Upload
fikri-farobi
View
228
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Description about IRR and Payback Period
Citation preview
Module 6: Internal Rate of Return and Payback Period
SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.
Outline Module 6 Rate of Return Internal Rate of Return (IRR) Cash Flow with Single Rate of Return Cash Flow with Multiple Rate of Return Payback Period Discounted Payback Period
Muhamad Abduh, Ph.D.6-2 SI-4251 Ekonomi Teknik
Rate of Return Rate of Return (ROR) is the rate of interest
paid on all unpaid balance of borrowed money, or the rate of interest earned on the unrecovered balance of an investment so that the final payment or receipt brings the balance to zero with interest considered
Internal Rate of Return (IRR) is the interest rate that causes the equivalent receipts of a cash flow equal to the equivalent payments of a cash flow
Muhamad Abduh, Ph.D.6-3 SI-4251 Ekonomi Teknik
i* PR = PP
EUAWR = EUAWP
FR = FP
PR – PP = 0FR – FP = 0EUAWR – EUAWP = 0
Finding Internal Rate of Return1. Draw cash flow diagram2. Convert all receipts into present, future or EUAW3. Convert all payments into present, future or EUAW4. Subtract (3) from (2) and set it equal to zero find i*5. Find i* that satisfies (4) by trial and error interpolation
Muhamad Abduh, Ph.D.6-4 SI-4251 Ekonomi Teknik
PR= I1(P/F, i*, 22) + SV(P/F, i*, 36)
0 1 2 3
A1
SVI1P O1
PP= P + A1(P/A, i*, 36) + O1(P/F, i*, 8)
PR - PP = I1(P/F, i*, 22) + SV(P/F, i*, 36) – [P + A1(P/A, i*, 36) + O1(P/F, i*, 8)] = 0
Rate of Return The relationship between Rate of Return and the Present Worth
Amount can be graphically describe as follows:
Cash flow shown above assures a single rate of return that:
Muhamad Abduh, Ph.D.6-5 SI-4251 Ekonomi Teknik
interest rate, i
Present worth,
PW
0i*
PW (i) > 0 for i < i*PW (i) = 0 for i = i*PW (i) < 0 for i > i*
Cash Flow with Single Rate of ReturnFor a cash flow will have a single rate of return, if satisfies the following conditions:Test # 1:1.F0 < 0
(the first non-zero cash is a disbursement)
2.One change in sign in the sequence F0, F1, F2, … Fn (the cash flow has an initial disbursement or a series of disbursement followed by a series of receipts)
3.PW(0) > 0 (the sum of all the receipts is greater than the sum of all the disbursements)
Test # 2:1.F0 < 0
(the first non-zero cash is a disbursement)
2.Find rate of return, i*, for the cash flow; for unknown i*, total unrecovered balance, Ut < 0 for t = 0, 1, 2, 3, … n-1
Muhamad Abduh, Ph.D.6-6 SI-4251 Ekonomi Teknik
Cash Flow with Multiple Rate of ReturnFor a cash flow will have a multiple rate of return, if not satisfies Test #1 Test #2
Muhamad Abduh, Ph.D.6-7 SI-4251 Ekonomi Teknik
interest rate, i
Present worth,
PW
0i* i*
Payback Period In business and industry it is common to evaluate alternatives (assets) in terms of
their payback or payout period. Payback without interest the length of time required to recover the first cost of
an investment from the net cash flow produce by that investment for interest rate of zero
This method has disadvantages as it fails to consider: the time value of money the consequences of the investment following the payback period
Payback with interest or discounted payback period this method determines the length of time required until the investment’s equivalent receipts exceed the equivalent capital outlays
Muhamad Abduh, Ph.D.6-8 SI-4251 Ekonomi Teknik
'n
t
tt iF
0
01
n
ttF
0
0
n’ = the smallest value that satisfies the equation
Payback Period without InterestExample:Three alternatives of investment are being considered without interest:
Muhamad Abduh, Ph.D.6-9 SI-4251 Ekonomi Teknik
end of year
A B C
0 - 1.000.000,- - 1.000.000,- - 700.000,-1 500.000,- 200.000,- - 300.000,-2 300.000,- 300.000,- 500.000,-3 200.000,- 500.000,- 500.000,-4 200.000,- 1.000.000,- 0,-5 200.000,- 2.000.000,- 0,-6 200.000,- 4.000.000,- 0,-
Present worth, i = 0
PW(i)A = 600.000,-
PW(i)B = 7.000.000,-
PW(i)C = 0,-
Payback period
3 years 3 years 3 years
Discounted Payback PeriodExample:Alternative A is being considered at the rate of return 15%
Muhamad Abduh, Ph.D.6-10 SI-4251 Ekonomi Teknik
end of year
A
0 - 1.000.000,-1 500.000,-2 300.000,-3 200.000,-4 200.000,-5 200.000,-6 200.000,-
Ft = - 1M + 500K(P/F, 15%, 1) + 300K(P/F, 15%, 2) + 200K(P/F, 15%, 3) + 200K(P/F, 15%, 4) + 200K(P/F, 15%, 5) > 0
Project Balance Evaluation of a proposed project is often done by analyzing the project balance. A project balance describes the equivalent of loss or profit of the project cash flow
as a function of time. At any given time, a project balance can be calculated as:
Visual description of a project balance project balance diagram Four important characteristics of project balance diagram are:
The net future worth of investment The time when the equivalent cash flow switch from negative to non-negative, or vice
versa The net equivalent cash flow exposed to risk of loss (the area where PB(i) is negative) The net equivalent cash flow earned (the area where the PB(i) is positive)
Muhamad Abduh, Ph.D.6-11 SI-4251 Ekonomi Teknik
1
0
)1()(
TT
ttT iFiPB
Project Balance
Muhamad Abduh, Ph.D.6-12 SI-4251 Ekonomi Teknik
0 1 2 3 4 5
10M
1M5M
8M
6M
3M
+-
PB(20)1= -11M
PB(20)0 = -10M
PB(20)2= -8.2M
PB(20)3= -1.84M
PB(20)4= 3.79M
PB(20)5= 7.55M
Project cash flow @ 20% discount rate
Homework #61. Work for alternative B and C of the example
(slide #8). Determine the discounted payback period for each alternative and suggest your selection.
2. For the same problem investment (#1), calculate the project balance for each alternative, draw the project balance diagram, and identify the future worth and exposure to risk of loss
Muhamad Abduh, Ph.D.6-13 SI-4251 Ekonomi Teknik