Understanding the time value of money is critical for making smart financial decisions When we talk about time value of money, two important concepts come up – present value and net present value At first glance, they may seem similar. But there are some key differences between present value and net present value that you need to know.
In this article, I will explain in simple terms:
- What is present value and net present value
- The key differences between present value and net present value
- When to use present value vs when to use net present value
- Examples to illustrate the calculation and differences
Let’s dive in!
What is Present Value?
Present value refers to the current worth of a future sum of money. It is based on the concept that money available now is worth more than the same amount in the future
Here’s a simple example to understand present value:
Let’s say you are offered $100 now or $100 a year from now. Which would you choose?
Most people would choose to get the $100 now because it can be invested and grow. The $100 you get a year later cannot be invested immediately. This illustrates the concept that money now is worth more than money later.
The present value formula uses this logic and calculates what a future sum of money is worth today.
The present value (PV) formula is:
PV = FV / (1 + r)<sup>n</sup>
Where:
- FV is the future value of the cash flow
- r is the interest rate or discount rate
- n is the number of periods
So if you were offered $110 one year from now, and the interest rate is 5%, the present value would be:
PV = $110 / (1 + 0.05)<sup>1</sup> = $104.76
Therefore, $104.76 today at 5% interest equals $110 in one year.
Present value helps you determine what amount you would need to invest today to get a certain desired future amount. It is useful for personal financial planning and investing.
What is Net Present Value?
Net Present Value (NPV) is a capital budgeting technique used by companies to analyze potential projects or investments.
It calculates the difference between the present value of future cash inflows and outflows. In simple terms:
NPV = Present Value of Future Cash Inflows – Present Value of Cash Outflows
The NPV formula is:
NPV = ∑ <sub>t=1</sub><sup>n</sup> (Ct / (1 + r)<sup>t</sup>) – C0
Where:
- Ct is the net cash flow at time t
- r is the discount rate
- t is the time period
- C0 is the initial investment
Let’s take an example:
A company has the opportunity to invest in a new machine costing $20,000. The machine is expected to generate additional cash flows of $5,000 per year for 5 years. The discount rate is 8%.
The NPV of this investment would be:
NPV = (-$20,000) + $5,000/(1.08)<sup>1</sup> + $5,000/(1.08)<sup>2</sup> + $5,000/(1.08)<sup>3</sup> + $5,000/(1.08)<sup>4</sup> + $5,000/(1.08)<sup>5</sup>
NPV = -$20,000 + $4,629 + $4,287 + $3,979 + $3,701 + $3,449
NPV = $46
Since the NPV is positive, this would be a good investment opportunity for the company.
NPV helps determine if a project will be profitable and worth investing in after accounting for the time value of money. Companies use it for capital budgeting decisions.
- Present Value calculates what a future amount is worth today
- Net Present Value calculates the difference between the present value of cash inflows and outflows to determine profitability
Now let’s dive deeper into the key differences between present value and net present value.
Key Differences Between Present Value and Net Present Value
Here are the main differences between present value (PV) and net present value (NPV) that you should be aware of:
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Purpose – PV helps determine the current equivalent of a future amount. NPV helps determine the profitability of a potential project.
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Inputs – PV only uses future cash inflows in its calculation. NPV uses both cash inflows and outflows.
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Use – PV is used mainly for personal finance decisions. NPV is used for corporate budgeting and investment decisions.
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Significance – While PV is useful, NPV better indicates the potential gain or loss from an investment.
Let’s expand on these differences:
1. Purpose
The main purpose of Present Value is to calculate what a future sum of money is worth today. It helps you evaluate deals like lottery payouts, pensions, and annuities.
Net Present Value has a different objective. It determines whether the returns from a project or investment will exceed the required rate of return. This helps companies evaluate the profitability of potential capital projects.
2. Inputs
PV only considers the future cash inflows. It ignores any upfront costs or cash outflows associated with receiving those inflows.
NPV accounts for both – the projected cash inflows and outflows. This gives a more complete picture of the net gains or losses from the investment.
3. Use
Individuals can use Present Value calculations to make personal finance and investment decisions. For example, you may compare the present value of lottery winnings paid now versus over 20 years.
Net Present Value, on the other hand, is mainly used by companies for capital budgeting decisions. They use it to analyze the profitability of proposed projects and determine which ones to invest in.
4. Significance
While Present Value is useful, it does not tell you the whole story. Knowing the present value of future cash inflows is only half the picture.
Net Present Value gives you a better indication of the potential profitability of a project because it accounts for the required investment as well.
When Should You Use Present Value vs Net Present Value?
When making any financial analysis, first think about what you want to figure out. This will dictate which concept – Present Value or Net Present Value – to use.
When to use Present Value:
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If you want to calculate the current equivalent of a future lump sum payment.
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When evaluating annuities, pensions, lottery payouts, and other future cash flow streams in isolation.
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To determine how much to save today to reach a future savings goal.
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To calculate the current value of an inheritance you expect to receive later.
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When making personal investment decisions weighing future returns.
When to use Net Present Value:
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When determining if a proposed project or investment will be profitable.
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For capital budgeting decisions on long-term projects and assets.
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To prioritize which project to invest in given multiple proposals and limited budget.
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When you need to account for the required upfront investment as well as future returns.
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To compare projects with different investment amounts and cash flow timings.
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Use Present Value for personal finance decisions weighing future cash flows.
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Use Net Present Value for business decisions evaluating investment profitability.
Examples Comparing Present Value and Net Present Value
Let’s look at some examples to reinforce when to use present value versus net present value.
Personal Investment Example
Say you inherit $100,000 and want to invest it to pay for your child’s college education in 18 years. The expected annual return on your investment is 4%. How much would it be worth in 18 years?
This involves calculating the future value of your investment. You can use the Present Value formula with variables flipped to get:
FV = PV x (1 + r)<sup>n</sup>
FV = 100,000 x (1 + 0.04)<sup>18</sup> = $180,612
So $100,000 invested today at 4% annually will grow to $180,612 in 18 years. This helps plan your savings goal amount.
Since it only considers the cash inflow, you would use Present Value here rather than Net Present Value.
Business Investment Example
A company is considering two potential projects:
Project A:
- Initial investment: $50,000
- Expected to generate $20,000 annual cash inflows for 5 years
- Discount rate: 10%
Project B:
- Initial investment: $100,000
- Expecte
Is NPV or ROI More Important?
Both NPV and ROI (Return on Investment) are important, but they serve different purposes. NPV provides a dollar amount that indicates the projected profitability of an investment, considering the time value of money. ROI, on the other hand, expresses the efficiency of an investment as a percentage, showing the return relative to the investment cost. NPV is often preferred for capital budgeting because it gives a direct measure of added value, while ROI is useful for comparing the efficiency of multiple investments.
What Is the Difference Between NPV and Internal Rate of Return (IRR)?
NPV and internal rate of return (IRR) are closely related concepts, in that the IRR of an investment is the discount rate that would cause that investment to have an NPV of zero. Another way of thinking about the differences is that they are both trying to answer two separate but related questions about an investment. For NPV, the question is, “What is the total amount of money I will make if I proceed with this investment, after taking into account the time value of money?” For IRR, the question is, “If I proceed with this investment, what would be the equivalent annual rate of return that I would receive?”
Net Present Value (NPV) explained
What is the difference between NPV and present value?
Meanwhile, net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. Present value tells you what you’d need in today’s dollars to earn a specific amount in the future. Net present value is used to determine how profitable a project or investment may be.
What is net present value?
Net Present Value is a financial metric used to determine the value of an investment by calculating the difference between the present value of cash inflows and the present value of cash outflows over a specified period.
What is the net present value rule?
The net present value rule states that if a return using NPV is above 0, the project may be worth an investment. To determine the net present value, each cash inflow and outflow must be discounted back to its present value. The discount value reflects the cost of capital and its risk. All of the final values are then summed up.
What is the Net Present Value (NPV) of a cash inflow?
This is the result of combining the present value of the cash inflow $6,210 (from the example above) and the $5,000 (which is the present of the $5,000 paid today). Assuming the same information, except that the rate for discounting the cash amounts is 12%, the net present value (NPV) is $670.
