Investment and BEP analysis

8/10/2019 Investment and BEP analysis

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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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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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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


Sandwich $2.95 $1.25 7,000


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)



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Multiproduct Example


Sandwich $2.95 $1.25 7,000



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 .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?

Documents

Investment and BEP analysis