#### Download the practice workbook 👉 HERE and follow along.

## Why Money Today is Worth More: Understanding Present Value

Present value is the idea that $10,000 today is worth more than $10,000 ten years from now. But why is that?

### The Power of Earning and Opportunity Costs

Money today can grow. This is called earning power. If you invest $10,000 now, it could become much more in ten years due to interest or investment returns. This potential growth is why having money now is so valuable.

This ties into opportunity costs. If you wait ten years to get the money, you miss out on the chance to invest it now and earn returns. The longer you wait, the more potential earnings you lose.

### The Impact of Inflation

Prices increase over time. This is known as inflation. As prices rise, the value of money falls. So, $10,000 today will buy more than $10,000 ten years from now. This is another reason why present money is more valuable than future money.

### The Uncertainty of Time and Risk

The future is unpredictable. There’s always a risk that the promised money might not be paid. This uncertainty makes future money less reliable. Events like market crashes, personal changes, or global issues can all impact this.

Risk is closely related to this uncertainty. The longer you wait to receive money, the higher the risk that something could go wrong. This risk reduces the value of future money compared to money you have today.

These factors together explain the Time Value of Money. This concept is often shown as a percentage, known as the **discount rate**, which reflects how these factors impact the value of money over time.

### Choosing the Discount Rate

Choosing the right discount rate can be subjective. It’s based on the expected return if you invest your money now. Often, a risk-free rate is used for this. This rate, sometimes called the hurdle rate, is the minimum return needed to make an investment worthwhile.

#### Using Risk-Free Rates

A common risk-free rate is the U.S. Treasury bond rate because it’s backed by the U.S. government. For example, if a two-year Treasury bond pays 4% interest, any investment must earn more than 4% to be worth the risk.

#### Using WACC

For companies, the discount rate often involves the Weighted Average Cost of Capital (**WACC**). WACC represents the average rate of return that investors expect and the cost of borrowing money. It combines the cost of equity (returns expected by shareholders) and the cost of debt (interest on loans) to reflect the company’s overall cost of capital.

The WACC varies by industry and typically ranges from 7% to 12%.

#### Why the Discount Rate Matters

The discount rate is crucial because it combines the time value of money with an interest rate. It helps calculate the present value of future money. This is key for lenders and investors to find fair values for future earnings or debts.

By understanding and choosing the right discount rate, you can make informed financial decisions. You might be evaluating personal investments or business projects. The discount rate helps you compare the value of money now versus in the future. It ensures you make the best choice.

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## Fundamentals of Financial Analysis

## How to Calculate Present Value in Excel

Is it better to receive $10,000 today or $10,800 over 4 years? To answer this, we need to compare their values today.

This is done by calculating the present value of the future payments of $10,800.

Let’s compare the two options in Excel:

**Option 1**: Receive $10,000 today.**Option 2**: Receive four payments of $2,700 over 4 years.

At first glance, $10,800 seems better than $10,000. However, this ignores the Time Value of Money, which means future payments are worth less than today’s money.

To account for this, we discount the future payments to find their present value. Let’s assume a discount rate of 5%. This rate implies that money is worth 5% less each year. It’s like the opposite of earning interest.

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## Excel Essentials for the Real World

### Manual Present Value (PV) Calculation in Excel

First, let’s manually calculate the present value. This helps us understand the formula.

To find the present value of the first payment (E11):

`=E7 / (1 + D9)`

💡 We divide instead of multiply because we’re moving backward in time. If we were moving forward, we’d multiply.

#### Calculating Remaining Years

For the remaining years, adjust the formula to account for the previous year’s value. For Year 2’s payment (F11), based on Year 1’s result (E11):

`=E11 / (1 + $D$9)`

Copy this formula for the remaining years (G11 and H11).

#### Present Value (PV) Formula Breakdown

The present value formula can be written as:

`=E7 / (1 + $D$9) ^ E3`

💡 The caret symbol (^) is used for exponentiation in Excel. You can find it above the number 6 on your keyboard.

Or using the POWER function:

`=E7 / POWER((1 + $D$9), E3)`

### Interpreting Present Value

To compare the options, we used the SUM function in Excel to add the values from cells E11 through H11. The total value over 4 years is $9,574.

This calculation shows that receiving $10,800 over 4 years at a 5% discount rate results in a present value loss of $426. Clearly, receiving $10,000 today is a better choice.

### Key Takeaways on Present Value (PV)

**Timing of Payments**: Payments made further in the future are less valuable. Always consider when payments will be made.**Discount Rate**: Think of the discount rate as a hurdle. The higher the discount rate, the harder it is to achieve a high present value.

## What Is Net Present Value (NPV)?

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period. It’s a key concept in capital budgeting and investment planning, helping to determine the profitability of a project or investment.

### Understanding NPV

NPV calculates the current value of a future stream of payments by applying a discount rate. Essentially, it tells you whether an investment will be profitable:

**Positive NPV**: Indicates a profitable investment worth undertaking.**Negative NPV**: Indicates a loss-making investment that should be avoided.

## How to Calculate Net Present Value (NPV) in Excel

Excel makes calculating Net Present Value (NPV) easy with its built-in NPV function.

### NPV Function Syntax

The syntax for the NPV function is:

`NPV(rate, value1, [value2], …)`

**rate**: Required. The discount rate over the length of the period.**value1, value2**, …: Value1 is required; additional values are optional. These are the cash flows (payments and income) occurring at the end of each period.

#### Important Points

- Ensure cash flows (value1, value2, etc.) are equally spaced in time and occur at the end of each period.
- Enter payment and income values in the correct sequence as NPV uses the order of values to interpret cash flows.
- Empty cells, logical values, text representations of numbers, error values, or non-numeric text are ignored.

### Example Net Present Value Calculation in Excel

To use the NPV function (starting in cell D13), write the following net present value formula:

`=NPV(D9, E7:H7)`

If you want to compare this with the original value from Option 1, modify the formula to subtract the NPV result from the initial amount:

`=NPV(D9, E7:H7) – D5`

In this case, the result shows a loss of $426 over the life of the loan, indicating a poor investment decision.

### Difference Between Present Value and Net Present Value

**Present Value (PV)**: This is the current worth of a single future sum of money or stream of cash flows given a specified rate of return. It does not consider the initial investment.**Net Present Value (NPV)**: NPV is the difference between the present value of cash inflows and outflows over a period. It considers the initial investment and calculates whether the total gains exceed the costs.

## NPV vs. Internal Rate of Return (IRR)

Net Present Value (NPV) and Internal Rate of Return (IRR) are two important metrics in investment analysis. While they are related, they provide different insights.

### Understanding NPV and IRR

**NPV**: Measures the difference between the present value of cash inflows and outflows. A positive NPV indicates a profitable investment.**IRR**: The discount rate that makes the NPV of an investment zero. It represents the projected annual return of a project.

### Comparing NPV and IRR

IRR is useful for comparing projects with different time spans by evaluating their expected return rates. For example, you can use IRR to compare the profitability of a five-year project versus a seven-year project.

#### Example

Imagine you have two projects:

**Project A**: A two-year project with a projected IRR of 10%.**Project B**: A ten-year project with a projected IRR of 8%.

While Project A has a higher IRR, it only lasts two years. After that, you would need to reinvest the capital, possibly at a lower return. Project B, despite having a lower IRR, provides returns over a longer period, which might be more stable.

### Key Takeaways

**IRR**: Great for comparing rates of return but doesn’t account for the reinvestment risk after the project ends.**NPV**: Provides a clear picture of an investment’s profitability over its entire lifespan, considering the time value of money.

By using both NPV and IRR, you can make more informed decisions about which projects to pursue based on their profitability and time spans.

## NPV vs. Return of Investment (ROI)

Understanding the difference between NPV (Net Present Value) and ROI (Return on Investment) helps in making informed financial decisions.

**NPV**: Calculates the difference between the present value of cash inflows and outflows over time, considering the time value of money. It gives a dollar amount that indicates the profitability of an investment.**ROI**: Measures the efficiency of an investment by calculating the percentage return relative to its cost. It highlights the relative performance of an investment.

### Is NPV or ROI More Important?

Both NPV and ROI are important, but they serve different purposes.

**NPV**: Often preferred for capital budgeting because it provides a direct measure of added value. It focuses on the absolute value created by an investment, offering a clear picture of its profitability.**ROI:**Useful for comparing the efficiency of multiple investments. It expresses the return as a percentage relative to the investment cost, making it easier to compare different investment opportunities.

### Key Takeaways

Use NPV to evaluate the overall profitability and value added by an investment.

Use ROI to compare the efficiency and relative performance of multiple investments.

## Download the Workbook

Enhance your learning experience by downloading our workbook. Practice the techniques discussed in real-time and master the time value of money in Excel with hands-on examples. Download the workbook here and start applying what you’ve learned directly in Excel.

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### Leila Gharani

I'm a 6x Microsoft MVP with over 15 years of experience implementing and professionals on Management Information Systems of different sizes and nature.

My background is Masters in Economics, Economist, Consultant, Oracle HFM Accounting Systems Expert, SAP BW Project Manager. My passion is teaching, experimenting and sharing. I am also addicted to learning and enjoy taking online courses on a variety of topics.