Present value

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In economics and finance, the current value ( PV ), also known as presenting a discount value , is the value of the expected revenue stream specified on assessment. The current value is always less than or equal to the future value because money has interest earning potential, a characteristic that is referred to as the time value of money, except during a negative interest rate, when the present value will be more than the future. value. The time value can be explained by a simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'more value' means greater value. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and generates one-day interest, making the total accumulation to be worth more than a dollar tomorrow. Interest can be compared with rent. Just as the rent is paid to the landowner by the lessee, without the ownership of the transferred asset, the interest is paid to the lender by the borrower who gains access to the money for a certain period of time before paying back. By letting the borrower have access to money, the lender has sacrificed this exchange rate, and is compensated in the form of interest. The initial amount of loan funds (present value) is less than the total amount of money paid to the lender.

The current value calculation, as well as the calculation of future value, is used to assess loans, mortgages, annuities, sinking, lasting, bond, and more. This calculation is used to make comparisons between cash flows that do not occur at the same time, because the time date should be consistent to make comparisons between values. When deciding between projects to invest, a choice can be made by comparing each of the present value of the projects by discounting the expected income stream at the appropriate project interest rate, or rate of return. The project with the highest current value, the most valuable at the moment, should be selected.

Video Present value

Purchase year

The traditional method of assessing future income flows as the current amount of capital is to double the average expected annual cash flow with some, known as "year purchases". For example, in selling to a third-party property leased to a lessee under a 99-year lease with a $ 10,000-a-year lease, the deal may be triggered on a "20-year purchase", which will reward the rent of 20 * $ 10,000, which is $ 200,000. This is equivalent to the current discounted 5%. For more risky investments, buyers will demand to pay for purchases in lower number of years. This is the method used for example by the British crown in setting the resale price for manors confiscated in the Dissolution of Monasteries in the early 16th century. The standard usage is the purchase of 20 years.

Maps Present value

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If a choice is offered between $ 100 today or $ 100 in one year, and there is a positive real interest rate throughout the year, , a rational person will choose $ 100 today. This is described by economists as a time preference. Timing preferences can be measured by risk-free auctioning - such as US Treasury bills. If the $ 100 note with zero coupon, paid in one year, sells for $ 80 now, then $ 80 is the present value of the note that will be worth $ 100 per year from now. This is because money can be put into a bank account or other (secure) investment that will return interest in the future.

An investor who has some money has two options: to spend it now or to save it. But the financial compensation to keep it (and not spend it) is that the value of money will increase through the compound interest that it will receive from a borrower (the bank account in which he deposited the money).

Therefore, to evaluate the real value of a certain amount of money today after a period of time, the economic agent increases the amount of money at a certain interest rate. Most actuarial calculations use the risk-free rate in accordance with the minimum guarantee level provided by the bank savings account, for example, assuming no risk of default by the bank to return the money to the account holder on time. To compare changes in purchasing power, the real interest rate (the nominal interest rate minus the inflation rate) should be used.

The operation evaluating the present value to the future value is called capitalization (how much $ 100 a day will be worth in 5 years?). The reverse operation - evaluating the present value of the amount of money in the future - is called a discount (how much $ 100 received in 5 years - on the lottery for example - is worth today?).

Therefore if one has to choose between receiving $ 100 today and $ 100 in a year, the rational decision is to choose $ 100 today. If the money is to be received within one year and assuming the savings account's interest rate is 5%, the person should be offered at least $ 105 in one year so the two options are equivalent (either receiving $ 100 today or receiving $ 105 in a year). This is because if $ 100 is stored in a savings account, its value will be $ 105 after one year, again assuming no risk of losing the initial amount through the default bank.

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Interest rate

Interest is the amount of extra money earned between the beginning and the end of the time period. Interest represents the time value of money, and can be considered as a necessary lease from the borrower to use the money from the lender. For example, when someone takes out a bank loan, they are charged interest. Or, when someone deposits money into the bank, their money earns interest. In this case, the bank is the borrower of the funds and is responsible for crediting the interest to the account holder. Similarly, when a person invests in a company (through corporate bonds, or through shares), the company borrows funds, and must pay interest to the individual (in the form of coupon payments, dividends, or stock price appreciation). The interest rate is a change, expressed as a percentage, in the amount of money over a period of compounding. The compounding period is the length of time that must occur before the interest is credited, or added to the total. For example, annually aggravated interest is credited once a year, and the compound period is one year. The quarterly compounded interest is credited four times a year, and the merger period is three months. The period of compounding can be over time, but some common periods are annually, semi-annual, quarterly, monthly, daily, and even continuously.

There are several types and terms related to interest rates:

• Compound interest, interest that increases exponentially over the next period,
• Simple flowers, extra interest that does not increase
• Effective, effective equivalent rate compared to several compound interest periods
• The nominal annual interest, the simple annual interest rate of several interest periods
• The discount rate, the interest rate is reversed when doing the calculation in reverse
• Compound interest constantly, the limit of interest rate mathematics with zero period of time.
• The real interest rate, which takes into account inflation.

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Calculation

The operation of evaluating the current amount of money in the future is called capitalization (how much will the value of 100 days be worth in 5 years?). The reverse operation - evaluating the present value of the amount of money in the future - is called a discount (how much will 100 be received in 5 years now?).

Spreadsheets generally offer a function to calculate the present value. In Microsoft Excel, there is a function of the present value for a single payment - "= NPV (...)", and the same set of payments, periodically - "= PV (...)". The program will calculate the present value flexibly for any cash flows and interest rates, or for different interest rate schedules at different times.

The current value of lump sum

Model penilaian sekarang yang paling umum digunakan menggunakan bunga majemuk. Rumus standarnya adalah:

${\ displaystyle PV = {\ frac {C} {(1 i) n}}} \,} Â Â$

Di mana ${\ displaystyle \, C \,}  ÂÂ$ adalah jumlah uang di masa depan yang harus didiskon, ${\ displaystyle \, n \,}  ÂÂ$ adalah jumlah periode gabungan antara tanggal sekarang dan tanggal di mana jumlah bernilai ${\ displaystyle \, C \,}  ÂÂ$ , ${\ displaystyle \, i \,}  ÂÂ$ adalah suku bunga untuk satu periode majemuk (akhir periode penggabungan adalah ketika bunga diterapkan, misalnya, setiap tahun, setengah tahunan, tiga bulanan, bulanan, setiap hari). Tingkat bunga, ${\ displaystyle \, i \,}  ÂÂ$ , diberikan sebagai persentase, tetapi dinyatakan sebagai desimal dalam rumus ini.

Seringkali, ${\ displaystyle v ^ {n} = \, (1 i) ^ -n}} Â Â$ disebut sebagai Faktor Nilai Sekarang

This is also found from the formula for future value with negative time.

Misalnya, jika Anda akan menerima $ 1000 dalam 5 tahun, dan suku bunga tahunan efektif selama periode ini adalah 10% (atau 0,10), maka nilai sekarang dari jumlah ini adalah

${\ displaystyle PV = {\ frac {\ $ 1000} {(1 0.10) 5}}} = \ $ 620.92 \,} Â Â$

The interpretation is that for an effective annual interest rate of 10%, an individual will be indifferent to receive $ 1000 in 5 years, or $ 620.92 today.

Daya beli dalam uang hari ini sejumlah ${\ displaystyle \, C \,}  ÂÂ$ uang, ${\ displaystyle \, n \,}  ÂÂ$ tahun ke depan, dapat dihitung dengan rumus yang sama, di mana dalam kasus ini ${\ displaystyle \, i \,}  ÂÂ$ adalah tingkat inflasi masa depan yang diasumsikan.

Nilai sekarang bersih dari aliran arus kas

Cash flow is the amount of money paid or received, distinguished by a negative or positive sign, at the end of a period. Conventionally, the cash flow received is denoted by a positive sign (total cash increases) and the cash flow paid is marked with a negative sign (total cash has decreased). The cash flows for a period represent a net change in the money for that period. Calculating the current net value, ${\ displaystyle \, NPV \,}$ , from a cash flow stream consisting of discounting each cash flow to date, using present value factors and the number of appropriate merge periods, and combining these values.

Misalnya, a good friend of Arus, is going to get rid of $ 100 per hour, periodically, $ 50 per akhir for a second period, under $ 35 per hour, and then get a bunk for a period of time, and then 5% (0.05) Arus Kas tersebut adalah

${\ displaystyle PV_ {1} = {\ frac {\ $ 100} {(1.05) 1}} = \ $ 95.24 \,} Â Â$

${\ displaystyle PV_ {2} = {\ frac {- \ $ 50} {(1.05) 2}} = - \ $ 45.35 \, } Â Â$

${\ displaystyle PV_ {3} = {\ frac {\ $ 35} {(1.05 )3}} = \ $ 30.23 \,} Â$ masing-masing

Denomin demikian nilai bersih sekarang akan menjadi

${\ displaystyle NPV = PV_1 PV_2 PV_3 = {\ frac {100} {(1.05) 1}} {\ frac {-50} {(1.05) 2}} {\ frac {35} {(1.05 )3}} = 95.24-45.35 30.23 = 80.12,} Â Â$

Di sini, ${\ displaystyle i ^ {4}} Â$ adalah tingkat bunga tahunan nominal, diperparah setiap triwulan, dan tingkat bunga per kuartal adalah ${\ displaystyle {\ frac {i ^ 4} {4}}} Â Â$

Nilai sekarang dari anuitas

Many financial arrangements (including bonds, other loans, leases, salaries, membership fees, annuities including direct annuity-depreciation and annuity, straight-line costs) establish a structured repayment schedule; payment of the same amount at regular time intervals. Such arrangements are called annuities. The expression for the present value of the payout is a summary of the geometry series.

Ada dua jenis anuitas: anuitas segera dan jatuh tempo anuitas. Untuk anuitas segera, ${\ displaystyle \, n \,}  ÂÂ$ pembayaran diterima (atau dibayar) pada akhir setiap periode, pada waktu 1 hingga ${\ displaystyle \, n \,}  ÂÂ$ , sedangkan untuk anuitas jatuh tempo, ${\ displaystyle \, n \,}  ÂÂ$ pembayaran diterima (atau dibayar) di awal setiap periode, pada waktu 0 hingga ${\ displaystyle \, n-1 \,}  ÂÂ$ . Perbedaan halus ini harus diperhitungkan ketika menghitung nilai sekarang.

Anuitas jatuh tempo adalah anuitas segera dengan satu periode bunga-bunga lagi. Dengan demikian, dua nilai sekarang berbeda dengan faktor ${\ displaystyle (1 i)}  ÂÂ$ :

${\ displaystyle PV _ {\ text {annuity due}} = PV _ {\ text {annuity immediate}} (1 i) \, \!}  ÂÂ$

Nilai sekarang dari anuitas segera adalah nilai pada saat 0 aliran arus kas:

${\ displaystyle PV = \ jumlah _ {k = 1} ^ {n} {\ frac {C} {(1 i) k}} = C \ kiri [{\ frac {1- (1 i) ^ {- n}} {i}} \ right], \ qquad (1)} Â Â$

dimana:

${\ displaystyle \, n \,}  ÂÂ$ = jumlah periode,

${\ displaystyle \, C \,}  ÂÂ$ = jumlah arus kas,

${\ displaystyle \, i \,}  ÂÂ$ = suku bunga atau tingkat pengembalian periodik yang efektif.

Pendekatan untuk perhitungan anuitas dan pinjaman

The above formula (1) for the immediate calculation of annuities offers little insight for the average user and requires the use of some form of computing machine. There is a less intimidating approach, easier to calculate and offer some insight for non-specialists. It was given by

Where, as above, C is the annuity payment, PV is the principal, n is the amount of payment, beginning at the end of the first period, and i is the interest rate per period. Equivalent C is the repayment of a periodic loan for a PV loan extended during n periods at the rate of interest, i. This formula is valid (for positive n, i) for ni <= 3. For completeness, for ni> = 3 the approximation is ${\ displaystyle C \ approx PVi}$ .

The formula can, in some circumstances, reduce the calculation to one of mental arithmetic alone. For example, what is the loan payment (forecast) for PV loan = $ 10,000 paid annually for n = 10 years at 15% interest (i = 0.15)? The approximate formula is C? 10,000 * (1/10 (2/3) 0,15) = 10,000 * (0,1 0,1) = 10,000 * 0,2 = $ 2000 per year by mental arithmetic only. The correct answer is $ 1993, very close.

The overall approach is accurate in  ± 6% (for all n> = 1) for the interest rate 0 <= i <= 0.20 and in Ã,  ± 10% for the interest rate 0.20 <= i <= 0.40. However, it is intended only for "rough" calculations.

Current rating of length

Suatu keberlangsungan mengacu pada pembayaran periodik, piutang tanpa batas, meskipun hanya sedikit instrumen semacam itu. Nilai sekarang dari keabadian dapat dihitung dengan mengambil batas dari rumus di atas sebagai n mendekati tak terhingga.

${\ displaystyle PV \, = \, {\ frac {C} {i}}. \ qquad (2)}  ÂÂ$

Formula (2) juga dapat ditemukan dengan mengurangkan dari (1) nilai sekarang dari suatu periode n yang tertunda secara perpetual, atau secara langsung dengan menjumlahkan nilai sekarang dari pembayaran

${\ displaystyle PV = \ sum _ {k = 1} ^ {\ infty} {\ frac {C} {(1 i) k} } = {\ frac {C} {i}}, \ qquad i & gt; 0,} Â Â$

which form a geometry series.

Again there is a difference between the length of time - when the payment is received at the end of the period - and the duration due to the payment received at the beginning of a period. And as with the annuity calculation, continuity and sustainability are immediately different from the factor ${\ displaystyle (1 i)}$ :

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂPÂ\; Â\; Â\; Â\; Â\; Â\; Â}$ _{         V                       immutability because                          =          P                 V                       perpetuity immediate                         (         1                   me        )                           {\ Displaystyle PV _ {\ text {perpetuity due}} = PV _ {\ text {perpetuity immediate}} (1 i) \, \!}  Â}

PV from a bond

The present value is additional. The present value of a bundle of cash flows is the sum of each of the current values.

In fact, the present value of cash flows at a constant mathematical interest rate is a point in the Laplace transform of the cash flows, evaluated by the transformation variable (usually denoted "s") equal to the interest rate. The full Laplace transform is the curve of all current values, plotted as a function of the interest rate. For discrete time, where payments are separated by large periods of time, the transformation is reduced to sum, but when payments are ongoing almost continuously, the mathematical continuous function can be used as an estimate.

This calculation should be applied with caution, because there is an underlying assumption:

• That it is not necessary to take into account price inflation, or alternatively, that inflation costs are included in the interest rate.
• That the likelihood of receiving a high payment - or, alternatively, the default risk is included in the interest rate.

See the time value of money for further discussions.

Variants/Approach

There are mainly two sense values ​​now. Whenever there is uncertainty in time and amount of cash flow, the current expected value approach will often be the right technique.

• Traditional Present Value Approach - in this approach a set of estimated cash flows and a single interest rate (equivalent to risk, usually the weighted average cost component) will be used to estimate fair value.
• The Expected Present Value Approach - in this approach several cash flow scenarios with different/expected probabilities and the risk-free rate adjusted for credit are used to estimate fair value.

Interest rate selection

The interest rate used is a risk-free interest rate if there are no risks involved in the project. The returns from the project must equal or exceed this rate of return or it would be better to invest capital in this risk-free asset. If there is a risk in this investment can be reflected through the use of risk premium. The required risk premium can be found by comparing the project with the required rate of return from other projects with similar risks. Thus it is possible for investors to take into account any uncertainty involved in various investments.

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Current rating method

An investor, money lender, must decide a financial project to invest their money, and the value now offers one method to decide. Financial projects require the initial expenditure of money, such as the stock price or the price of corporate bonds. The project claims to restore initial expenditure, as well as some surplus (eg, interest, or future cash flows). An investor can decide which project to invest by calculating the present value of each project (using the same interest rate for each calculation) and then comparing it. The project with the smallest value at the moment - the fewest initial expenditure - will be chosen because it offers the same return as other projects for the least amount of money.

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See also

• Capital budgeting
• Age value
• Liquidation
• Net present value

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References

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Further reading

Henderson, David R. (2008). "Current value". Economic Concise Encyclopedia (2nd ed.). Indianapolis: Library of Economy and Freedom. ISBN: 978-0865976658. OCLC: 237794267.

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