investment and bep analysis
TRANSCRIPT
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Investment analysis: Tools for
Evaluating Alternatives
Outline
Mutually exclusive and independent
projects
Use of present, future and annual
worth analysis to evaluate
alternatives
Payback period
Rate of return
Benefit-cost ratio
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Tools for Evaluating
Alternatives
There are various tools or
methods by which alternatives
can be evaluated economically
using the factors learned.
Purpose
Compare mutually exclusive
alternatives
Basis: present worth, future worth
and annual worth analysis
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Category of projects
To help formulate alternatives,
a project is categorized as one
of the following:
Mutually exclusive: Only one of
the viable projects can be
selected by the economic analysis
Independent:More than one viableproject may be selected by the
economic analysis.
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Tools for Evaluating alternatives
Present Worth Analysis Formulating Mutually Exclusive
Alternatives
Present Worth Analysis of Equal-life
Alternatives Present worth Analysis of DifferentLife
Alternatives
Future Worth Analysis
Payback Period Analysis
Annual Worth Analysis Rate of Return Analysis
Benefit/Cost Ratio Analysis
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Present worth Analysis of Equal-
Life Alternatives
One alternative: Calculate PW at
the MARR.
If PW 0, the requested MARR is
met or exceeded.
The alternative is financially
viable.
Two or more alternatives:Calculate the PW of each
alternative.
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Present worth Analysis of Equal-
Life Alternatives
Two or more alternatives:
Calculate the PW of each
alternative at the MARR.
Select the alternative with the
largest PW value
This means that select the
alternative with less negative ormore positive.
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Selection of alternative
following the guideline
PW1 PW2 Selectedalternative
$ -1500 $ -500 2
-500 +1000 2
+2500 -500 1
+2500 +1500 1
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Present worth Analysis of Equal-
Life Alternatives
If the projects are independent,
the selection guideline is as
follows:
For one or more independent
projects, select all projects with
PW 0 at the MARR.
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Example 5.1
Perform apresent worth analysis of equal-
service machine with costs shown below,
if the MARR is 10% per year. Revenue for
all the alternatives are expected to be
the same.
Electric
powered
Gaspowered
Solarpowered
First cost, $Annual operating cost (AOC), $
Salvage value S, $
Life, years
- 2500- 900
200
5
- 1500- 700
350
5
- 6000- 50
100
5
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Example 5.1
Solution
These are service alternatives.
The PW of each machine is calculated at
i = 10% for n = 5 years.PWE= -2500 - 900(P/A,10%,5) + 200(P/F,10%,5)= $-5788
PWG= -3500 - 700(P/A,10%,5) + 350(P/F,10%,5)= $-5936
PWS= -6000 - 50(P/A,10%,5) + 100(P/F,10%,5)= $-6127
[See the calculations in excel file]
The electric-powered machine is selected since the PWof its costs is the lowest, it has numerically thelargest PW value.
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Example 5.2
A project engineer with EnvironCare is assigned to
start up a new office in a city where a 6-year
contract has been finalized to take and to analyze
ozone-level readings. Two lease options are
available, each with a first cost, annual leasecost, and deposit-return estimates as shown below:
Location A Location B
First cost, $Annual lease cost, $ per year
Deposit return, $
Lease term, years
- 15,000-3,500
1,000
6
- 18,000-3,100
2,000
9
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Example 5.2
(a)Determine which lease option should be selected onthe basis of a present worth comparison, if the MARR
is 15% per year.
(b) EnvironCare has a standard practice of evaluatingall projects over a 5-year period. If a study period
of 5 years is used and the deposit returns are not
expected to change, which location should be used?
(c) Which location should be selected over a 6-year
study period if the deposit return at location B isestimated to be $6000 after 6 years.
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Break-Even Point
Breakeven Analysis
Single-Product Case
Multiproduct Case
Reference: OperationsManagement, Heizer &
Render, 8th
ed (p-287)
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Learning Objectives
When you complete this topic, youshould be able to:Describe or Explain:
Break-even analysisAssumptions
Graphical and Algebraic
ApproachDetermining BEP for single and
multi-product cases
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Break-Even Analysis
A critical tool for determiningcapacity a facility must have to
achieve profitability Objective is to find the point in
dollars (or ringgits) and units atwhich, cost equals revenue
Requires estimation of fixedcosts, variable costs, andrevenue
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Break-Even Analysis
-The Elements
Fixed costs are costs that continue even if nounits are produced
Depreciation, taxes, debt, mortgagepayments
Variable costs are costs that vary with thevolume of units produced
Labor, materials, portion of utilities Contribution is the difference between
selling price and variable cost
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Break-Even Analysis
-The Elements
Costs and revenue are linear
functions(In reality, the case is not so)
There is no time value of money
Assumptions
We actually know that these (variable & fixed) costs are not easy to estimate.
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Break-Even Analysis
Total revenue line
Total cost line
Variable cost
Fixed cost
Break-even pointTotal cost = Total revenue
900
800
700
600
500
400
300
200
100
| | | | | | | | | | | |0 100 200 300 400 500 600 700 800 900 10001100
Costin
dollars
Volume (units per period)
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Break-Even Analysis
BEPx= Break-even point inunits
BEP$= Break-even point indollars
P = Price per unit (after
all discounts)
x = Number of unitsproduced
TR = Total revenue = PxF = Fixed costsV = Variable costs per unit
TC = Total costs = F + Vx
TR = TCor
Px = F + Vx
Break-even point occurs when
BEPx=F
P - V
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Break-Even Analysis
BEPx= Break-even point inunits
BEP$= Break-even point indollars
P = Price per unit (after
all discounts)
x = Number of unitsproduced
TR = Total revenue = PxF = Fixed costsV = Variable costs
TC = Total costs = F + Vx
BEP$= BEPx P
= P
=
=
F(P - V)/P
FP - V
F1 - V/P
Profit = TR - TC
= Px - (F + Vx)= Px - F - Vx
= (P - V)x - F
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Break-Even Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEP$= =F
1 - (V/P)
$10,0001 - [(1.50 + .75)/(4.00)]
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Break-Even Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEP$= =F1 - (V/P) $10,0001 - [(1.50 + .75)/(4.00)]
= = $22,857.14$10,000.4375
BEPx= = = 5,714F
P - V
$10,0004.00 - (1.50 + .75)
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Break-Even Example
50,000
40,000
30,000
20,000
10,000
| | | | | |0 2,000 4,000 6,000 8,000 10,000
Dollars
Units
Fixed costs
Totalcosts
Revenue
Break-evenpoint
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Break-Even Example
BEP$=F
1 - x (Wi)Vi
Pi
Multiproduct Case
where V = variable cost per unit
P = price per unitF = fixed costs
W = percent each product is of total dollar salesi = each product
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Multiproduct BEP Example
Annual ForecastedItem Price Cost Sales Units
Sandwich $2.95 $1.25 7,000
Soft drink .80 .30 7,000Baked potato 1.55 .47 5,000Tea .75 .25 5,000Salad bar 2.85 1.00 3,000
Fixed costs = $3,500 per month
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Multiproduct BEP Example
Annual ForecastedItem Price Cost Sales Units
Sandwich $2.95 $1.25 7,000
Soft drink .80 .30 7,000Baked potato 1.55 .47 5,000Tea .75 .25 5,000Salad bar 2.85 1.00 3,000
Sandwich $2.95 $1.25 .42 .58 $20,650 .446 .259
Soft drink .80 .30 .38 .62 5,600 .121 .075Baked 1.55 .47 .30 .70 7,750 .167 .117potatoTea .75 .25 .33 .67 3,750 .081 .054Salad bar 2.85 1.00 .35 .65 8,550 .185 .120
$46,300 1.000 .625
Annual WeightedSelling Variable Forecasted % of Contribution
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)
Fixed costs = $3,500 per month
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Multiproduct Example
Annual ForecastedItem Price Cost Sales Units
Sandwich $2.95 $1.25 7,000
Soft drink .80 .30 7,000Baked potato 1.55 .47 5,000Tea .75 .25 5,000Salad bar 2.85 1.00 3,000
Fixed costs = $3,500 per month
Sandwich $2.95 $1.25 .42 .58 $20,650 .446 .259
Soft drink .80 .30 .38 .62 5,600 .121 .075Baked 1.55 .47 .30 .70 7,750 .167 .117potato
Tea .75 .25 .33 .67 3,750 .081 .054Salad bar 2.85 1.00 .35 .65 8,550 .185 .120
$46,300 1.000 .625
Annual WeightedSelling Variable Forecasted % of Contribution
Item (i) Price (P)Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col7)
BEP$=F
1 - x (Wi)
Vi
Pi
= = $67,200$3,500 x 12
.625
Dailysales = = $215.38
$67,200312 days
.446 x $215.38$2.95
= 32.6 33sandwiches
per day
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Problems for practice (to be solved in the class)
(1) Given the following data, calculate BEP(x), BEP ($),and the profit at 100,000 units:P= $8/unit, V = $4/unit and F =$50,000.
(2) A prolific author is considering starting her ownpublishing company. She will call it DSI Publishing,Inc. DSIs estimated costs are-------------------------------------------------------------------Fixed $250,000.00
Variable cost per book $20.00Selling price per book $30.00
How many books must DSI sell to break even? Whatis its break-even point in dollars?
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Problem #3 (to be solved at home)
As manager of a theatre company you have decided that concession saleswill support themselves. The following Table provides the info you have beenable to put together thus far :
Item Sell ing Price Variable co st % of revenue
Soft dr ink $ 1.00 $o.65 25
Mixed fru it Ju ice 1.75 0.95 25
Co ffee 1.00 0.30 30
Cand y 1.00 0.30 20
Last years manager has advised you to be sure to add 10% ofvariable cost as a waste allowance for all categories.
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You estimate labor cost to be $250.00 (5 booths with 3 peopleeach). Even if nothing is sold, your labor cost will be $250.00,so you decide this as fixed cost. Booth rental, which is acontractual cost at $50.00 for each booth per night, is also a
fixed cost.
(a) What is the break-even volume per evening performance?
(b) How much mixed fruit juice would you expect to sell at thebreak-even point?
Problem #3 (to be solved at home)
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Problem # 4(to be solved and submitted with assignment)
Jacks Grocery is manufacturing astore branditem that has a variable cost of $0.75 per unit and a sellingprice of $1.25 per unit. Fixed costs are $12,000. Current volume is 50,000 units. The Grocery can substantially
improve the product quality by adding a new piece of equipment at an additional fixed cost of $5,000. Variable
cost would increase to $1.00, but their volume should increase to 70,000 units due to the higher quality product.
Should the company buy the new equipment?
What are the break-even points ($ and units) for the two processes considered in Problem 4?