Transcript INTERNAL RATE OF RETURN

How Time and Interest
Affect Money
Ir. Haery Sihombing MT.
Pensyarah Pelawat
Fakulti Kejuruteraan Pembuatan
Universiti Teknologi Malaysia Melaka
BASIC OF A COUNTING
RELATED TO COST
INTRODUCTION
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 COST ACCOUNTING
Accounting is the collection and aggregation of
information for decision maker- including
managers, investor, regulators, lenders, and the
public.
Accounting system affect behavior and
management and have affects across
departments, organizations, and even countries.
Information contained within an accounting system has the power to
influence actions. Accounting information systems are particularly
strong behavioral drivers within the context of a corporation – where
profits and the bottom line are daily concerns.
COST ACCOUNTING
There are three type of accounting systems
1. NATIONAL ACCOUNTING SYSTEMS
National accounts are national income and production accounts,
such Gross National Product (GNP) and Gross Domestic Product
(GDP) which aim to measure and track an economy’s
contribution to the well-being of its inhabitants. National income
accounts show the national demand or goods and services and are
used to track and measure economic growth.
Conventional economic thinking has assumed that the increases in goods and
services produced domestically (GDP) and national income (GNP) are adequate
yardstick to economic health
Example:
The world bank uses per capita GNP as a major criterion for classifying national
economies
COST ACCOUNTING
1. NATIONAL ACCOUNTING SYSTEMS
COST ACCOUNTING
2. FINANCIAL ACCOUNTING SYSTEMS
Financial accounts, such as balance sheets and income
statements are used to keep track of business incomes and
outflows. These financial reports are for use by persons outside
the firm – for example: lenders or investors.
There are relevant to the enterprise as a whole and are generally subject to strict
government rules
The most common financial accounting reports are for external use by are the
financial statements in a firm’s annual report to shareholders. In the United States
and most developed countries, these reports conform to generally accepted
accounting principles developed predominantly by the Financial Accounting
Standards Board (FASB) and the Securities and Exchange Commission (SEC)
COST ACCOUNTING
The overall objective of a firm’s financial
accounting statements
1. The overall objective of a fir’s financial accounting statements are:
2. To provide information useful for making rational investment and credit
decisions
3. To allow investors and creditors to assess the amount, timing, and
uncertainty of cash flows
4. To provide information about the economic resources of a firm and the
claims on those resources
5. To provide information about a firm’s operating performance during
period
6. To provide information on how a firm obtains and uses money and other
financial resources.
7. To provide information on how management ha discharges its stewardship
responsibility to owners and the public.
COST ACCOUNTING
Type of Financial Accounting Statements
COST ACCOUNTING
3. MANAGEMENT or COST ACCOUNTING SYSTEMS
and CAPITAL BUDGETING
Management or cost accounting systems are part of an
enterprise’s information system and refer to the internal
cost tracking and allocation systems to track costs and
expenditures. These are internal rather than external
accounting systems. There are no fixed rules governing how
an entity should keep track of cash flows internally,
although there are many formal methods available for users.
Capital budgeting is basically a form of predictive cost
accounting over a set time frame which is used to analyze
the costs of alternative projects or expenditures over the
specified period of time
COST ACCOUNTING





The main objectives of managerial/cost
accounting are (Hilton, 1998):
Providing managers with information for decision making
and planning.
Assisting managers in directing and controlling operations.
Motivating managers towards the organization’s goals.
Measuring the performance of managers and sub-units
within the organization.
COST ACCOUNTING
INTRODUCTION

TIME VALUE OF MONEY :
THE ECONOMIC VALUE OF A SUM
DEPENDS ON WHEN IT IS RECEIVED.
Because money has both EARNING as well as
PURCHASING POWER over time (it can be
put to work, earning more money for its owner)
A Ringgit received today has a greater value
than Ringgit received at some future time
1.
Foundations: Overview
1. F/P and P/F Factors
2. P/A and A/P Factors
3. F/A and A/F Factors
4. Interpolate Factor Values
5. Calculate i
6. Calculate “n”
7. Spreadsheets
F/P and P/F Factors
Section 1
1 Basic Derivations: F/P factor

F/P Factor To find F given P
Fn
To Find F given P
………….
n
P0
Compound forward in time
1 Basic Derivations: F/P factor
= P(1+i)

= F1(1+i)…..but:

= P(1+i)(1+i) = P(1+i)2

=F2(1+i) =P(1+i)2 (1+i)
= P(1+i)3
In general:

F1
F2
F2
F3
Fn = P(1+i)n
Fn = P(F/P,i%,n)
1 Present Worth Factor from F/P




Since Fn = P(1+i)n
We solve for P in terms of FN
P = F{ 1/ (1+i)n} = F(1+i)-n
Thus:
P = F(P/F,i%,n) where
(P/F,i%,n) = (1+i)-n
Thus, the two factors are:
1. F = P(1+i)n finds the future worth of P;
2. P = F(1+i)-n finds the present worth from F
1 P/F factor –Discounting back in time

Discounting back from the future
Fn
………….
P
n
P/F factor brings a single
future sum back to a specific
point in time.
P/A and A/P Factors
Section 2
2 Example- F/P Analysis
Example: P= $1,000;n=3;i=10%
 What is the future value, F?

F = ??
0
P=$1,000
1
2
3
i=10%/year
F3 = $1,000[F/P,10%,3] = $1,000[1.10]3
= $1,000[1.3310] = $1,331.00
2 Example – P/F Analysis

Assume F = $100,000, 9 years from now. What is
the present worth of this amount now if i =15%?
F9 = $100,000
i = 15%/yr
0
1
2
3
…………
8
9
P= ??
P0 = $100,000(P/F, 15%,9) = $100,000(1/(1.15)9)
= $100,000(0.2843) = $28,430 at time t = 0
2 Uniform Series Present Worth and
Capital Recovery Factors
Annuity Cash Flow

P = ??
1
2
3
…………..
..
0
$A per period
..
n-1
n
2 Uniform Series Present Worth and
Capital Recovery Factors

Desire an expression for the present
worth – P of a stream of equal, end of
period cash flows - A
P = ??
0
1
2
3
n-1
A = given
n
2 Uniform Series Present Worth and
Capital Recovery Factors

Write a Present worth expression
 1
1
1
1 
P  A

 .. 

1
2
n 1
n
(1  i)
(1  i) 
 (1  i) (1  i)
[1]
Term inside the brackets is a geometric progression.
Mult. This equation by 1/(1+i) to yield a second equation
2 Uniform Series Present Worth and
Capital Recovery Factors

The second equation
 1
P
1
1
1 
 A

 .. 

2
3
n
n 1 
1 i
(1  i) (1  i) 
 (1  i) (1  i)
[2]
To isolate an expression for P in terms of A, subtract
Eq [1] from Eq. [2]. Note that numerous terms will
drop out.
2 Uniform Series Present Worth and
Capital Recovery Factors

Setting up the subtraction
 1
P
1
1
1
1 
 A

 ...
2
3
4
n
n 1 
(1  i)
(1

i
)
(1

i
)
(1

i
)
(1

i
)
(1

i
)


[2]
 1
1
1
1 
- P  A  (1  i)1  (1  i)2  ..  (1  i)n1  (1  i)n 
[1]
=
 1
i
1 
P  A


n 1
1 i
(1  i) 
 (1  i)
[3]
2 Uniform Series Present Worth and
Capital Recovery Factors

Simplifying Eq. [3] further
 1
i
1 
P  A


n 1
1 i
(1  i) 
 (1  i)

A 1
P 
 1
n 1
i  (1  i)

 (1  i ) n  1 
P  A
for i  0
n 
 i (1  i ) 
F/A and A/F Factors
Section 3
3 F/A and A/F Derivations
$F
Annuity Cash Flow

…………..
0
$A per period
N
Find $A given the
Future amt. - $F
3 Sinking Fund and Series Compound
amount factors (A/F and F/A)



Take advantage of what we already have
Recall:
Also:
 1 
PF
n
 (1  i) 
 i (1  i ) n 
A P

n
 (1  i )  1 
Substitute “P” and
simplify!
3 F/A and A/F Derivations
$F
Annuity Cash Flow

…………..
0
$A per period
N
Find $F given the $A
amounts
3 Example -1



Formosa Plastics has major fabrication
plants in Texas and Hong Kong.
It is desired to know the future worth of
$1,000,000 invested at the end of each year
for 8 years, starting one year from now.
The interest rate is assumed to be 14% per
year.
3 Example-1
•A = $1,000,000/yr; n = 8 yrs, i = 14%/yr
•F8 = ??
3 Example-1
 Solution:
The cash flow diagram shows the annual
payments starting at the end of year 1 and
ending in the year the future worth is desired.
Cash flows are indicated in $1000 units. The F
value in 8 years is
F = l000(F/A,14%,8) = 1000( 13.23218)
= $13,232.80 = 13.232 million 8 years
from now.
3 Example-1

How much money must Carol deposit every year
starting, l year from now at 5.5% per year in order
to accumulate $6000 seven years from now?
3 Example -2

Solution

The cash How diagram from Carol's
perspective fits the A/F factor.

A= $6000 (A/F,5.5%,7) =
6000(0.12096) = $725.76 per year
The A/F factor Value 0f 0.12096 was
computed using the A/F factor formula

Interpolation in Interest Tables
Section 4
4
Interpolation of Factors
•
All texts on Engineering economy will provide
tabulated values of the various interest factors
usually at the end of the text in an appendix
•
Refer to the back of your text for those tables.
4 Interpolation of Factors
•
Typical Format for Tabulated Interest Tables
4 Interpolation (Estimation Process)
•
At times, a set of interest tables may not have
the exact interest factor needed for an analysis
•
One may be forced to interpolate between two
tabulated values
•
Linear Interpolation is not exact because:
•
The functional relationships of the interest
factors are non-linear functions
•
Hence from 2-5% error may be present with
interpolation.
4 An Example
•
Assume you need the value of the A/P factor
for i = 7.3% and n = 10 years.
•
7.3% is most likely not a tabulated value in
most interest tables
•
So, one must work with i = 7% and i = 8% for
n fixed at 10
•
Proceed as follows:
4 Basic Setup for Interpolation
•Work with the following basic relationships
4 i = 7.3% using the A/P factor
•
For 7% we would observe:
N
10
COMPOUND
PRESENT
SINKING
COMPOUND
CAPITAL
AMT. FACTOR
WORTH
FUND
AMOUNT
RECOVERY
F/P
P/F
A/F
F/A
A/P
1.9672
0.5083
0.0724
13.8164
0.14238
A/P,7%,10) = 0.14238
4 i = 7.3% using the A/P factor
•
For i = 8% we observe:
N
10
COMPOUND
PRESENT
SINKING
COMPOUND
CAPITAL
AMT. FACTOR
WORTH
FUND
AMOUNT
RECOVERY
F/P
P/F
A/F
F/A
A/P
2.1589
0.4632
0.0690
14.4866
0.14903
(A/P,8%,10) = 0.14903
4 Estimating for i = 7.3%
•
Form the following relationships
4 Final Estimated Factor Value
•
Observe for i increasing from 7% to 8% the
A/P factors also increases.
•
One then adds the estimated increment to the
7% known value to yield:
4. The Exact Value for 7.3%
•
Using a previously programmed spreadsheet
model the exact value for 7.3% is:
Determination of Unknown
Number of Interest
Section 5
5 When the i – rate is unknown
• A class of problems may deal with all of
the parameters know except the interest
rate.
•For many application-type problems, this
can become a difficult task
•Termed, “rate of return analysis”
•In some cases:
•i can easily be determined
•In others, trial and error must be used
5 Example: i unknown
• Assume on can invest $3000 now in a
venture in anticipation of gaining $5,000
in five (5) years.
•If these amounts are accurate, what
interest rate equates these two cash
flows?
5 Example: i unknown
• The Cash Flow Diagram is…
$5,000
0
$3,000
1
2
3
4
5
•F = P(1+i)n
•5,000 = 3,000(1+i)5
•(1+i)5 = 5,000/3000 =
1.6667
5 Example: i unknown
• Solution:
0
$3,000
1
$5,000
2
3
4
5
•(1+i)5 = 5,000/3000 =
1.6667
•(1+i) = 1.66670.20
•i = 1.1076 – 1 = 0.1076 =
10.76%
5 For “i” unknown
• In general, solving for “i” in a time value
formulation is not straight forward.
•More often, one will have to resort to
some form of trial and error approach as
will be shown in future sections.
•A sample spreadsheet model for this
problem follows.
5 Example of the IRR function
=IRR($D7:$D12)
Determination of Unknown
Number of Years
Section 6
6 Unknown Number of Years
• Some problems require knowing the
number of time periods required given the
other parameters
•Example:
•How long will it take for $1,000 to double
in value if the discount rate is 5% per
year?
•Draw the cash flow diagram as….
6 Unknown Number of Years
Fn = $2000
0
1
2
...
. . . …….
n
P = $1,000
i = 5%/year; n is unknown!
56
6 Unknown Number of Years
• Solving we have…..
0
1
2
Fn =
$2000
...
. . . …….
n
P = $1,000
•Fn=? = 1000(F/P,5%,x): 2000 =
1000(1.05)x
•Solve for “x” in closed form……
6 Unknown Number of Years
• Solving we have…..
•(1.05)x = 2000/1000
•Xln(1.05) =ln(2.000)
•X = ln(1.05)/ln(2.000)
•X = 0.6931/0.0488 = 14.2057 yrs
•With discrete compounding it will take
15 years to amass $2,000 (have a little
more that $2,000)
6 No. of Years – NPER function
• From Excel one can formulate as:
=NPER(C23,C22,C20,C21)
Spreadsheet Application –
Basic Sensitivity Analysis
Section 7
7 Basic Sensitivity Analysis
• Sensitivity analysis is a procedure applied
to a formulated problem whereby one can
assess the impact of each input parameter
relating to the output variable.
•Sensitivity analysis is best performed
using a spreadsheet model.
•The procedure is to vary the input
parameters within certain ranges and
observe the change on the output variable.
7 Basic Sensitivity Analysis
• By proper modeling, one can perform
“what-if” analysis on one or more of the
input parameters and observe any changes
in a targeted output (response) variable
•Commercial add-in packages are available
that can be linked to Excel to perform such
an analysis
•Specifically: Palisade Corporation’s
TopRank Excel add-in is most appropriate.
7 Basic Sensitivity Analysis
• When you build your own models, devise
an approach to permit varying at least one
of the input parameters and store the
results of each change in the output
variable…then plot the results.
•If a small change in one of the input
parameters represents a significant
change in the output variable then…
•That input variable is “sensitive”
7 Basic Sensitivity Analysis
• If an input parameter is deemed
“sensitive” then some effort should go into
the estimation of that parameter
•Because it does influence the response
(output) variable.
•Less sensitive input parameters may not
have as much effort required to estimate
as those input parameters do not have that
much impact on the targeted response
variable.
7 Basic Sensitivity Analysis
• When you build your own models, devise
an approach to permit varying at least one
of the input parameters and store the
results of each change in the output
variable…then plot the results.
•If a small change in one of the input
parameters represents a significant
change in the output variable then…
•That input variable is “sensitive”
Summary
• This chapter presents the fundamental time
value of money relationships common to
most engineering economic analysis
calculations
•Derivations have been presented for:
•Present and Future Worth- P/F and F/P
•Annuity Cash flows – P/A, A/P, F/A and
A/F
Summary
• One must master these basic time value
of money relationships in order to proceed
with more meaningful analysis that can
impact decision making.
•These relationships are important to you
professionally and in your personal lives.
•Master these concepts!!!