Analisa Investasi (proyek)(ekonomi teknik)

Hermanto Saliman

Investasi dan Biaya modal- Investasi adalah suatu istilah dengan beberapa pengertian yang

berhubungan dengan keuangan dan ekonomi. Istilah tersebut berkaitan dengan akumulasi suatu bentuk aktiva dengan suatu harapan mendapatkan keuntungan dimasa depan. Terkadang, investasi disebut juga sebagai penanaman modal.

- Berdasarkan teori ekonomi, investasi berarti pembelian (dan produksi) dari modal barang yang tidak dikonsumsi tetapi digunakan untuk produksi yang akan datang (barang produksi). Contohnya membangun rel kereta api atau pabrik. Investasi adalah suatu komponen dari PDB dengan rumus PDB = C + I + G + (X-M). Fungsi investasi pada aspek tersebut dibagi pada investasi non-residential (seperti pabrik dan mesin) dan investasi residential (rumah baru). Investasi adalah suatu fungsi pendapatan dan tingkat bunga, dilihat dengan kaitannya I= (Y,i). Suatu pertambahan pada pendapatan akan mendorong investasi yang lebih besar, dimana tingkat bunga yang lebih tinggi akan menurunkan minat untuk investasi sebagaimana hal tersebut akan lebih mahal dibandingkan dengan meminjam uang. Walaupun jika suatu perusahaan lain memilih untuk menggunakan dananya sendiri untuk investasi, tingkat bunga menunjukkan suatu biaya kesempatan dari investasi dana tersebut daripada meminjamkan untuk mendapatkan bunga.

Unsur Keuangan

Depresiasi

• Depresiasi atau penyusutan dalam akuntansi adalah alokasi sistematis jumlah yang dapat disusutkan dari suatu aset selama umur manfaatnya.[1]. Penerapan depresiasi akan memengaruhi laporan keuangan, termasuk penghasilan kena pajak suatu perusahaan.

• Metode yang paling mudah dan paling sering digunakan untuk menghitung penyusutan adalah metode penyusutan garis lurus (straight-line depreciation). Tapi selain itu, ada pula metode penghitungan lain yang bisa juga digunakan, seperti metode penyusutan dipercepat, penyusutan jumlah angka tahun, dan saldo menurun ganda.

• Metode Garis-lurus:

Revenue

- Arus masuk bruto dari manfaat ekonomi yang timbul dari aktivitas normal perusahaan selama satu periode, bila arus masuk itu mengakibatkan kenaikan ekuitas, yang tidak berasal dari kontribusi penanaman modal.(Ikatan Akuntansi Indonesia (1999:233)

- In general usage, revenue is income received by an organization in the form of cash or cash equivalents. Sales revenue or revenues is income received from selling goods or services over a period of time. Tax revenue is income that a government receives from taxpayers.

Biaya

- Biaya adalah semua pengorbanan yang perlu dilakukan untuk suatu proses produksi, yang dinyatakan dengan satuan uang menurut harga pasar yang berlaku, baik yang sudah terjadi maupun yang akan terjadi. Biaya terbagi menjadi dua, yaitu biaya eksplisit dan biaya implisit. Biaya eksplisit adalah biaya yang terlihat secara fisik, misalnya berupa uang. Sementara itu, yang dimaksud dengan biaya implisit adalah biaya yang tidak terlihat secara langsung, misalnya biaya kesempatan dan penyusutan barang modal.

Jenis Biaya

- Biaya variabelBiaya variabel memiliki karakteristik sebagai berikut : 1. Biaya yang jumlah totalnya akan berubah secara sebanding (proporsional) dengan perubahan volume kegiatan, semakin besar volume kegiatan semakin tinggi jumlah total biaya variabel, semakin rendah volume kegiatan semakin rendah jumlah biaya variabel.2. Pada biaya variabel, biaya satuan tidak dipengaruhi oleh volume

kegiatan, jadi biaya semakin konstan.

- Biaya tetapBiaya tetap memiliki karakteristik sebagai berikut : 1. Biaya yang jumlah totalnya tetap konstan tidak dipengaruhi oleh

perubahan volume kegiatan atau aktivitas sampai dengan tingkatan tertentu.2. Pada biaya tetap, biaya satuan (unit cost) akan berubah berbanding terbalik dengan perubahan volume penjualan, semakin tinggi volume kegiatan semakin rendah biaya satuan, semakin rendah volume kegiatan semakin tinggi biaya satuan.

Capex and Opex(owning and operating cost)

- Capital expenditures (CAPEX or capex) are expenditures creating future benefits. A capital expenditure is incurred when a business spends money either to buy fixed assets or to add to the value of an existing fixed asset with a useful life extending beyond the taxable year.

- operational expenditure (OPEX) is an ongoing cost for running a product, business, or system.[1] Its counterpart

owning and operating cost

Profit and loss

- Profit dalam Bahasa Indonesia berarti keuntungan atau laba. Profit diperoleh ketika TR (total revenue) lebih besar dari TC (total cost).

- Loss is adalah perbedaan negatif antara revenue dengan biaya produksi .

- Laba /Rugi dalam akuntansi didefinisikan sebagai selisih antara harga penjualan dengan biaya produksi. Perbedaan diantara keduanya adalah dalam hal pendefinisian biaya.

- Laba/Rugi dalam ilmu ekonomi murni didefinisikan sebagai peningkatan /penurunan kekayaan seorang investor sebagai hasil penanam modalnya, setelah dikurangi biaya-biaya yang berhubungan dengan penanaman modal tersebut (termasuk di dalamnya, biaya kesempatan).

Pajakdan

Pendapatan Negara Bukan Pajak (PNBP)- Pajak adalah iuran wajib yang dipungut oleh pemerintah dari masyarakat (wajib

pajak) untuk menutupi pengeluaran rutin negara dan biaya pembangunan tanpa balas jasa yang dapat ditunjuk secara langsung.

- Penerimaan Negara Bukan Pajak adalah seluruh penerimaan Pemerintah Pusat yang tidak berasal dari penerimaan perpajakan.Kelompok PNBP sesuai peraturan perundang-undangan meliputi:a. Penerimaan yang bersumber dari pengelolaan dana Pemerintah;b. Penerimaan dari pemanfaatan sumber daya alam;c. Penerimaan dari hasil-hasil pengelolaan kekayaan negara yang dipisahkan;d.  Penerimaan dari kegiatan pelayanan yang dilaksanakan Pemerintah;e. Penerimaan berdasarkan putusan pengadilan dan yang berasal dari pengenaan denda administrasi;f. Penerimaan lainnya yang diatur dalam Undang-undang tersendiri.

Contoh :Royalty adalah bagian produksi atau penghasilan yg dibayarkan kpd

orang yg mempunyai hak memberi izin pengusahaan (eksplorasi) minyak, dsb;

PENGELOLAHAN BIAYA (COST MANAGEMENT)

Perencanaan Sumber Daya

Perkiraan Biaya

Budgeting

Output • Keperluan Sumber Daya perkegiatan

Output • Estimasi Biaya• Data Pendukung

Output • Tindakan Koreksi• Revisi angka Anggaran

Pengendalian Biaya

Output • Budget perkegiatan• Renc. Penarikan Dana

Teknik & Metode Bersangkutan

Perkiraan BiayaA. Masukan

1. Lingkup dasar2. Jadwal proyek3. Perencanaan sumberdaya4. Daftar resiko5. Faktor lingkungan perusahaan6. Proses aset organisasi

B. Perangkat dan teknis1. Penilaian akhli2. Estimasi analog3. Estimasi parametrik4. Estimasi bottom up5. Estimasi tiga titik6. Analisa cadangan7. Kualitas biaya8. Estimasi manajemen proyek9. Analisa penawaran penjual

C. Keluaran1. Estimasi biaya aktivitas2. Estimasi dasar3. Update dokumen proyek

AnggaranA. Masukan

1. Estimasi biaya aktivitas2. Estimasi dasar3. Lingkup dasar4. Jadwal proyek5. Kalendar sumberdaya6. Kontrak7. Proses aset organisasi

B. Perangkat dan teknik1. Biaya agregasi2. Analisa sumberdaya3. Penilaian akhli4. Hubungan historis5. Rekonsiliasi batas pendanaan

C. Keluaran1. Kinerja biaya dasar2. Kebutuhan dana proyek3. Update dokumen proyek

Pengendalian BiayaA. Masukan

1. Rencana manajemen proyek2. Kebutuhan dana proyek3. Informasi kinerja kegiatan4. Proses aset organisasi

B. Perangkat dan teknik1. Manajemen nilai yang diperoleh2. Peramalan3. Melengkapi indek kinerja4. Penilaian kinerja5. Analisa varian (perbedaan)6. Manajemen proyek

C. Keluaran1. Pengukuran kinerja2. Peramalan anggaran3. Update proses aset organisasi4. Perubahan yang diperlukan5. Update rencana manajemen proyek6. Update dokumen proyek

No. Item Total

1 Revenue

2 Royalty

3 Expenses- variable cost- fix cost- depreciation

4 Earning before tax

5 Tax

6 Earning after tax

LaporanKeuangan

Laporan Laba Rugi

Aliran KasNo. Item Unit price Year Total

0 1 2 …1 Investment activity

- investment- salvage

2 Revenue

3 Royalty

4 Expenses- variable cost- fix cost- depreciation

5 Earning before tax

6 Tax

7 Earning after tax

8 depreciation

9 Net cash flow

10 Cum. cash flow

Neraca

Nilai Uang dan Waktu

BasicsYear-End ConventionUnless otherwise indicated, it is assumed that all receipts and disbursements take place at the end of the year in which they occur.

InterestMoney paid for the use of borrowed money.

Simple InterestNominal Rate of Interest

Compounded Interestthe percentage is not paid at the end of the period, then, this amount is added to the original amount (principal) to calculate the interest for the second term.

Why Interest exist?

Taking the lender’s view of point:

• Risk : Possibility that the borrower will be unable to pay

• Inflation : Money repaid in the future will “value” less• Transaction Cost : Expenses incurred in preparing the loan agreement• Opportunity Cost : Committing limited funds, a lender will be unable to

take advantage of other opportunities.• Postponement of Use: Lending money, postpones the ability of the

lender to use or purchase goods.

From the borrowers perspective …. Interest represents a cost !

Interest Formulas

r = Nominal rate of interest

i = Effective interest rate per period

• When the compounding frequency is annually: r = i

• When compounding is performed more than once per year, the effective rate (true annual rate) always exceeds the nominal annual rate: i > r– A = Series of n equal payments made at the end of

each period– i = Effective interest rate per period

Compounding Frequency

• It is also important to be able to calculate the effective interest rate (i) for the actual interest periods to be used.

• The effective interest rate can be obtained by dividing the nominal interest rate by the number of interest payments per year (m)

i = (r/m)

where: i = effective interest rate for the period r = nominal annual interest rate

ri i i i i i

!----------!----------!----------!----------!----------!----------!0 1 2 3 4 5 6

Compounding Frequency

• Compounding can be performed at any interval (common: quarterly, monthly, daily)

• When this occurs, there is a difference between nominal and effective annual interest rates

• This is determined by:

i = (1 + r/x)x – 1

where: i = effective annual interest rate r = nominal annual interest rate x = number of compounding periods per

year

ri i i i i i

!----------!----------!----------!----------!----------!----------!0 1 2 3 4 5 6

Solving Interest ProblemsStep #1: Abstracting the Problem• Interest problems based upon 5 variables:

P, F, A, i, and n• Determine which are given (normally three) and what needs to

be solved

Solving Interest Problems

Step #2: Draw a Cash Flow Diagram

C

ash

Flo

w-

+

P

A1 A2 A3 A4 A5 A6

F

Time

Receipts

Disbursements

Present Value

If you want to find the amount needed at present in order to accrue a certain amount in the future, we just solve Equation 1 for P and get:

P = F / (1+r)n (2)

Notation: (P/F,i,n) means “Find P, given F, at a rate i for n periods” This notation is often shortened to P/F

Future Value

The compound interest relationship may generally be expressed as:

F = P (1+r)n (1)

Where F = Future sum of moneyP = Present sum of moneyr = Nominal rate of interestn = number of interest periods

Notation: (F/P,i,n) means “Find F, given P, at a rate i for n periods”

This notation is often shortened to F/P

Annuities

• Uniform series are known as the equal annual payments made to an interest bearing account for a specified number of periods to obtain a future amount.

C

ash

Flo

w-

+

P

A1 A2 A3 A4 A5 A6

F

Time

Annuities Formula

• The future value (F) of a series of payments (A) made during (n) periods to an account that yields (i) interest:

F = A [ (1+i)n – 1 ] (5) i

Where F = Future sum of moneyn = number of interest periodsA = Series of n equal payments made at the end of

each periodi = Effective interest rate per period

• Derivation of this formula can be found in most engineering economics texts & study guides

Notation: (F/A,i,n) or if using tables F = A (F/A,i,n)

Sinking Fund

• We can also get the corresponding value of an annuity (A) during (n) periods to an account that yields (i) interest to be able to get the future value (F) :

Solving for A: A = i F / [ (1+i)n – 1 ] (6)

Notation : A = F (A/F,i,n)

Present Worth of an Uniform Series

• Sometimes it is required to estimate the present value (P) of a series of equal payments (A) during (n) periods considering an interest rate (i)

From Eq. 1 and 5

P = A [ (1+i)n – 1 ] (7) i (1+i)n

Notation: P = A (P/A,i,n)

Uniform Series Capital Recovery

• This is the corresponding scenario where it is required to estimate the value of a series of equal payments (A) that will be received in the future during (n) periods considering an interest rate (i) and are equivalent to the present value of an investment (P)

Solving Eq. 7 for A

A = i P (1+i)n (8) (1+i)n -1

Notation: A = P (A/P,i,n)

Gradient Series

• Thus far, most of the course discussion has focused on uniform-series problems

• A great many investment problems in the real world involve the analysis of unequal cash flow series and can not be solved with the annuity formulas previously introduced

• As such, independent and variable cash flows can only be analyzed through the repetitive application of single payment equations

• Mathematical solutions have been developed, however, for two special types of unequal cash flows:

• Uniform Gradient Series• Geometric Gradient Series

Uniform Gradient Series

• A Uniform Gradient Series (G) exists when cash flows either increase or decrease by a fixed amount in successive periods.

• In such cases, the annual cash flow consists of two components: (1) a constant amount (A1) equal to the cash flow in the first period(2) a variable amount (A2) equal to (n-1)G

As such: AT = (A1) + (A2)

A2 = G [(1/i) – (n/i)(A/F,i,n)]

where: [(1/i) – (n/i)(A/F,i,n)] is called the uniform gradient factorand is written as (A/G,i,n)

Therefore: AT = (A1) + G(A/G,i,n))

Uniform Gradient Series

Example: An engineer is planning for a 15 year retirement. In order to supplement his pension and offset the anticipated effects of inflation and increased taxes, he intends to withdraw $5,000 at the end of the first year, and to increase the withdrawal by $1,000 at the end of each successive year. How much money must the engineer have in this account at the start of his retirement, if the money earns 6% per year, compounded annually?

Want to Find: PGiven: A1, G, i, and n

T = 0

P

1

$5000

$6000

2 14 15

$18000

$19000

$7000

$8000

3 4

Uniform Gradient Series

Example:

AT = (A1) + G(A/G,i,n)

A2 = G(A/G,i,n) = $1000 (A/G,6%,15) = $1000 (5.926) = $5926

AT = $5000 + $5926 = $10,926

P = AT (P/A,i,n) = $10,926 (P/A,6%,15) = $10,926 (9.7123) = $106,120

Geometric Gradient Series

• Since receipts and expenditures rarely increase or decrease every period by a fixed amount, Uniform Gradient Series (G) problems have limited applicability

• With Geometric Gradients, the increase or decrease in cash flows between periods is not a constant amount but a constant percentage of the cash flow in the preceding period.

• Like Uniform Gradients, Geometric Gradients limited applicability but are sometimes used to account for inflationary cost increases

AK = A (1 + j)K-1

Where:j equals the percent change in the cash flow between periods

A is the cash flow in the initial periodAK is the cash flow in any subsequent period

Cash flow analysis

As we have addressed the fundamental concepts associated with engineering economics and cash flows, is now time to convert these estimates into measures of desirability as a tool for investment decisions.

We will use the following criteria:

– Present & Future Value– Annual Value– Benefit / Cost Ratio– Payback period– Internal Rate of Return– Variations of IRR

Present Value

The Present value or present worth method of evaluating projects is a widely used technique. The Present Value represents an amount of money at time zero representing the discounted cash flows for the project.

T = 0 +/- Cash Flows

PV

Net Present Value (NPV)

The Net Present Value of an investment it is simply the difference between cash outflows and cash inflows on a present value basis.

In this context, the discount rate equals the minimum rate of return for the investment

Where:

NPV = ∑ Present Value (Cash Benefits) - ∑ Present Value (Cash Costs)

Future Value

The future value method evaluates a project based upon the basis of how much money will be accumulated at some future point in time. This is just the reverse of the present value concept.

T = 0 +/- Cash Flows

FV

Annual Value

• Sometimes it is more convenient to evaluate a project in terms of its annual value or cost. For example, it may be easier to evaluate specific components of an investment or individual pieces of equipment based upon their annual costs as the data may be more readily available for analysis.

Benefit/Cost Ratio

• The benefit/cost ratio is also called the profitability index and is defined as the ratio of the sum of the present value of future benefits to the sum of the present value of the future capital expenditures and costs.

B/C Ratio Example

• Present value cash inflows Project A Project B

$500,000 $100,000

• Present value cash outflows (costs)$300,000 $ 50,000

• Net Present Value$200,000 $ 50,000

• Benefit/Cost Ratio 1.67 2.0

Payback PeriodThis is one of the most common evaluation criteria used by engineering and resource companies.

The Payback Period is simply the number of years required for the cash income from a project to return the initial cash investment in the project.

The investment decision criteria for this technique suggests that if the calculated payback is less than some maximum value acceptable to the company, the proposal is accepted.

The following example illustrates five investment proposals having identical capital investment requirements but differing expected annual cash flows and lives.

Internal Rate of Return

Internal Rate of Return refers to the interest rate that the investor will receive on the investment principal

IRR is defined as that interest rate (r) which equates the sum of the present value of cash inflows with the sum of the present value of cash outflows for a project. This is the same as defining the IRR as that rate which satisfies each of the following expressions:

∑ PV cash inflows - ∑ PV cash outflows = 0 NPV = 0 for r

∑ PV cash inflows = ∑ PV cash outflows

In general, the calculation procedure involves a trial-and-error solution unless the annual cash flows subsequent to the investment take the form of an annuity. The following examples illustrate the calculation procedures for determining the internal rate of return.

IRR Analysis

The acceptance or rejection of a project based on the IRR criterion is made by comparing the calculated rate with the required rate of return, or cutoff rate established by the firm. If the IRR exceeds the required rate the project should be accepted; if not, it should be rejected.

If the required rate of return is the return investors expect the organization to earn on new projects, then accepting a project with an IRR greater than the required rate should result in an increase of the firms value.

NPV and IRR

What is in the Discount Rate?

According to practice, the discount rate has to cover the following items:– Opportunity Costs– Transaction Costs– Compensate for Risk– Cover anticipated Inflation

Some of these items can be accounted for in other financial analysis methods and do not have to be address in the discount rate itself.

Financial Cost of Capital

The financial cost of capital is based on the assumption that financing is unlimited and the company can always pay off loans or buy stock back, so the financial cost of capital rate of return is the average cost of debt after tax (remember interest is tax deductible) and the cost of equity (what the share holders desired return is using the capital asset pricing model CAPM)

Marginal Weighted Average Cost of Capital

The cost of capital is the minimum rate of return that a firm needs to earn on new investments to maintain the existing value of it’s shares of common stock. To determine the cost of capital a weighted average of all sources of capital must be evaluated. The weighted average should include a mix of debt and equity on an after tax basis.

Hurdle Rate

The hurdle rate is a common term used by companies as an expression of their rate of return used for financial analysis.

This is generally a higher number than the FCC (finance cost of capital) rate as they add an imposed “economic hurdle” for the project to overcome. This helps companies express that a project that just achieves a FCC rate of return does not add real value to the company.

Opportunity Cost of Capital

The opportunity cost of capital is the most common method of establishing the investor’s minimum rate of return.

This is based upon the expected returns that the company will generate in the next 1 to 15 years. It is the average return that investors expect to make over the next few years expressed as a compound interest.

Mutual Exclusive # umur sama

# umur tidak sama

FxAx Ax Ax

X = !-------------!-------------!------------!0 1 2 3Px

NPV(x) = ..?..IRR(x) = ..?..

FyAy Ay Ay

Y =!-------------!-------------!------------!

0 1 2 3Py

NPV(y) = ..?..IRR(y) = ..?..

# umur sama

Mutual Exclusive umur tidak sama

Fx

Ax Ax Ax Ax AxX = !--------------!------------!-------------!-------------!------------!

0 1 2 3 4 5Px

FyAy Ay Ay

Y = !--------------!------------!-------------!0 1 2 3Py

- Fy FxAx-Ay Ax-Ay Ax-Ay Ax Ax

X – Y = !--------------!------------!-------------!-------------!------------!0 1 2 3 4 5Px-Py

NPV(x) = ..?.. NPV(y) = ..?.. NPV(x-y) = ..?..IRR(x) = ..?.. IRR(y) = ..?.. IRR(x-y) = ..?..

Mutual Exclusive umur tidak sama

Fx

Ax Ax Ax Ax AxX = !--------------!---------------!---------------!---------------!--------------!

0 1 2 3 4 5Px

FyAy Ay Ay

Y = !--------------!---------------!---------------!0 1 2 3Py

Fy + Fx(mod)Ax Ax Ax - -

X (mod) = !--------------!---------------!---------------!--------------!---------------!0 1 2 3 4 5Px

NPV(x) = ..?.. NPV(y) = ..?.. NPV(mod) = ..?..IRR(x) = ..?.. IRR(y) = ..?.. IRR(mod) = ..?..

Mutual Exclusive umur tidak sama

Fx

Ax Ax Ax Ax AxX = !--------------!---------------!---------------!---------------!--------------!0 1 2 3 4 5Px FyAy Ay AyY = !--------------!---------------!---------------!0 1 2 3PyFy F(mod)Ay Ay Ay A(mod) A(mod)Y(mod) = !--------------!---------------!---------------!--------------!---------------!0 1 2 3 4 5Py

NPV(x) = ..?.. NPV(y) = ..?.. NPV(mod) = ..?..IRR(x) = ..?.. IRR(y) = ..?.. IRR(mod) = ..?..

Mutual Exclusive umur tidak sama

FxAxAxAx

X = !--------------!---------------!---------------!0 1 2 3Px FyAyAy

Y = !--------------!---------------!0 1 2PyFx FxAx Ax Ax Ax Ax Ax

X(mod) = !----------------------!---------------------!--------------------!--------------------!--------------------!---------------------!0 1 2 3 4 5 6Px Px

Fy Fy FyAy Ay Ay Ay Ay Ay

Y(mod) = !----------------------!---------------------!--------------------!--------------------!--------------------!---------------------!0 1 2 3 4 5 6Py Py Py

NPV(x) = ..?.. NPV(y) = ..?.. NPV(Xmod) = ..?.. NPV(Ymod) = ..?..IRR(x) = ..?.. IRR(y) = ..?.. IRR(Xmod) = ..?.. IRR(Xmod) = ..?..

Lease versus Borrow and Purchase

The following example shows how to use these steps. A trucking contractor has two choices:

(1) buy a new tri-axle dump truck or

(2) lease it for three years. The dump truck has a useful life of five years and costs $100,000. The Helpful Bank is willing to loan the contractor $88,000 at 7 percent interest and requires a down payment of $12,000 and annual payments of $20,891, which are due at the end of each of the next five years.

Aplikasi

16-59

Analisa Resiko

Variabel RangePesimis perkiraan Optimis

Investasi + # -

Penjualan - # +

Biaya variabel + # -

Sensitivity Analysis

Break Even Point

NPV = (- Po) + PW ( N (sales/unit – variabel cost/unit) – (fix cost + depresiasi))

Po = PW(i,n) (N (sales/unit – variabel cost/unit) – (fix cost + depresiasi))

N = jumlah unit

Decision Trees

NPV=0

Don’t test

Test (Invest $200,000)

Success

Failure

Pursue project NPV=$2million

Stop projectNPV=0

Real Options

1. Option to expand2. Option to abandon3. Timing option4. Flexible production facilities

Thank You

Reference

Hugh MillerColorado School of MinesMining Engineering DepartmentFall 2007