The time value of money is used to move capital through various accounting periods and define its true present value. In this article we will learn what the time value of money is, why and how it is used, as well as two corporate finance concepts that utilise the time value of money.
Understanding The Time Value of Money (TVM)
The time value of money is the concept that money has a different value over time. For example, £1,000 today is worth more than £1,000 in one year, because in one year the £1,000 will have accrued interest.
However, if the annual interest rate is 5% currently – which of the following options would you rather receive?
- £1,000 today
- £1,100 in a year from today
If you picked the former, then the £1,000 will increase to £1,050 with the 5% interest rate. This would be less than the £1,100 that we would receive in a year from today.
Therefore, it is important that when valuing money we are valuing it on the same time frame.
Money today is classed as the ‘present value’, or PV.
Money in the future is classed as the ‘future value‘, or FV.
The time value of money is used in corporate finance as a method to determine a project’s viability.
When we move money forward into the future, we need to multiply. And when we move money backwards into the present, we need to divide.
What Is The Discount Rate?
The discount rate is the interest rate, and we use the discount rate in order to discount future money back to the PV and move calculate the value of present money in the future.
For example, if we had the choice of being given £11,000 in a year from today or £9,500 today, it is impossible to know which is the better choice unless we know the discount rate.
If the discount rate is 10%, then £11,000 discounted back to the present value would be £11,000 divided by 1.1 (10%) in our calculators. This would show a PV of £10,000 – making the £11,000 in a year from today more attractive.
But what if the discount rate was 20%? Would we still rather the £11,000 in a year from now, or receive the £9,500 today?
To work this out, we would input £11,000 divided by 1.2 (20%) in our calculators. This would give us £9,166.67 at today’s present value. Therefore, we would opt to take the £9,500 today rather than the £11,000 in a year from today.
The discount rate is always the rate in which we use to adjust money to different values in time.
What Is Net Present Value (NPV)?
Net Present Value (NPV) is one method used to determine a project’s viability.
The NPV of a project is the different between both the present value of future cash inflows and the present value of future cash outflows over a specific period of time.
For example, if we wish to analyse the viability of a mine, we would need to work out how much capital expenditure is required to develop the mine to production, and we would then need to work out how much capital the mine is going to bring us.
Let’s assume that we need £1,000,000 to purchase the mine, and a year later, we would need another £500,000, and a year later we would require another £750,000.
Our capital expenditure, or cash outflows, would look like this:
Year 0 £1,000,000
Year 1 £500,000
Year 2 £750,000
We would need to work out the PV of this capital and discount it back to Year 0.
We would not need to adjust the £1,000,000, as that is the current PV.
For Year 1, we would need to discount the £500,000 back to Year 0. If the discount rate is 5%, then we would need to discount £500,000 by 1.05 (5%) to get £476,190.47.
For Year 2, we would need to discount this £500,000 back to Year 0 too. In order to do this, we would need to discount across two periods.
Discounting the £750,000 to Year 1 would be £714,285.71. However, we need the capital to be discounted to Year 0, and so we would discount £714,285.71 again by 5% to get £680,272.11.
An easier way to do this would be to take the FV of the money at Year 2 and divide this by 1.05 squared. If the money was at year three, we would do 1.05 cubed.
Therefore, the total discounted value of our total cash outflows would £1,000,000 + £476,190.47 + £680,272.11 which is £2,156,462.58.
We would need to do the exact same technique on the future cash inflows of the project.
We take the project’s cash flows and discount all of them back to Year 0.
We then take the total discounted capital expenditure and add the total discounted cash inflows.
If the number is positive, then the project is value accretive. We would accept the project.
If the number is negative, then the project does not create value as we are spending more on the project than it will bring in when put in terms of PV. We would therefore decline the project.
How To Use Net Present Value For Projects
NPV is a good way to decide if the project will deliver value. However, this can be manipulated.
As NPV uses the discount rate, this is discretionary when assessing the risk of the project. A larger discount should be used if the risks within the project are high. This larger discount rate factors in the risk and is more conservative.
Be careful of companies boasting about a high NPV for their project – especially if they do not include the discount rate. Without a discount rate included it is impossible to know how management have factored risk into the project.
It is also worth being careful of a low discount rate used to calculate the NPV for an asset or project. This is because a low discount rate assumes a low degree of risk.
Think about it: if you were lending money to a company in Zimbabwe that had found gold, but hadn’t yet built the infrastructure required in order to develop the money, and also hadn’t received all of the financing required – would you lend them money at a 5% return? Or would you want a higher return to compensate for the level of risk?
What is Internal Rate of Return (IRR)?
The internal rate of return is a metric used in corporate finance to give an idea about the profitability of a potential investment or project.
The internal rate of return is the discount rate that makes the NPV of a project zero. Therefore, it gives the expected rate of return that will be generated on a potential investment or project.
Whereas the NPV calculates the economic viability of a project or investment, IRR looks at which project or investment will deliver the highest rate of return.