## TVM quick dive.

As a finance professional or investor, you know how important it is to make informed financial decisions. The concept of time value of money is a fundamental principle in finance that helps you understand the value of money over time. We'll show you how to calculate the time value of money using Python. Our examples will help you master this essential technique and optimize your investment strategy. Whether you're a beginner or an experienced finance professional, our guide will provide you with the knowledge and tools you need to make better financial decisions.

*
Coding: The Silent Symphony.
- Updated:
2024-05-19 by Andrey BRATUS, Senior Data Analyst.*

The basic idea of Time Value of Money is that money today is worth more than the same amount of money in the future. This is due to the potential earning capacity of money over time. The concept is based on the principle that a dollar today is worth more than a dollar tomorrow because of the opportunity cost of not having that dollar today. Time Value of Money is used in various financial calculations, including present value, future value, and annuity calculations. It is a fundamental principle in finance and is used to evaluate investment opportunities, determine loan payments, and plan for retirement.

In other words the basic idea behind Time Value of Money (TVM) is One Dollar today will worth more than one dollar tomorrow because you can invest or save your money today and earn interest tomorrow.

All required TVM calculations can be easily realised with Python.

#### Future Value (FV) - Compounding formula:

**πΉπ = ππ(1 + π)^n**

Where:

FV: Future Value

PV: Present Value (today)

r: Interest Rate (per period)

n: number of periods

```
PV = 100
r = 0.05
n = 3
FV = PV * (1 + r)**n
```

You can also calculate FV using NUMPY library which is much more simple way to do it.

```
import numpy as np
import numpy_financial as npf
PV = 0
cf = -2000
r = 0.03
n = 25
FV = npf.fv(rate = r, nper = n, pmt = cf, pv = PV)
FV
```

#### Present Value (PV) - Discounting formula:

**ππ = πΉπ / (1 + π)^π**

Where:

FV: Future Value

PV: Present Value (today)

r: Interest Rate (per period)

n: number of periods

```
FV = 20000
n = 4
r = 0.045
PV = FV / (1 + r)**n
```

You can also calculate PV using NUMPY library which is much more simple way to do it.

```
import numpy as np
import numpy_financial as npf
FV = 20000
r = 0.03
n = 25
cf = 5000
PV = npf.pv(rate = r, nper = n, pmt = cf, fv = FV)
PV
```

#### Interest Rates formula:

**π = ( πΉπ/ππ) ^ 1/π β 1**

Where:

FV: Future Value

PV: Present Value (today)

r: Interest Rate (per period)

n: number of periods

```
pv = 10000
fv = 15000
n = 10
r = (fv / pv)**(1/n) - 1
```

#### Stock Returns (Price Return) formula:

**π = ππ‘+1/ππ‘ β 1**

Where:

Pt: Price @ timestamp t

Pt+1: Price @ t+1

r: Period Return (Price Return)

```
p0 = 976
p1 = 1053
p_ret = p1 / p0 - 1
```

#### Stock Returns (Total Return = Price Return + Dividend Yield) formula:

**π = (ππ‘+1 + π·π‘+1) / ππ‘ β 1 = ππ‘+1 / ππ‘ β 1 + π·π‘+1 / ππ‘**

Where:

Pt: Price @ timestamp t

Pt+1: Price @ t+1

Dt+1: Dividend payment @ t+1

r: Period Return (Total Return)

```
div = 40
div_y = div / p0
total_ret = p_ret + div_y
```

## 10 real life examples of Time Value of Money use.

Retirement Planning: Saving money for retirement is an example of Time Value of Money. The earlier you start saving, the more time your money has to grow, and the more money you will have at retirement.

Loan Repayment: When you take out a loan, you are essentially borrowing money from a lender. The lender charges interest on the loan, which means that you will pay back more than you borrowed. This is an example of Time Value of Money because the lender is compensated for the opportunity cost of lending you the money.

Mortgage Payments: When you buy a house, you typically take out a mortgage to finance the purchase. The mortgage payments include both principal and interest, with the interest being an example of Time Value of Money.

Bond Investing: Bonds are a type of investment that pays interest to the investor. The interest payments are an example of Time Value of Money because the investor is compensated for the opportunity cost of lending money to the bond issuer.

Stock Investing: Investing in stocks is another example of Time Value of Money. When you buy a stock, you are essentially buying a share of ownership in a company. If the company performs well, the value of your stock will increase over time, which means that your money has grown in value.

Savings Accounts: Putting your money in a savings account is an example of Time Value of Money because the bank pays you interest on your deposit. The interest payments compensate you for the opportunity cost of not having access to your money.

Annuities: An annuity is a financial product that pays a fixed income stream to the investor over a set period. The income stream is an example of Time Value of Money because it compensates the investor for the opportunity cost of not having access to their money.

Capital Budgeting: Capital budgeting is a process used by businesses to evaluate investment opportunities. The process involves estimating the future cash flows from an investment and discounting them back to their present value using Time Value of Money concepts.

Insurance: Insurance companies use Time Value of Money concepts to determine the premiums they charge for policies. The premiums are based on the expected future value of claims and are discounted back to their present value.

Inflation: Inflation is an example of Time Value of Money because it reduces the purchasing power of money over time. This means that the same amount of money today will not be able to buy as much in the future due to inflation.

## Conclusion.

To summarise, the concept of Time Value of Money is fundamental in finance, and it is crucial to understand it to make informed financial decisions. Time Value of Money refers to the idea that money today is worth more than the same amount of money in the future due to its potential earning capacity. This concept is based on the principle that a dollar today is worth more than a dollar tomorrow because of the opportunity cost of not having that dollar today. The Time Value of Money is used in various financial calculations, including present value, future value, and annuity calculations. It is also used to compare investment opportunities and determine the best course of action. Understanding the Time Value of Money is essential for evaluating investment opportunities, such as stocks, bonds, and real estate. It is also crucial for financial planning, including retirement planning, loan repayments, and budgeting. Furthermore, Time Value of Money helps individuals and businesses make better financial decisions by considering the opportunity cost of their investments. In summary, the Time Value of Money is a critical concept in finance that helps individuals and businesses make informed financial decisions by considering the potential earning capacity of their money over time.