EKONOMI REKAYASAPERTEMUAN II

INTERNAL RATE OF RETURN (IRR)

Oleh :Arwan Apriyono

Paulus Setyo Nugroho

PROGRAM STUDI TEKNIK SIPIL JURUSAN TEKNIK FAKULTAS SAINS DAN TEKNIK UNSOED

TAHUN 2011

INTRODUCTION

Decision making methods- NPV/NPW- ROR/IRR

- B/C

Fundamental knowledge

-Value of money (PV, FV, AV)-Interest (Rate , Compound)-Cost and Benefit-Cast flow diagram

Infuence Factor-Inflation & Deflation-Tax-Depreciation

FinansialDecision Making

the internal rate of return is the interest rate at which the benefits are equivalent to the costs or the present worth (PW) is 0

PW of benefits - PW of costs = 0

PW of benefits/PW of Cost = 1

Net Present Worth = 0

EUAB- EUAC=0

PW of costs = PW of benefits

Definition

1. Instead of lending money, we might invest $8200 in a machine tool with a 5-year useful life and an equivalent uniform annual benefit of $2000.

An appropriate question is,What rate of return would we receive on this investment?

Example

$8200

$2000

Then look at the compound interest tables for the value of i where (PIA, i, 5) = 4.1;

If no tabulated value of i gives this value, we will then find values on either side of the desired value (4.1) and interpolate to find the IRR.

Example

In this example, no interpolation is needed because the internal rate of return is exactly 7%.

If IRR is not exactly the value (7%), we need to take interpolation linear as example bellow

Example

With i = 6% (P/A,i,5) = 4.212

With i = 8% (P/A,i,5) = 3.993

Example

8 %

6 %

3.993 4.2124.1

?

2. An investment resulted in the following cash flow. Compute the rate of return.

Example

$700

$250$175

$325

$100

In this situation,we have two different interest factors in the equation.We wilL not be able to solve it as easily as Example 1. Since there is no convenient direct method of solution,we will solve the equation by trial and error.

Example

Try i = 5% first

EUAB- EUAC = 0 100 + 75(A/G, 5%, 4) - 700 (A/P, 5%, 4) = 0 100 + 75(1.439) – 700 (0.2820) = 0 EUAB – EUAC = 208 -197 = + 11

The EUAC is too low. If the interest rate is increased, EUAC will increase. Try i =8%:

Example

i = 8%

EUAB- EUAC = 0 100 + 75(A/G, 8%, 4) - 700 (A/P, 8%, 4) = 0 100 + 75(1.404) – 700 (0.3049) = 0 EUAB – EUAC = 205 -211 = - 6

This time the EUAC is too large. We see that the true rate of return is between 5% and 8%. Try i =7%:

Example

i = 7%

EUAB- EUAC = 0 100 + 75(A/G, 7%, 4) - 700 (A/P, 7%, 4) = 0 100 + 75(1.416) – 700 (0.2952) = 0 EUAB – EUAC = 206 -206 = 0

The IRR is 7%

Example

Rate of return analysis is probably the most frequently used exact analysis technique in industry.

The advantage to rate of return analysis is no interest rate introduced into the calculation, instead we compute a rate of return from the cash flow. Whereas In both present worth and annual cash flow calculations, one must select an interest rate for use in the calculations and this may be a difficult and controversial item.

To decide how to proceed, the calculated rate of return is compared with a preselected minimum attractive rate of return, or simply MARR. This is the same value of i used for present worth and annual cash flow analysis. If the value of ROR is higher than the MARR, then the project is good.

Advantage of ROR

When there are two alternatives, rate of return analysis is performed by computing the incremental rate of return (DIRR) on the difference between the alternatives.

Since we want to look at increments of investment the cash flow for the difference between the alternatives is computed by taking the higher initial-cost alternative minus the lower initial cost alternative.

Two-Alternative Situation :DIRR ≥ MARR Choose the higher-cost alternativeDIRR < MARR Choose the lower-cost alternative

Incremental Analysis

STEP OF INCREMENTAL ANALYSIS

Step 1: Set up the cash flow of all alternatives in ascending order of initial investment.

Step 2: Discard all alternatives that have an ROR less than the MARR. This step can be ignored but performing it will save time on the rest of the steps.

Step 3: Construct the cash flow of the difference of alternatives two by two, starting from the two with the lowest ROR. Always subtract the one with lowest initial investment from the one with the higher initial investment. A check on this step is that the cash flow at time zero of the differential should always be negative.

If the ROR of the differential is higher than the MARR, the alternative with the higher initial investment is preferred, otherwise the one with the lower initial investment is preferred.

Next we compare the preferred alternative with the next alternative on the list in the same manner.

Incremental Analysis

1. An investor is offered two investment opportunities. Project A is an investment in frozen yogurt equipment that requires an initial investment of $40,000 with a life of three years. Its annual operating costs and annual incomes are presented in table A. The equipment can be sold at the end of year 3 at a resale value of $5,000.

Sample Incremental

Analysis

The second opportunity is purchase of printing equipment with an initial investment of $200,000. Annual operating costs and annual incomes are presented in table B. The equipment can be sold at the end of year 5 at a resale value of $20,000.

If the MARR for this investor is 10%, which project should he invest in? Ignore tax and depreciation.

Sample Incremental

Analysis

Year A B B-A

0 -40 k -40 k -200 k -200 k -160 k

1 25 k 10 k 110 k 0 0

-15 k - 100 k

2 33 k 15 k 135 k 25 k 10 k

-18 k -110 k

3 45 k + 5 k 30 k 170 k 55 k 25 k

-20 k - 115 k

4 210 k 90 k 90 k

-120 k

5 230k+20 k 120 k 120 k

-130 k

Langkah pengerjaan:1. Hitung IRR project A; apakah layak? Lebih dari MARR ?2. Hitung IRR project B; apakah layak? Lebih dari MARR ?3. Tuliskan incremental analysis dari project yang layak

Gambarkan CFD dari tabel di atas4. Hitung IRR of incremental CFD; IRR > MARR ? Jika ya ambil yang investasi lebih besar, jika IRR < MARR ambil yang investasi lebih kecil

STEP 1 Calculate ROR of alternative A

NPW = -40000+10000(P/F,i*,1)+15000(P/F,i*,2)+30000(P/F,i*,3)

By trial and error, i* = 14.7% i* > 10% (Acceptable)

Sample Incremental

Analysis

STEP 2 Calculate ROR of Alternative B

Calculating ROR as we did in the case of project A we obtain ROR=11% > 10 % (acceptable)

Sample Incremental

Analysis

STEP 3 Take Incremental Analysis

We have to use the incremental cash flow diagram, i.e.,. B-A. In calculating ROR, we do not have to equalize the lives. That makes it easier. The incremental cash flow is

Sample Incremental

Analysis

Year Alternative A Alternative B B - A

0 40000 200000 160000

1 10000 10000 0

2 15000 25000 10000

3 30000 55000 25000

4 0 90000 90000

5 0 120000 120000

STEP 4 Calculate ROR of Incremental Cash Flow Diagram

The ROR for this incremental cash flow is calculated as follows:

By trial and error, i* = 10.5. Therefore, i*>10%; hence, project B is preferred.

This means it is better to invest all the available money ($200,000) in project B at 10.5% rather than invest $40,000 in project A and the rest at MARR of 10%.

Sample Incremental

Analysis