the context of money)

It is the compensation receivable for the postponement of consumption of money. I know it’s a mouthful but let me explain it through an example:

Suppose you have two choices

Choice 1: To receive $5000 today.

Choice 2: To receive $5000 one year after.

Which choice would you prefer?

Obviously you will go with choice one. Why? Because if you have the option to enjoy the fruits of money now why would you risk postponing it to a year. It’s better to consume the money today than to consume it later.

But not always you want to use your cash today, either because it is not practicable or it is not beneficial.

Instead, you may want to:

• Save money for future.
• Lend it to someone.
• Invest it in stocks.
• Invest it in a business.
• Or postpone the consumption of money for some other purpose.

In all the above cases, you have deferred the benefit of consumption to future. And if you are a rational person you wouldn’t like to do it for free. You will demand an inventive or compensation for doing so.

It will be a logical demand because of the these three reasons:

• Inflation: it may go up. A rise in inflation will decrease the purchasing power of money. for example, if inflation is 5% then you will have to pay $5250 to purchase a car a year later that you can purchase with $5000 now.
• Risk free rate of return: it’s the return that anybody can earn from the risk free investments. So it is natural that you would also like to earn the same amount of return from a risk-less abstinence from swiping your debit card. For example, you deposit cash in a bank or in government bonds. In such cases you are almost certain to receive your money back. That means the default risk is very low. The borrowers would just like to compensate you by paying rent (interest) for letting them use your cash.
• Risk: it means you are not certain about the payoff at the end of the period of investment. You may end up earning more than the risk free rate of return or you may end up even losing your initial investment value. It is the variability of actual payoff from the expected payoff. More risky your borrower, more compensation you would demand.

Quantifying the time value

We have seen why money has a time value and how it depends on the three factors. Now let us proceed to quantify the time value of money.

Time value of money = Expected inflation rate + Real rate of return on risk free investment + Risk premium.

Expected inflation rate: Compensation towards the fall in the purchasing power of money.

Real rate of return on risk free investment: Risk free rate of return (-) inflation rate. It’s the compensation over the inflation rate anyone can earn.

Risk premium:?Return from a risky investment (–) risk free rate of return. It’s the extra premium over and above the risk free return for taking risk. It is decided by the returns provided by comparable investments which are subject to the same level of risk. It depends upon the?perception of risk?of each individual or organisation hence?subjective. It’s because of this factor, time value of money can be different for different individuals as regards to a same investment and different investments can have different time value of money for same individual.

How time value of money is helpful?

Suppose you receive $500 today, $1000 one year later and $3000 two year later. How much money you have received over two years? Is it 500+1000+3000=4500? No, because the amount of money received or paid in different points of time are not comparable. They are not expressed in terms of a specific year’s value of money. In such case, to make them comparable, you need to find out either the?present value?of money received?(convert them into base year’s value) or the?future value?of money received (convert them into the terminal year’s value). To do this, you will need to perform compounding and discounting.

Compounding and discounting

In compounding you move from present value to arrive at the future value. It is the process of reinvesting the return (compensation). If return is r% on investment for ‘n’ years, investment will grow to: investment amount*(1+r)^n. This (1+r)^n is called future value factor. So?Future value = Present value * FVF. Suppose, in the example given above , you expect 10% of return from investment.

FVF for $500 invested for 2 years @10% is 1.21, for $1000 invested for 1 year it is 1.1 and for $3000 invested for 0 year it is 1. So the value of money received by you in terms of the value at the end of 2nd?year is: $605 + $1100 + $3000 = $4705. This is the future value of the money received by you expressed in terms of terminal years value(2nd?year).

Now coming to discounting you move from future value to arrive at present value. Discounting means reverse compounding. If return (compensation) is r% on investment for ‘n’ years, value of investment at present is: future value* 1/(1+r)^n. This 1/(1+r)^n is called present value factor. So?Present value = Future Value * PVF.?Now let us put the data in a table.

PVF for $500 discounted for 0 year is 1, for $1000 discounted for 1 year is .909 and for $3000 discounted for 2 years is .826. So the value of money received by you in terms of the value of base year is $500 + $909 + $2478 = $3887 ( value of money today).

If the return received or amount paid by you is same for every year this is called annuity. Annuity can be regular or immediate.

PV of annuity regular: Suppose you started receiving the return from the end of this year for ‘n’ number of years. The present value of all your receipt is: annuity * PVAF. Present value annuity factor = (1-PVF)/r.

PV of annuity immediate: Suppose you started receiving the return from today. The present value of all your receipt is: PV of annuity regular (for n-1 years) + annuity.

FV of annuity regular: Suppose you started depositing an equal amount from the end of this year for ‘n’ number of years. The future value of all your deposits at the end of ‘n’ year will be: annuity * FVAF. Future value of annuity factor = (FVF-1)/r.

FV of annuity immediate: Suppose you started depositing an equal amount from today for ‘n’ number of years. The future value of all your deposits at the end of ‘n’ year will be: FV of annuity regular * (1+r).

Now suppose you are going to receive an equal amount for infinite number of years. This is called perpetuity.

PV of perpetuity regular?is: perpetual return/r.

PV of perpetuity immediate?is: PV of perpetuity regular + perpetuity.

Effective annual rate: the rate receivable in an investment may be r% per annum compounded annually (stated rate) or it may be receivable r% per annum compounded half yearly, quarterly or monthly etc. If it is quoted at a rate which is compounded at a higher frequency as compared to an annual compounding, then it has to be converted into effective annual rate. Effective annual rare (EAR) = [1+(stated rate/n)]^n -1.

Applicability of Time Value of Money

Apart from IFRS, there are numerous application of TVM in finance. There is hardly any area in finance where TVM is not applicable.

Valuation:?The value of an asset is the present value of future cash flows generated by it. For example the value of a share is the present value of future dividends. To arrive at the present value you have to discount the future cash flows with TVM.

Capital budgeting:?Capital budgeting decisions are long term investment decisions. To find out whether a project is viable you have to compare the present value of future cash inflows with the present value of cash outflows. The difference between the PV of cash inflows and PV of cash outflows is called net present value (NPV). Projects with a positive NPV are selected and the projects with negative NPV are to be rejected

Cost of capital: it is the minimum rate of return a project should earn to satisfy the investors’ expectations. Investors’ expectations are based on their risk perceptions. TVM is the quantification of investors’ expectations. Cost of capital should be used as the discount rate in the capital budgeting decisions.

To find out IRR:?IRR means internal rate of return. It is the rate of return at which the projects NPV is zero. Means it is the rate of return at which PV of cash inflows are equal to the PV of cash outflows. If a project is to be selected, its IRR must be greater than the cost of capital.

Conclusion

Money and Time are crucial to accounting and finance . While financial reporting focuses on providing investors fair financial data, finance is concerned with wealth maximisation and creation of prosperity. A business needs both. Time value of money is a beautiful tool to understandings the relationship between all of these.