The interal rate of return ( IIR ) is one of the most widely  used capital budgeting techniques. The Internal rate of return ( IRR ) is the discount rate that equates the NPV of an investment opportunity with $0 ( because the present value of cash inflows equals the initial investment ). It is the rate of return that the firm will earn if it invest in the project and receives the gives cash inflows. Mathematically, the IRR is the value of r in Equation NPV to equal $0.

Formula to determine IRR

 tanDecision Criteria

When IRR is used to make accept-reject decisions, the decision criteria are as follows :

• If the IRR is greater than the cost of capital, accept the project.
• If the IRR is less than the cost of capital, reject the project.

these criteria guarantee that the firm will earn at least its required return. such an outcome should increase the market value of the firm and therefore the wealth of its owner.

The method used by large companies to evaluate investment  project is called net present values ( NPV ). the intuition behind the NPV method is simple.When firms make investments, they are spending money that they obtained in one form or another. from investor. Investor Expect a return of money that they give to firms, so a firm should undertake an investment only if the present value of the cash flow that the investment generates is greater than the cost of making investment in the first place. Because the NPV method takes into  account the time value of investor's money, it is more sophisticated capital budgeting technique than payback period rule. The NPV method discounts the firm's cash flows at the firm's cost of capital.This rate is the minimum return that must be earned on a project to satisfy the firm's investors. Project with lower return fail meet investor's expectations and therefore decrease firm value, and projects with higher returns increase firm value.

The net present value ( NPV ) is found by subtracting a project's initial investment ( CF-0 ) from present value of its cash inflows ( CF-t) discounted at a rate equal to the firms cost of capital ( r ).

when NPV is used, both inflows and outflows are measure in terms of present dollars. For a project that cash outflows beyond the initial investment, the net present value of a project would be found by subtracting the present value of outflows from the present value of inflows.

Decision Criteria 

When NPV is used to make accept - reject decision, the decisions criteria are as follows :

• If the NPV is greater than $0 than, accept the project.
• If the NPV is less than $0 than, reject the project.

if the NPV is greater than $0, the firm will earn a return greater than its cost of capital. such action should increase the market value of the firm, and therefore the wealth of its owners by an amount equal to NPV.

Example 

We can illustrate the net present value ( NPV ) approach by using the Bennet Company data presented below. If the firm has a 10% cost of capital, the net present values for project A ( an annuity ) and B ( a mixed stream) can be calculated below :

Time Line For project A

Time Line for Project B

These calculation result in net present values for project A and B of $11,071 and $10,924, respectively. Both projects are acceptable, because the net present value of each is greater than $0. If the project were being ranked, however , project a would be considered superior to B, because it has higher net present value tan that of B ( $11,071 versus $10,924).

Payback periods are commonly used to evaluate proposed investments. The Payback Periods is the amount of time required for the firm to recover its initial investment in a project, as calculated from cash inflows. In the case of an annuity, the Payback Period can be found by dividing the initial investment by the annual cash inflow. For mixed stream of cash inflow, the yearly cash inflow must be accumulated until the initial investment is recovered. Although popular, the Payback Period is generally  viewed as an unsophisticated ca[ital budgeting technique, because it does not explicitly consider the time value of money.

Decision Criteria

When the Payback period is used to make accept - reject decisions, the following decision criteria apply :

• If the payback period is less than the maximum acceptable payback period, accept the project.
• If the payback period is greatest than maximum acceptable payback period, reject the project.

The length of the maximum acceptable payback period is determined by management. This value is set subjectively on the basis of a number of  factors, including the type of project ( expansion, replacement, or renewal, other ), the perceived risk of the project, and the perceived relationship between payback period and the share value. It is simply a value that management feels, on average, will result in value - creating investment decisions.

Personal Finance Example 

Seema Mahdi is considering investing $ 20,000 to obtain a 5% interest in rental property. Her good friend Akbar Ahmed, put the deal together and he conservatively estimates that Seema should received between $4,000 and $ 6,000 per year in cash from her 5% interest in property. The deal is structured in a way that forces all investor to maintain their investment in the  property for at least 10 years. Seema expects to remain in the 25% income-tax bracket for quite a while. To be acceptable, Seema requires the investment to pay itself back in terms of after-tax cash flows in less than 7 years.

Seema's calculation of the payback period on this deal begins with calculation of the payback period of the range of annual after-tax cash flow :

after -tax cash flow = ( 1 - tax rate ) x pre-tax cash flow

                              = (  1- 0.25 ) x $ 4000  = $ 3000

                              = (  1- 0.25 ) x $ 6000  = $ 4500

The after cash flow ranges from $ 3000 to $ 4500. Dividing the $ 20.000 initial investment by each of the estimated after -tax cash flows, we get the payback period :

Payback Period = Initial investment / After-tax cash flow 

                         = $ 20.000 / $ 3000 = 6.67 years

                         = $ 20.000 / $ 4500 = 4.44 years

Because Seena proposed rental property investment will pay itself back between 4.44 and 6.67 years, which is a range below her maximum payback of 7 years, the investment is acceptable.

Persoalannya adalah ketika menentukan jumlah simpanan yang harus dilakukan saat ini, untuk mendapatkan jumlah uang sebanyak yang diharapkan, dengan tingkat bunga dan waktu tertentu.

Misalkan kita menginginkan jumlah uang di masa mendatang sebesar F, dengan suku bunga i %, dan tenggang waktu n tahun, maka nilai simpanan sekarang yaitu P diperoleh dengan :

Persoalan bunga berbunga di bagi menjadi :

1. Bunga Diskrit ( bunga nominal )
2. Bunga Kontinyu ( bunga efektif )

Penjelasan :

Bunga diskrit, berarti nilai bunga diperhitungkan pada setiap akhir periode waktu selama periode penelaahannya ( biasanya selama satu tahun).

Bunga kontinyu, diasumsikan bahwa bunga dihitung dan ditambahkan ke pinjaman pokok setiap saat selama satu tahun, jadi bunga bisa di hitung per bulan, per tiga bulan, atau enam bulan sekali.

Dalam pembahasan ekonomi teknik, bunga yang dipakai adalah bunga hasil penyimpanan uang, yang akan di hitung pada setiap akhir periode dan ditambahkan ke pokok pinjaman untuk periode berikutnya.

Contoh soal :
 uang sebesar Rp. 1000,- disimpan dengan tingkat suku bunga 5% pertahun, maka akhir tahun ketiga nilai uang tersebut menjadi Rp. 1157.60,- dengan perhitungan sebagai berikut :

Tahun ke-	Bunga 5 % per periode tahun	Jumlah uang per periode tahun
1	5% x Rp. 1000,- = Rp. 50,-	Rp. 1150,-
2	5% x Rp. ,050 = Rp. 52,5	Rp. 1102,5-
3	5% x Rp. 1102.50- = Rp. 55,10,-	Rp. 1157,60,-

Formula :

Tingkat suku bunga adalah rasio antara uang yang dibebankan atau dibayarkan diakhir periode waktu tertentu, biasanya satu tahun atau kurang, yang ditetapkan sebelumnya dengan uang yang dipinjam pada awal periode tersebut.
Untuk Simple interest atau bunga sederhana, bunga yang harus dibayar pada setiap periode tidak dimasukan ke dalam pokok pinjaman.

Contoh :

Jika sejumlah uang dengan nilai Rp. 1000,- dipinjam selama 3 tahun dengan bunga 5% pertahun, maka setelah 3 tahun nilai uang tersebut menjadi Rp. 1.150,-

Diperoleh dari :

Bunga pertahun                           = 5% x Rp. 1000,- = Rp. 50

Bunga 3 tahun                             = 3 x Rp.50,-         = Rp. 150,-

Jumlah modal yang dipinjam        = Rp. 1000,-

Jumlah yang harus dibayar           = Rp. 1150,-

Formula :

F ( future) = Nilai uang saat tahun ke n

P ( Present) = Nilai saat tahun ini

i ( Interest rate ) = tingkat suku  bunga ( %)

n =  Periode waktu

maka     :               F = P ( 1+ in )

 

Pertumbuhan uang di dalam waktu harus diperhitungkan di dalam semua kombinasi danperbandingan pembayaran.
( J.C.L Fish, Engineering Economic, 2th Edition, New York, Mc Graw Hill Book,Inc 1923)

kebanyakan persoalan di dalam ekonomi melibatkan dan menentukan apa yang ekonomis dalam jangka panjang. Dalam hal ini, kita perlu mengenal nilai uang dalam kurun waktu tertentu.
1 dollar sekarang akan lebih besar nilai nya dari pada 1 dollar di tahun mendatang.

Form :

nilai uang sebesar x pada tahun n
nilai uang sebesar x-i pada tahun ke ( n + 1)

case :
A meminjam uang sebesar Rp.1.000.000, dengan tingkat suku bunga 6 % pertahun, dan masa pinjaman 5 tahun.

Persoalan : Bagaiman cara pengembalian pinjaman tersebut.