The Time Value of Money
Fundamentals of time value concepts
Scholars in the financial sector concur that the time value of money concept suffices “at the basis of the profitability analysis in financial management” (Ball, 2017, p. 14; Scitovsky, 2016, p. 23). Accordingly, investors hold that money is worth more presently than can be accredited in the future (Ball, 2017, p. 18). Subsequently, it is for the same reason that lenders are inspired to discount money, whose servicing may warrant for an extended period. All these notions are premised on the realisation that most individuals prefer to receive money today rather than the same amount at a future date as they understand that money may have a different value in future, most probably a lesser one. Consequently, several discourses on the time value of money have led to the formulation of techniques that allow for comparing and calculating of the time value of money, which comprises Discounting, Compounding, Indexing, and Capitalisation.
Discounting and compounding process and their uses and the rationale for using the discounting process rather than compounding process in decision making
Most lending institutions prefer compounding and discounting techniques for calculating the time value of money (Schmidt, 2016, p. 82). The dictates of compounding techniques are such that the current amount of money ought to be converted into a future value using the compounded interest factor (Joshi, 2019, p. 27). Conversely, the discounted formula of estimating the time value of money allows for the calculation of the current value of money basing on a projected future value (Brody and Hughston, 2018, p. 308). Therefore, the compounding technique serves best when there is a need to determine the future values of the cash flow, whereas discounting allows for the determination of “the present value of future cash flow”.
Key Differences between Compounding and Discounting (Joshi, 2019, p. 31-37; Petters and Dong, 2016, p. 41-53; )
The basis for Comparison Discounting Compounding
Meaning Serve by allowing for the determination of the present value of future cash flows for a determined period Suffice in situations that necessitate for the determination of the future value of a present investment
Concept There must be a certain amount of money that an entity ought to invest today to get a specific amount in future Investments made today must warrant for an augmented value at a future date
Uses Discount rate Compound rate
Known Future Value Present Value
Factor Discounting/Present Value Factor Compounding/Future Value Factor
Formulas PV= FV/(1+r)^n
Whereby FV=Future Value
r= Discounting rate
n= allocated time
Vo=Vn X 1/(1+K)^n FV= PV(1+r)^n
Whereby PV= Present Value
r= Compounding rate
n= allocated time
Vn=V0(1=k)^n
Where V0=invested capital
K=profitability rate
n= time interval
Vn= Estimated capital Value
The rationale for using Discounting technique rather than Compounding
As was nuanced earlier, discounting technique allows for the determination of the present value of future cash flows for a determined period, thereby implying that the process validates the amounts to be invested if a specific amount must be realised in the future (Sgambati, 2016, p. 274). On the other hand, compounding interest serves lending institutes in such a manner that, they can be able to gauge whether an idea is feasible and the terms attracting before implementing a project (Sgambati, 2016, p. 276). Consequently, the discounting technique is much preferred as it allows for easier Cost-Benefit Analysis (CBA). Correspondingly, the purpose of CBA is to verify the economic merit of public investment projects (Nas, 2016, p. 27) However, most entities find compounding techniques somewhat conniving as ensuing processes attract interest on both the principal and the accumulated interest earned whereas the discounting technique only charges interest on the principal (Nas, 2016, p. 29).
Application of Discounting on the Time Value of Money
The application of the time value of money principle that is premised on the discounted cash flow concept submits to the idea that money to be received or paid at a later date will bear a less value compared to that which it attracts today (Mohanty, 2016, p. 19). Accordingly, the processes that benchmark the discounted cash flow aims to correct such a discrepancy by supplying a future value that is greater than the present value, to cover defining economic facets such as inflation (Schmidt, 2016, p. 28).
Wu, Al-Khateeb, Teng, and Cárdenas-Barrón (2016, p. 108) outline two central terms that ground the discounted cash flow analysis, which defines the time value of money to include: (1) Present value (PV); and (2) Future value. At this moment, the present value represents the current value of future cash flow, whereas the future value denotes the value that flows in and out of the cash flow at a designated time, but in the future (Wu et al., 2016, p. 110). For instance, an entity could wait for a $200 cash inflow to arrive in three years, which has a present value of about $70. Suffice to note, when it comes to discounting, the present value is always less in worth compared to the future value. Also, several scholars have examined scenarios that could further lower the present value below its future value to include risks, arising opportunities, inflation rate, and other uncertain macroeconomic factors (DeFusco et al., 2015).
Realisations such as the ones reached hereinabove, affirm of the importance of the time value of money underlying premises; being that the value is real and measurable. Also, the study recognises the most important construct about the time value of money, which is that the processes that ensue can be used to determine the Net Present Value of an investment, as well as, the values in cash flow streams. DeFusco and his proponents present an elaborate scenario of how the cash flow events that capture both the present and future value of investment might look like for an investment that is worth $100 today.
Accordingly, the key elements of the time value of money have been captured, indicating both the present and future values at two discount rates; 8 per cent and 15 per cent. Correspondingly, the Black bars indicate the value of cash flows in figures that reflect future value. Moreover, the Blue and Green bars represent figures that highlight the current (present) value. In conclusion, the workings reveal that the net values after five years, that the investment would be worth $500 but if one was to rely on present value, then they will enjoy a discounted rate to receive a sum whose figure is less than $500.
Use of time in the valuation of financial instruments such as bonds, equity, and preference shares and capital budgeting
It is now safe to posit that the concept of the time value of money gains much tract because a dollar on hand today is worth more than that promised in the future. Therefore, seasoned investors use time as a financial instrument when gauging the present and future worth of illiquid investments such as bonds, shares, equities, and also in capital budgeting.
Capital budgeting
A company seeking to increase productivity may budget for the acquisition of a new technological line, by contrasting against the terms set for different options, based on the incoming and outgoing flows.
Figure 2 highlights figures representing the costs of initial investment and the determined flows in 4 years, whereas the residual value of the company at the time of borrowing only amounted to 930,000. Providentially, an astute investor, should seek to evaluate the two available options to understand the most viable option. Correspondingly, figure 3 identifies the cumulated discounted cash-flows for the two available options.
The purpose of the ensuing processes is to determine the payback period, for which the cumulated discounted cash flows for the two options also ought to be established.
Accordingly, the workings show that the 3,500,000 loans extended in project A will be paid back in two years period. As such, the company will, in the third year, recuperate 1,800,000. Subsequently, daily cash flow for year three can be calculated as follows:
CF3zi 2000000/365= 5,479. 45 thousands of lei per day
Therefore the remaining 200000 to be paid in the third year will take 37 days, as shown below:
t1= 200000/5479, 45= 36, 5 days. In summary, the terms of option A are such that the loan ought to be repaid in 2 years and 37 days.
The same workings for Option B indicate that it will take 2 years and 84 days to repay a loan of the same amount, thereby implying that the company will have to make daily deposits of about 4110. In conclusion, project one suffices as the best option for the company.
Also, the same parameters that apply to capital budgeting suffice when gauging the viability of bonds, shares, and equities. Investors who engage in the capital and financial markets measure the value of the investments bearing in mind that money to be expected at a later date ought to be greater in value, compared to the worth of the same investment at current rates. Accordingly, they either use discounting or compounding techniques, depending on the working principles of the agreement at hand.
Conclusion
In conclusion, it is now apparent that most individuals prefer to receive money sooner rather than later, except if the amount on offer attracts a value that is greater in worth than the one being curtailed presently. Accordingly, most astute investors employ discounting techniques to determine the future value of their investments before real implementation. When discounting, investors should be keen to evaluate both the future value of their initial investments, as well as the payback period, not forgetting the costs of daily disbursements. In summary, the study has affirmed that seasoned investors ought to be keen at how they treat their investments, lest they incur losses inspired by such matrices as inflation, new opportunities, and other macroeconomic anomalies.
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