**Formula of Present Value (PV) Calculation (Table of Contents)**

## What is the Present Value Formula?

The term “present value” refers to the present-day value of a certain amount of money or cash flows in the future. The future cash flows are discounted using a specified rate of return. The PV formula can be derived by dividing the future cash flow by one plus the discount rate raised to the number of periods.

PV Formula is represented as,

**PV = C / (1 + r)**

^{n}where, PV = Present value

- C = Future cash flow
- r = Discount rate
- n = Number of periods

For a series of future cash flows with multiple timelines, the formula for present value can be expressed as,

**PV =** **C _{1} / (1 + r) ^{n}_{1} +**

**C**+

_{2}/ (1 + r)^{n}_{2}**C**

_{3}/ (1 + r)^{n}_{3}+ ……. + C_{k}/ (1 + r)^{n}_{k}### Explanation of the Present Value Formula

The calculation of present value can be done by using the following steps:

**Step 1:** Firstly, determine the future cash flows for each period which are then denoted by C_{i} where i varies from 1 to k.

**Step 2:** Next, determine the discount rate or the specified rate at which the future cash flows have to be discounted. It is a very important factor and is decided either on the basis of the market trend or the risk appetite of the investor. The discount rate is denoted by r.

**Step 3:** Next, determine the number of periods for each of the cash flows. It is denoted by n.

**Step 4:** Next, calculate the present value for each cash flow by dividing the future cash flow (step 1) by one plus the discount rate (step 2) raised to the number of periods (step 3).

**PV _{i} = C_{i} / (1 + r) ^{n}_{i}**

**Step 5: **Finally, the PV formula of all the cash flows can be derived by adding all the respective present values calculated in the above step.

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**PV =** **C _{1} / (1 + r) ^{n}_{1} +**

**C**+

_{2}/ (1 + r)^{n}_{2}**C**

_{3}/ (1 + r)^{n}_{3}+ ……. + C_{k}/ (1 + r)^{n}_{k}### Examples of Present Value Formula (with Excel Template)

Let’s see some simple to advanced examples of Present Value formula to understand it better.

#### Present Value Example #1

**Let us take the example of John who is expected to receive $1,000 after 4 years. Determine the present value of the sum today if the discount rate is 5%.**

- Given, Future cash flow, C = $1,000
- Discount rate, r = 5%
- Number of periods, n = 4 years

Therefore, the present value of the sum can be calculated using the below formula as,

PV = C / (1 + r) ^{n}

= $1,000 / (1 + 5%) ^{4}

**Present Value will be –**

**PV = $822.70 ~ $823**

Therefore, the present value of the $1,000 to be received after 4 years is $823.

#### Present Value Example #2

**Let us take another example of a project having a life of 5 years with the following cash flow. Determine the present value of all the cash flows if the relevant discount rate is 6%.**

- Cash flow for year 1: $400
- Cash flow for year 2: $500
- Cash flow for year 3 : $300
- Cash flow for year 4: $600
- Cash flow for year 5: $200

Given, Discount rate, r = 6%

Cash flow, C_{1} = $400 No. of period, n_{1} = 1

Cash flow, C_{2} = $500 No. of period, n_{2} = 2

Cash flow, C_{3} = $300 No. of period, n_{3} = 3

Cash flow, C_{4} = $600 No. of period, n_{4} = 4

Cash flow, C_{5} = $200 No. of period, n_{5} = 5

Therefore, calculation of present value of cash flow of year 1 can be done using the below formula as,

PV of cash flow of year 1, PV_{1} = C_{1} / (1 + r) ^{n}_{1}

= $400 / (1 + 6%)^{1}

**PV of cash flow of year 1 will be –**

**PV of cash flow of year 1 = $377.36**

Similarly, we can calculate PV of cash flow of year 2 to 5

- PV of cash flow of year 2, PV
_{2}= C_{2}/ (1 + r)^{n}_{2}

= $500 / (1 + 6%)^{2}

= $445.00

- PV of cash flow of year 3, PV
_{3}= C_{3}/ (1 + r)^{n}_{3}

= $300 / (1 + 6%)^{3}

= $251.89

- PV of cash flow of year 4, PV
_{4}= C_{4}/ (1 + r)^{n}_{4}

= $600 / (1 + 6%)^{4}

= $475.26

- PV of cash flow of year 5, PV
_{5}= C_{5}/ (1 + r)^{n}_{5}

= $200 / (1 + 6%)^{5}

= $149.45

Therefore, the calculation of present value of the project cash flows is as follows,

PV = $377.36 + $445.00 + $251.89 + $475.26 + $149.45

**PV = $1,698.95 ~ $1,699**

Therefore, the present value of all the project cash flows is $1,699.

### Relevance and Uses

It is essential to understand the concept of present value that states that a sum of money today is worth much more than the same sum of money in the future. The entire concept of the time value of money revolves around the same theory. Another exciting aspect of present value is the fact that the present value and the discount rate are reciprocal to each other, such that an increase in discount rate results in the lower present value of the future cash flows. Therefore, it is important to determine the discount rate appropriately as it is the key to a correct valuation of the future cash flows.

### Recommended Articles

This has been a guide to the Present Value Formula. Here we discuss the calculation of the present value using its formula along with examples and downloadable excel template. You can learn more about financial analysis from the following articles –

- Formula of Present Value Factor
- Formula of Net Present Value
- Calculate Present Value of an Annuity
- PV vs NPV – Compare

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