Internal rate of return

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internal rate of return ( IRR ) is the method of calculating the rate of return. The term internal refers to the fact that the calculations do not involve external factors, such as inflation or capital costs.

This is also called discounted cash flow rate of (DCFROR).

In the context of savings and loans, the IRR is also called the effective interest rate.

Video Internal rate of return

Definisi

The internal rate of return on an investment or project is an "annual effective compound annual return rate" or rate of return that sets the net present value of all cash flows (both positive and negative) of the same investment to zero. Equivalently, it is the discount rate at which the present net value of future cash flows equals the initial investment, as well as the discount rate at which the present total sum of costs (negative cash flows) equals the total present value of the benefit (positive cash flow).

Intuitively speaking, IRR is designed to take into account time and money time preferences. An investment return received at a given time is worth more than the same return received later, so the latter will result in a lower IRR than the previous one, if all other factors are equal. Fixed income investment where money is once deposited, this deposit interest is paid to the investor at a certain interest rate every time period, and the original deposit does not increase or decrease, will have an IRR equal to the specified interest rate. An investment that has the same total return as the previous investment, but the delay of return for one or more time periods, will have a lower IRR. This lower IRR will show the interest rate of a fixed income investment that will have the same overall value as the pending investment.

Maps Internal rate of return

Use of IRR

Profitability of Investment

Corporations use IRR in capital budgeting to compare the profitability of a capital project in terms of rate of return. For example, a company will compare investments in a new plant versus an existing plant expansion based on the IRR of each project. To maximize returns, the higher the IRR of the project, the more desirable it is to do the project. If all projects require the same amount of upfront investment, the project with the highest IRR will be considered the best and done first.

Maximize Net Present Value

Internal rate of return is an indicator of profitability, efficiency, quality, or investment return. This is different from the current net value, which is an indicator of the net value or the magnitude plus the investment.

By applying internal rate-return methods to maximize corporate value, any investment will be accepted, if its profitability, as measured by internal rate of return, is greater than the acceptable minimum rate of return. The right minimum level to maximize the value added to the firm is the capital cost, ie the internal rate of return of the new capital project must be higher than the cost of the firm's capital. This is because investment with an internal rate of return that exceeds the cost of capital has a positive net worth.

However, selection of investments may be subject to budget constraints, or they may be mutually exclusive competing projects, such as the choice between or capacity or ability to manage more projects can be practically limited. In the example cited above, about a company that compares investments in a new plant versus an existing plant extension, there may be a reason the company will not be involved in both projects.

Fixed Income

IRR is also used to calculate results to maturity and results for calls.

Liability

Both the internal rate of return and the net present value can be applied to liabilities and investments. For liabilities, a lower internal rate of return is preferred over a higher rate.

Capital Management

Corporations use internal rate of return to evaluate stock issues and stock buyback programs. Repurchase of shares if the capital returned to shareholders has a higher internal rate of return than a candidate's investment project or acquisition project at current market prices. Funding new projects by increasing new debt can also involve measuring the cost of new debt in terms of yields to maturity (internal rate of return).

Personal Equity

IRR is also used for private equity, from a limited partner perspective, as a measure of the performance of a general partner as an investment manager. This is because it is a common partner that controls cash flow, including the withdrawal of commitments from limited partners.

src: hbr.org

Calculation

Given the pair collection (time, cash flow) involved in a project, the internal rate of return follows from the current net value as a function of the rate of return. The rate of return for which this function is zero is the internal rate of return.

Mengingat pasangan (periode, arus kas) ( ${\ displaystyle n}  ÂÂ$ , ${\ displaystyle C_ {n}}  ÂÂ$ ) di mana ${\ displaystyle n}  ÂÂ$ adalah bilangan bulat non-negatif, jumlah total periode ${\ displaystyle N}  ÂÂ$ , dan ${\ displaystyle \ mathrm {NPV}}  ÂÂ$ , (nilai sekarang bersih); IRR diberikan oleh ${\ displaystyle r}  ÂÂ$ di:

${\ displaystyle \ mathrm {NPV} = \ jumlah _ {n = 0} ^ {N} {\ frac {C_ {n}} {(1 r) ^ { n}}} = 0}  ÂÂ$

Perhatikan bahwa dalam rumus ini, ${\ displaystyle C_ {0}}  ÂÂ$ (<= 0) adalah investasi awal pada awal proyek. Periode ${\ displaystyle n}  ÂÂ$ biasanya diberikan dalam beberapa tahun, tetapi perhitungannya dapat dibuat lebih sederhana jika ${\ displaystyle r}  ÂÂ$ dihitung menggunakan periode di mana sebagian besar masalah didefinisikan (misalnya, menggunakan bulan jika sebagian besar arus kas terjadi pada interval bulanan) dan dikonversi ke periode tahunan sesudahnya.

Any fixed time can be used instead of the current (eg, the end of an annuity interval); the obtained value is zero if and only if the NPV is zero.

In the case that the cash flows are random variables, as in the case of life annuities, the expected value is incorporated into the above formula.

Often, the ${\ displaystyle r}$ that satisfies the above equation can not be found analytically. In this case, numerical methods or graphical methods should be used.

Example

If an investment can be given by a sequence of cash flows

lalu IRR ${\ displaystyle r}  ÂÂ$ diberikan oleh

${\ displaystyle \ mathrm {NPV} = -123400 {\ frac {36200} {(1 r) ^ {1}}} {\ frac {54800} { (1 r) ^ {2}}} {\ frac {48100} {(1 r) ^ {3}}} = 0.}  ÂÂ$

In this case, the answer is 5.96% (in the calculation, that is, r =.0596).

Numerical solutions

Karena di atas adalah manifestasi dari masalah umum menemukan akar dari persamaan ${\ displaystyle \ mathrm {NPV} (r) = 0}  ÂÂ$ , ada banyak metode numerik yang dapat digunakan untuk memperkirakan ${\ displaystyle r}  ÂÂ$ . Misalnya, menggunakan metode garis potong, ${\ displaystyle r}  ÂÂ$ diberikan oleh

${\ displaystyle r_ {n 1} = r_ {n} - \ mathrm {NPV} _ {n} \ cdot \ left ({\ frac {r_ {n} - r_ {n-1}} {\ mathrm {NPV} _ {n} - \ mathrm {NPV} _ {n-1}}} \ right).}  ÂÂ$

di mana ${\ displaystyle r_ {n}}  ÂÂ$ dianggap sebagai ${\ displaystyle n}  ÂÂ$ ^th aproksimasi IRR.

This ${\ displaystyle r}$ can be found at an arbitrary level of accuracy. Different accounting packages can provide functions for different levels of accuracy.

Perilaku konvergensi oleh berikut:

• Jika fungsi ${\ displaystyle \ mathrm {NPV} (i)}  ÂÂ$ memiliki akar tunggal tunggal ${\ displaystyle r}  ÂÂ$ , maka urutannya akan menyatu menjadi ${\ displaystyle r}  ÂÂ$ .
• Jika fungsi ${\ displaystyle \ mathrm {NPV} (i)}  ÂÂ$ memiliki ${\ displaystyle n}  ÂÂ$ akar sebenarnya ${\ displaystyle \ scriptstyle r_ {1}, r_ {2}, \ dots, r_ {n}}  ÂÂ$ , maka urutannya menyatu dengan salah satu akar, dan mengubah nilai dari pasangan awal dapat mengubah akar yang menjadi konvergennya.
• Jika fungsi ${\ displaystyle \ mathrm {NPV} (i)}  ÂÂ$ tidak memiliki akar sebenarnya, maka urutannya cenderung ke arah ?.

Memiliki ${\ displaystyle \ scriptstyle {r_ {1} & gt; r_ {0}}}  ÂÂ$ ketika ${\ displaystyle \ mathrm {NPV} _ {0} & gt; 0}  ÂÂ$ atau ${\ displaystyle \ scriptstyle {r_ {1} & lt; r_ {0}}}  ÂÂ$ ketika ${\ displaystyle \ mathrm {NPV} _ {0} & lt; 0}  ÂÂ$ dapat mempercepat konvergensi ${\ displaystyle r_ {n}}  ÂÂ$ untuk ${\ displaystyle r}  ÂÂ$ .

Solusi numerik untuk arus keluar tunggal dan banyak aliran masuk

Yang menarik adalah kasus di mana aliran pembayaran terdiri dari satu aliran keluar, diikuti oleh beberapa arus masuk yang terjadi pada periode yang sama. Dalam notasi di atas, ini sesuai dengan:

${\ displaystyle C_ {0} & lt; 0, \ quad C_ {n} \ geq 0 {\ text {for}} n \ geq 1. \,}  ÂÂ$

In this case the NPV of the payout flow is convex, which strictly decreases the function of the interest rate. There is always one unique solution for IRR.

(yang paling akurat ketika ) telah terbukti hampir 10 kali lebih akurat daripada rumus garis potong untuk berbagai suku bunga dan dugaan awal. Misalnya, menggunakan aliran pembayaran {-4000, 1200, 1410, 1875, 1050} dan tebakan awal ${\ displaystyle r_ {1} = 0,25}  ÂÂ$ dan ${\ displaystyle r_ {2} = 0,2}  ÂÂ$ rumus garis potong dengan koreksi memberikan perkiraan IRR 14,2% (kesalahan 0,7%) dibandingkan dengan IRR = 13,2% (7% kesalahan) dari metode garis potong.

If applied repeatedly, either the secant or enhanced formula always incorporates the right solution.

Metode sekian dan formula yang ditingkatkan bergantung pada tebakan awal untuk IRR. Tebakan awal berikut mungkin digunakan:

${\ displaystyle r_ {1} = \ kiri (A/| C_ {0} | \ right) ^ {2/(N 1)} - 1 \,}  ÂÂ$

${\ displaystyle r_ {2} = (1 r_ {1}) ^ {p} -1 \,}  ÂÂ$

dimana

${\ displaystyle A = {\ teks {jumlah inflows}} = C_ {1} \ cdots C_ {N} \,}  ÂÂ$

$            {\displaystyle         p        =                  \frac{              }{}}$ log                               (                                 A                                               /                                                |                                                C                                     0                                                                 |                              )                                          log                               (                                 A                                               /                                                                   N                    P                    V                                                      1                   ,                    saya                    n                                               )                                          .                  {\ displaystyle p = {\ frac {\ log (\ mathrm {A}/| C_ {0} |)} {\ log (\ mathrm {A}/\ mathrm {NPV} _ {1, in})}}.}   

Di sini, ${\ displaystyle \ mathrm {NPV} _ {1, in}}  ÂÂ$ merujuk ke NPV dari arus masuk saja (yaitu, mengatur

Source of the article : Wikipedia