Present Value Calculator of a Capital Due in “n” Years

Written by: H. Candido on 2024-05-17

Financial decisions often require combining cash flows or comparing values ​​with different temporal manifestations. To “move them back in time” in order to find their corresponding value today, it is necessary to update them by discounting them.

The Present Value

Net Present Value (NPV) is a financial metric used to evaluate the profitability of an investment or project. It calculates the present value of all expected future cash flows (both incoming and outgoing), discounted back to today using a specified discount rate (usually the cost of capital or required rate of return).

Present Value Calculator

Given the Interest Rate, the Future Value, the Period, the calculator returns the Present Value.

How to use the calculator

To use the calculator, simply,

1. enter the Future Value of capital  C
2. enter the number of years  n
3. indicate the yearly Interest rate  r  %

The calculator will automatically determine the present value  VA  of the capital  C  which will be due in  n  years, at the rate  r  %.

The time factor: actualization and capitalization

The time factor assumes considerable importance in the economic field both with regard to the past and the future. In fact,

1. inflationary dynamics lead to a continuous erosion of the purchasing power of currencies, so being able to have data parameterized to these dynamics is a need often felt by economists but also by all of us for practical reasons,
2. not to mention that financial analysts often make their assessments based on the actualization of the cash flows of companies in their evolutionary or stabilization phases.

As regards the future projection of the value of money, we can make a simple consideration: one dollar available today has an actual value that is greater than the value of the same available in a few years, simply because it can be invested today and can generate interest in the meantime.

In fact (generally speaking) a capital employed at a discount rate for   [ latex]n[/latex] years, generates a “final” capital (called the principal) that will be greater than the initial capital. The discounting that we deal with in this article with the attached calculator, consists in finding the equivalence in real terms of two “equal” capitals that have different maturities in time: or of the same capital at different times, which is the same. More precisely: knowing a certain “final” capital, the discount rate ,  the reference time , our calculator identifies its current value   .         

• So, in this context the terms “current” and “actualization” have to do with the idea of ​​capital being “brought back” in time.
• while the term capitalization is identified with “carrying forward in time” the real value of a given capital.

By means of actualization (obviously assuming a positive rate of return on capital), by moving a capital “back in time” it is “discounted”: it is no coincidence that it is often said that the current value is equal to its final “discounted” value.

Time, convenience, financial risks

Both in the corporate and capital markets, financial operations take into account some elements above all: the main ones are those related to time and risk. But also to rationality in the case of rational investors, that is, those who seek the most convenient return with the least possible risk. 

Time . As we have already said when talking about time, a euro today is worth more than a euro tomorrow, because the former can be invested and earn interest (rate of return). 

Convenience.  The existence of competitive capital markets allows investors with temporally different financial availability as well as subjects who need capital at different times to have the same “opinion” about the convenience of a given investment. 

Risks.  As far as risks are concerned, a euro invested in a safe investment (e.g. government bonds) is worth more than a euro invested in a risky investment at the same rate, since rational people aim for the highest return with the least possible risk.

Formula to calculate the Present Value of a capital

The present value   of a capital  payable in x years   is:

Where,

•   this is what is called the actualization (or discount) factor
• t  is the number of years
• r  is the remuneration or discount rate on an annual basis
• There is capital in so many years

From a qualitative analysis of the Present Value formula, we can say the following.  The discount factor   measures the current value of a euro available in a certain number of years at the rate   . The discount rate  is the remuneration that is given up today to have more capital tomorrow.

• The discount rate is also called the opportunity cost of capital, and is the return expected by those who invest (in shares or other securities).
• So if the flows from these investments are safe, the yield on government bonds will be used, otherwise an additional “premium” for risk will need to be considered.

The Present Value (PV)   is obtained by discounting the expected cash flows from an investment.

An example: let’s assume we are sure of cashing in €1,000 in three years without running any risk.
If the interest rate on government bonds, therefore on non-risky bonds, were equal to 1%, the current value of the sum of €1,000 would be equal to: =  = €970.59

Why and when is Present Value calculation used?

The calculation of the present value is a fundamental tool in the financial and economic fields. It is used for:

• Evaluate investments : Compare alternatives that generate returns at different times.
• Analyze loans or mortgages : Determine whether a future payment makes sense compared to its value today.
• Insurance and pension valuations : calculate the present value of pensions or annuities.
• Business decisions : such as project financing or business plan evaluation.

It is essential when time impacts the value of money, which is always.

Examples of how Present Value is used in financial decisions

A classic example is the evaluation of investment projects. THink about a company that wants to invest in a new piece of machinery. To determine whether the investment is worthwhile, the company must calculate the present value of the future cash flows that the machinery will generate. This process, known as discounted cash flow analysis (DCF), allows the present value of the cash flows to be compared to the initial cost of the machinery. If the PV of the future cash flows exceeds the initial cost, the investment is considered profitable.

Another example involves financing decisions . Suppose a company is considering whether to issue bonds or take out a bank loan. Using present value, the company can compare the total cost of both options, taking into account future interest payments and the time value of money. This allows it to choose the financing option that is cheaper in the long run.

Leasing decisions also use present value. Companies often have to decide whether to purchase an asset or lease it. By calculating the present value of the lease payments and comparing it to the purchase cost, the company can determine which option is more financially advantageous.

On a personal level, present value is used in retirement planning. People calculate the present value of their savings and future contributions to determine whether they will have enough money for retirement. This process helps set savings goals and make decisions about investments and retirement contributions.

Additionally, present value is essential when evaluating home purchase options. When comparing mortgages with different interest rates and payment terms, the present value of future monthly payments can help you choose the most cost-effective financing option.

Finally, present value is used in portfolio management decisions . Investors use PV to value bonds and determine their expected return by comparing the purchase price to the present value of future interest payments and principal at maturity.

Comparison of Present Value with other financial concepts, such as future value or NPV

Present Value (PV) is just one of several financial concepts used to evaluate investments and make economic decisions. Other complementary concepts are future value (FV) and Net Present Value (NPV).

Future Value (FV) represents the amount of money an investment will earn at a future date, given a certain interest rate. Unlike Present Value, which discounts future cash flows to their present value, future value compounds the present value to a future period. The formula for Future Value is FV = PV * (1 + r)^n, where r is the Interest Rate and n is the number of periods. This concept is useful for projecting how much a current investment will grow over time, helping investors plan for the long term.

Net Present Value (NPV) , on the other hand, is a more complex measure that combines both the concepts of Present Value and Future Value to assess the profitability of an investment project. NPV is calculated by subtracting the initial investment from the present value of the future cash flows expected from the investment. The NPV formula is: NPV = Σ (FCt / (1 + r)^t) – C, where FCt are the future cash flows, r is the discount rate, t is the period, and C is the initial cost. A positive NPV indicates that the investment is expected to generate a return that is greater than the cost of capital, making it attractive.

A comparison of PV, FV, and NPV highlights different time perspectives and financial applications. Present value is ideal for assessing how much a series of future cash flows are worth today, providing a basis for comparing different investments. Future value is useful for projecting the growth of an investment over time, which is essential for long-term planning and determining investment goals. Finally, net present value is an overall measure that integrates the concepts of PV and FV to determine the net profitability of a project, taking into account both initial costs and future benefits.

It is important to note that all these measures are highly dependent on the discount rate chosen, which reflects the cost of capital or the expected return. The choice of discount rate can significantly influence the results, and therefore must be made carefully, considering the risks and opportunities of the financial market.

In summary, while present value provides an immediate assessment of future cash flows, future value and net present value offer complementary perspectives that can guide more informed and strategic financial decisions. Understanding and applying these concepts can help investors optimize their portfolios and companies make more sound investment decisions.

Frequently Asked Questions (FAQ)

1. What does the discount rate represent?
The discount rate represents the expected return on an alternative investment, or how much it “costs” to wait to receive a sum in the future.

2. What is the formula for present value?
The formula is: Present Value=C(1+r)n\text{Present Value} = \frac{C}{(1 + r)^n}Present Value=(1+r)nC

Where:

• CCC is the future capital
• rrr is the annual discount rate
• nnn is the number of years

3. What if the rate is 0%?
In this case, the present value is equal to the future value, because money does not lose value over time.

4. Does the calculation only apply to single future amounts?
No. There is also the net present value (NPV) , which considers multiple future cash flows. This tool is widely used in business investments.

5. How do you choose the right discount rate?
It depends on the context. It could be the yield of a risk-free alternative (e.g. BTP), the inflation rate, or the average cost of capital for a company.

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