Unlike the Payback and the Accounting rate of investment (ARR) methods mentioned in my previous blogs, the net present value (NPV) method does take into account the time value of money.
The time value for money (TVM) is the concept that a sum of money is worth more now then the same sum will be at a future date due to ints earning potential in the interim. The time value for money is the core principle of finance. A sum of money in the hand has greater value then the same sum to be paid in the future. It is also referred as the 'present discounted value'.
Investors prefer to receive money today rather then the same amount of money in the future, because the sum of money once invested grows over time. For example, money deposited into savings account, grows in interest. Over time interest is added to the principal, earning more interest. It money is not invested, the value erodes over time. It will have less buying power because inflation reduces its value. Today, £10,000 has more value and utility then it will in two years from now on due to the opportunity costs associated with the delay so the delayed payment is a missed opportunity.
In short steps, the formula for net present value procedure is as follows:
Calculate the annual net cashflows expected to arise from the project;
Select an appropriate rate of interest, or required rate of return
Obtain a discount factor appropriate to the chosen rate of interest or rate of return
Multiply the annual net cashflow by the appropriate discount factor
Add together the present values for each of the net cashflows
Compare the total net present value with the initial outlay
Accept the project which the total VPN is positive
Example
There are certain advantages of this method. Particularly that the use of net cash flows emphasise the importance of liquidity. Different accounting methods are not relevant as they do not affect the calculation of the net cash flows. Time value of money is taken into account.
Disadvantages are linked to difficulties in estimating the initial cost of the project and the time periods in which instalments must be paid back. It also may be difficult to calculate accurately the net cashflow for each year of the project's life. It is also challenging to select an appropriate rate of interest. One rate that could be chosen is the rate that company could earn if it decided ti invest the funds outside the business (the external interest rate). This rate, therefore, would be based on estimate of what return the company expect to earn on the existing investments.
This method takes into account the timing of the net cashflows, the projects profitability and the return on the original investment. A project, however, does not have to be accepted because it has a positive NPV because non-financial factors have to be allowed for. In some cases less profitable projects may go ahead, if they are concerned with employee safety and welfare.
The use
It can be highly beneficial to know how to calculate net present value. Net present value is the difference between the net present value of our cash inflows and the present value of our cash outflows over a given period. It is used to measure profitability of a project or investment. It essentially looks at the money we expect to make from the investment and translating those returns into a pound value of the present day. We can work out on whether a particular investment is worthwhile.
Because inflation can erode buying power, NPV provides useful measure of our project's potential profitability.
If the project has only one cash flow, we can use the following formula to calculate NPV:
NPV = Cash flow / (1 + i)^t – initial investment
In this case, i = required return or discount rate and t = number of time periods.
If we are dealing longer projects with multiple cashflows, we will need to use slightly different formula:
NPV = Today’s value of the expected cash flows − Today’s value of invested cash
If we end up with positive net present value it indicates that earnings exceed the costs and the investment is likely to be profitable. If the NVP is negative, it might result in loss.
Investopedia provides a simple NPV calculator that you can use to determine the difference between the value of your cash inflows and cash outflows.
Different perspective
We know that NPV is used to calculate the current value of a future stream of payments from a project or investments. We need to estimate timing and the future cashflows and pick up a discount rate equal to minimum acceptable rate on return. The discount rate may reflect our cost of capital or the returns available on the alternative investments.
We know that the NPV formula is as below:
Source: Investopedia, https://www.investopedia.com/terms/n/npv.asp
The NPV can be used to compare rates of return of different projects or to compare the project rate of return with 'hurdle rate' required to approve the investment.
Hurdle Rate
Let's take a look at a simplified example of a hurdle rate. Hammer Supply Company is looking to purchase a new piece of machinery. It estimates that with this new piece of machinery, it can increase its sales of hammers, resulting in a return of 11% on its investment. The WACC for the firm is 5% and the risk of not selling additional hammers is low, so a low risk premium is assigned at 3%. The hurdle rate is then:
WACC (5%) + Risk premium (3%) = 8%
As the hurdle rate is 8% and the expected return on the investment is higher at 11%, purchasing the new piece of machinery would be a good investment.
Riskier projects generally have a higher hurdle rate, while those with lower rates come with lower risk. Companies often use their weighted average cost of capital (WACC) as the hurdle rate.
WACC
Weighted average cost of capital (WACC) represents a firm’s average after-tax cost of capital from all sources, including common stock, preferred stock, bonds, and other forms of debt. WACC is the average rate that a company expects to pay to finance its assets.
WACC is calculated by multiplying the cost of each capital source (debt and equity) by its relevant weight by market value, then adding the products together to determine the total. WACC is the discounted rate that a company uses to estimate its net present value. WACC is also important when analysing the potential benefits of taking on projects or acquiring another business. The WACC formula uses both the company’s debt and equity in its calculation. There are many calculators available online to calculate WACC: https://www.calkoo.com/en/wacc-calculator
If you're still unsure whether you understand the concept of the weighted average cost of capital, take a look at the example below. It explains how to calculate WACC for a small company in detail.
Determine how much of your capital comes from equity. For example, you have $700,000 in assets.
Write down your debts – for instance, you might have taken a loan of $500,000.
Estimate the cost of equity. Let's assume it is equal to 15%.
Check the cost of debt, too. For example, the interest rate on your loan might be equal to 8%.
Decide on what is the corporate tax rate. We will assume it is 20%.
Substitute all these values into the WACC formula: WACC = E / (E + D) × Ce + D / (E + D) × Cd × (100% - T) WACC = $700,000 / ($700,000 + $500,000) × 15% + $500,000 / ($700,000 + $500,000) × 8% × (100% - 20%) WACC = 0.583 × 0.15 + 0.417 × 0.08 × 0.8 WACC = 0.0875 + 0.0267 WACC = 11.42%
In the calculation of the NPV, no matter how the discount rate is determined, negative NPV shows that the expected return will fall short and project will not create value.
The discount rate is central to the formula.
A positive NPV indicates that the projected earnings, generated by a project or investment - discounted for their present value - exceed the anticipated costs and positive NPV project will be profitable.
In Excel, there is an NPV function that can be used to easily calculate the net present value of a series of cash flows. The NPV function in Excel is simply NPV, and the full formula requirement is:
=NPV(discount rate, future cash flow) + initial investment
Source: Investopedia, Accessed from https://www.investopedia.com/terms/n/npv.asp
In the example above, the formula entered into the grey NPV cell is:
=NPV(green cell, yellow cells) + blue cell
= NPV(C3, C6:C10) + C5
Calculating the NPV
For example, a company invests in the equipment that costs £1 million and its expected to generate revenue of £25,000 a month in revenue for 5 years. Alternatively the company could invest the moment with alternative return of 8%.
First, we need to calculate the NPV of initial investment. The equipment will be paid upfront so it is the first cashflow included in the calculation. The expenditure of £1 million does not need to be discounted.
Then, we need to calculate NPV for future cashflows.
We need to identify the number of periods and as the equipment will generate monthly revenue over 5 years, so 60 periods will be included in the calculation.
We need to identify the discount rate. As the alternative investment is expected to return 8% per year and our is calculated monthly we convert it into the monthly rate 0.64%.
Periodic Rate=((1+0.08)1/21)−1=0.64%
The investor can perform calculation easily as per table below:
Source: Investopedia, Accessed from https://www.investopedia.com/terms/n/npv.asp
The full calculation of the present value is equal to the present value of all 60 future cash flows, minus the $1 million investment.
Summary
Net present value is used to determine whether or not an investment, project, or business will be profitable down the line. Essentially, the NPV of an investment is the sum of all future cash flows over the investment’s lifetime, discounted to the present value.
There are many different types of formulas that can calculate NPV. another one below:
Cash Flow
Cash flows are any money spent or earned for the sake of the investment, including things like capital expenditures, interest, and loan payments. Each period’s cash flow includes both outflows for expenses and inflows for profits, revenue, or dividends.
Number of Periods (n)
The number of periods equals how many months or years the project or investment will last. Sometimes, the number of periods will default to 10, or 10 years, since that is the average lifespan of a business. However, different projects, companies, and investments may have more explicit timeframes.
Discount Rate (r)
In most situations, the discount rate is the company’s weighted average cost of capital (WACC). A company’s WACC is how much money it needs to make to justify the cost of operating and includes things like the company’s interest rate, loan payments, and dividend payments.
Cash flows need to be discounted because of a concept called the time value of money. This concept is the belief that money today is worth more than money received at a later date. For example, £10 today is worth more than £10 a year from now because you can invest the money received now to earn interest over that year. Additionally, interest rates and inflation affect how much £1 is worth, so discounting future cash flows to the present value allows us to analyse and compare investment options more accurately.
Bibliography:
Forage, 2023, "How to calculate Net Present value", accessed from https://www.theforage.com/blog/skills/npv, Accessed on 23/04/2023
GoCardless, 2022, "How to calculate Net Present Value (NPV)", Accessed from https://gocardless.com/guides/posts/how-to-calculate-net-present-value/, Accessed on 23/04/2023
Investopedia, 2023, "Time value of money explained with formula and examples", Accessed from https://www.investopedia.com/terms/t/timevalueofmoney.asp#:~:text=What%20Is%20the%20Time%20Value,earnings%20potential%20in%20the%20interim., Accessed on 23/04/2023
Investopedia, 2023, "Hurdle rate: What it is and how businesses and investors use it", Accessed from https://www.investopedia.com/terms/h/hurdlerate.asp, Accessed on 23/04/2023
Investopedia, 2022, "Weighted Average Cost of Capital (WACC) Explained with formula and example, Accessed from https://www.investopedia.com/terms/w/wacc.asp, Accessed on 23/04/2023
Omni Calculator, Accessed from https://www.omnicalculator.com/finance/wacc, Accessed on: 23/04/2023
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