3.0. Core application of data analytics

3.2. Financial management

Time value of money analysis for different types of cash flows

In financial analysis, understanding the Time Value of Money (TVM) is paramount. It's the cornerstone principle that underscores how the timing and nature of cash flows can significantly impact their worth. Whether it's comparing the value of a lump sum today to a series of future payments or assessing the profitability of investments with different cash flow patterns, TVM analysis is an indispensable tool for making sound financial decisions. Dive into our insights to uncover the intricacies of TVM across various cash flow scenarios.

What is Time Value of Money (TVM)

Time Value of Money (TVM) is a fundamental financial concept that recognizes the idea that a sum of money today is worth more than the same sum of money in the future. It is based on the principle that money has a time-dependent value due to its earning potential, risk, and opportunity cost.

The core concept of TVM can be summarized in two main principles:

1. Future Value (FV): This principle calculates how much a present sum of money will be worth in the future, taking into account a specified interest rate or rate of return. In other words, it quantifies the growth of money over time. The formula for calculating the future value is:
   
   FV = PV × (1 + r)^n
   • FV is the future value of the investment.
   • PV is the present value or initial amount of money.
   • r is the interest rate or rate of return per period.
   • n is the number of periods.


2. Present Value (PV): This principle calculates the current worth of a future sum of money, considering a specific discount rate. It's the process of discounting future cash flows to their equivalent value in today's terms. The formula for calculating the present value is:
   
   PV = FV / (1 + r)^n
   • PV is the present value of the future cash flow.
   • FV is the future cash flow amount.
   • r is the discount rate or rate of return per period.
   • n is the number of periods.

TVM is essential in various financial applications, including investment analysis, loan pricing, budgeting, retirement planning, and evaluating the profitability of projects. It helps individuals and businesses make informed financial decisions by comparing the value of money received or invested at different points in time. TVM takes into account factors like inflation, risk, and the potential returns on investments, enabling better resource allocation and financial planning.

What is Cash flows

In the context of Time Value of Money (TVM) analysis, cash flows refer to the series of incoming and outgoing monetary payments or receipts that occur over time. These cash flows can be associated with various financial transactions, investments, or projects and are an integral part of TVM calculations. Understanding the timing and magnitude of cash flows is essential for assessing the present and future value of money.

Cash flows in TVM analysis are typically categorized into two main types:

Inflows: These are positive cash flows representing money received or earned. Examples include revenues from sales, interest income, dividends, rental income, or proceeds from the sale of an asset.

Outflows: These are negative cash flows representing money paid out or expended. Examples include expenses, loan repayments, purchasing assets, operating costs, and taxes.

In TVM analysis, the timing of these cash flows is critical because the value of money changes over time. Money received or paid in the future is worth less than the same amount received or paid today due to factors like inflation and the potential to earn returns on investments. Therefore, TVM calculations involve discounting or compounding these cash flows to determine their present value (PV) or future value (FV) at a specific point in time.

The formulas used for TVM calculations, such as present value (PV) and future value (FV), consider the timing and amount of cash flows, along with a discount rate or rate of return, to quantify the time-based value of money. These calculations enable individuals and businesses to make informed financial decisions, compare investment opportunities, evaluate the profitability of projects, and assess the impact of different cash flow scenarios on their financial objectives.

Example 1

Time Value of Money (TVM) calculation using the concept of future value (FV):

Scenario: Imagine you have $1,000 that you can invest in a savings account that pays an annual interest rate of 5%. You want to know how much this $1,000 will be worth in 5 years.

Formula for Future Value (FV):

FV = PV × (1 + r)^n

Where:

• FV = Future Value
• PV = Present Value (initial amount of money)
• r = Annual interest rate (expressed as a decimal)
• n = Number of years

Calculation:

In this scenario:

• PV (Present Value) = $1,000
• r (Annual interest rate) = 5% = 0.05 (as a decimal)
• n (Number of years) = 5
• Now, plug these values into the formula:

FV = $1,000 × (1 + 0.05)^5
FV = $1,000 × (1.05)^5
FV = $1,000 × 1.27628 (rounded to five decimal places)
FV ≈ $1,276.28

So, if you invest $1,000 in a savings account with a 5% annual interest rate, it will be worth approximately $1,276.28 in 5 years. This calculation demonstrates the time value of money, showing how the money you have today can grow in value when invested at an interest rate over time.

Using ecxel

You can easily calculate the future value (FV) of an investment using the built-in Excel function called "FV."

Assuming you have the following information in an Excel worksheet:

• Present Value (PV): In cell B1, enter the initial amount of $1,000.
• Annual Interest Rate (r): In cell B2, enter the annual interest rate as a decimal (e.g., 5% as 0.05).
• Payment(PMT): In cell B3,monthly payments
• Number of Years (n): In cell B4, enter the number of years, which is 5 in this example.

To calculate the future value (FV) in Excel:

1. In an empty cell (let's say B5), enter the following formula:
   
   =FV(B2, B4,B3, -B1)
   
   
   • B2 is the cell with the annual interest rate (rate).
   • B4 is the cell with the number of years (nper).
   • B3 Which is 0 represents that there are no additional contributions or payments made over the years (pmt).
   • -B1 is used to make the initial investment negative because it's an outgoing payment (present value).
2. Press Enter.
   
   Excel will calculate and display the future value (FV) of your investment in cell D1, which should be approximately $1,276.28, matching the calculation we did manually earlier.

Note:

In excel formulas outgoing payments are put in negative.

How to calculate future value(FV) in excel

How to calculate present value(PV) in excel

How to calculate Monthly payment(PMT) in excel

Suppose you want to take out a car loan for $20,000 with an annual interest rate of 4.5%, to be paid off over 5 years (60 months). You want to calculate the monthly payment amount.

In an Excel worksheet, you can set up the following:

• Principal Loan Amount (PV): In cell B1, enter $20,000 as the loan amount.
• Annual Interest Rate (r): In cell B2, enter 4.5% as 0.045 (annual interest rate as a decimal).
• Number of Payments (n): In cell B4, enter 60 for the number of months.

To calculate the monthly payment using the PMT function:

1. In an empty cell (e.g., B3), enter the following formula:
   
   =PMT(B2/12, B4, -B1)
   
   
   • B2/12 is used to convert the annual interest rate into a monthly rate (dividing by 12 months).
   • B4 is the number of monthly payments.
   • -B1 is used to make the loan amount negative since it's an outgoing payment (loan).


2. Press Enter.
   
   Excel will calculate and display the monthly payment for your car loan in cell D1. In this example, the calculated monthly payment should be approximately $372.86. This represents the amount you need to pay each month to fully repay the $20,000 car loan over a 5-year period at a 4.5% annual interest rate.

How to calculate rate(r) in excel

NOTE:

When calculating the monthly payment (PMT) for a loan or investment using the PMT function in Excel:

The principal loan amount (PV) is considered an outflow because it represents the initial amount borrowed or invested, which you need to repay or recoup over time. Therefore, it should be entered as a negative value to indicate that it's an outgoing payment.

Conversely, when calculating the interest rate (RATE) for a loan or investment using the RATE function in Excel:

The principal loan amount (PV) is considered an inflow because it represents the initial amount received as a loan or investment. In this context, you should enter it as a positive value to indicate that it's an incoming payment.

So, the sign convention in financial calculations is consistent with the flow of cash:

• Money you receive or borrow is typically represented as positive.
• Money you pay or invest is typically represented as negative.

This consistency in representing cash flows ensures that financial functions and calculations yield accurate results and meaningful interpretations.