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Annual Worth Analysis-Engineering Economics-Lecture Slides, Slides of Microeconomics

M. J. P. Rohilkhand UniversityMicroeconomics

This lecture is part of lecture series for Engineering Economics course at M. J. P. Rohilkhand University. It was delivered by Dr. Badrinath Singh to cover following points: Annual, Worth, Analysis, Equivalent, Uniform, Cost, Technique, Comparison, Cash, Flow

Typology: Slides

2011/2012

Uploaded on 07/06/2012

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bg1
4/4/2012
1
Introduction
The annual worth analysis is commonly
considered to be more desirable over the PW
and the FW methods because the AW value
is easy to calculate; the measure of worth---
AW in dollars per year is understood by most
individuals; and its assumptions are
essentially identical to those of PW method.
Annual Worth Analysis
•AW is also referred to as: equivalent annual worth
(EAW), equivalent annual cost (EAC), annual
equivalent (AE), and equivalent uniform annual cost
(EUAC).
•The estimates of equivalent annual worth amount is
the same for all name variations.
•The alternatives selected by the AW method will
always be the same as that selected by the PW
method, and all other alternative methods.
3
Advantages of Annual Worth
•Popular Analysis Technique
•Easily understood results are
reported in $ / time period
•Eliminates the LCM problem
associated with the present worth
method
–Only have to evaluate one life cycle of a
project
4
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pf4
pf5

Partial preview of the text

Download Annual Worth Analysis-Engineering Economics-Lecture Slides and more Slides Microeconomics in PDF only on Docsity!

Introduction

The annual worth analysis is commonly

considered to be more desirable over the PW

and the FW methods because the AW value

is easy to calculate; the measure of worth---

AW in dollars per year is understood by most

individuals; and its assumptions are

essentially identical to those of PW method.

Annual Worth Analysis

  • AW is also referred to as: equivalent annual worth

(EAW), equivalent annual cost (EAC), annual

equivalent (AE), and equivalent uniform annual cost

(EUAC).

  • The estimates of equivalent annual worth amount is

the same for all name variations.

  • The alternatives selected by the AW method will

always be the same as that selected by the PW

method, and all other alternative methods.

3 Advantages of Annual Worth

  • Popular Analysis Technique
  • Easily understood results are reported in $ / time period
  • Eliminates the LCM problem associated with the present worth method - Only have to evaluate one life cycle of a

project

4 docsity.com

Annual Worth Calculations

• Generally,

  • A = P(A/P, i%, n) capital recovery method
  • A = F(A/F, i%, n) sinking fund
  • P and F represent one time occurances

• Convert all cash flows to their end of period

equivalent amounts

For comparison, in Example 5. 2 about office lease

options, a P analysis was performed over 18 years, the

LCM of 6 and 9 years.

5

A project engineer is assigned to start up a new office in a

city where a 6 - year contract has been finalized. Two lease

options are available, each with a first cost, annual lease

cost, and deposit-return estimates shown below.

6

Determine which lease option should be selected on

the basis of a present worth comparison, if the MARR

(minimum attractive rate of return) is 15 % per year.

Present Worth Example: Unequal lives

• Comparison must be made over equal time periods;

Compare over the least common multiple, LCM.

• Since the leases have different terms (service lives),

compare them over the LCM of 18 years.

• For life cycles after the first, the first cost is repeated in year

0 of each new cycle, which is the last year of the previous

cycle. These are years 6 and 12 for location A and year 9

for B.

• The cash flow diagram is in Figure 5 – 2.

• Calculate PW at 15 % over 18 years.

7 8

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13 Capital Recovery and AW Values

  • Assume the potential purchase of any productive asset
  • One needs to know or estimate:
    • Initial Investment - P
    • Estimated Future Salvage Value - S
    • Estimated life of the asset - N
    • Estimated operating costs and timing
    • Operative interest rate – i% 14 CAPITAL RECOVERY COST (CR)
  • CR = the equivalent annual worth of the asset given: Capital Recovery (CR) is the annualized equivalent of the initial investment, P 0 and the annualized amount of the future salvage value Fn
P 0
FN

0 1 2 3 N- 1 N

S

Lockheed Martin is increasing its booster thrust power to win more satellite launch contracts from European companies interested in opening up new global communications markets. An earth-based tracking equipment is expected to require an investment of $13 million with $8 million committed now and the remaining $5 million expended at the end of year 1 of the project. Annual operating costs (AOC) for the system are expected to start the first year and continue at $0.9 million per year. The useful life of the tracker is 8 years with a salvage value of $0.5 million. Calculate the AW value for the system, if the corporate MARR is currently 12% per year. 15 The cash flows for the tracker system must be converted to an equivalent AW cash flow sequence over 8 years. The AOC is A = - $ 0. 9 per year, and the capital recovery is calculated by using Equation [ 6. 3 ]. The present worth P in year 0 of the two separate investment amounts of $ 8 and $ 5 is determined before multiplying by the A/P factor. The correct interpretation of this result is very important to Lockheed Martin. It means that each year for 8 years, the equivalent total revenue from the tracker must be at least $2,470,000 just to recover the initial present worth investment plus the required return of 12% per year. This does not include the AOC of $0.9 million each year. A = - 2.47 - 0.9 = $3.37 million per year

A = - 8 (A/P, 12%, 8) - 5 (P/F, 12%, 1) (A/P, 12%, 8) + 0.5 (A/F, 12%, 8) - 0.

A = - 8 (0.2013) - 5 (0.8929) (0.2013) + 0.5 (0.0813) - 0.9 = - $3.36845 million 16 docsity.com

The owner of PizzaRush.com plans to purchase and install 5 portable,

in-car systems to increase delivery speed and accuracy. The systems

provide a link between the web order-placement software and the On-

Star© system for satellite-generated directions to any address in the

Los Angeles area. The expected result is faster, friendlier service to

customers, and more income for PizzaRush.

Each system costs $4600, has a 5 - year useful life, and may be

salvaged for an estimated $300. Total operating cost for all systems is

$650 for the first year, increasing by $50 per year thereafter. The MARR

is 10%. Perform an annual worth evaluation.

What annual incremental income is necessary to recover the investment

at the MARR of 10% per year?

17

  • CR = - 5(4600)(A/P,10%, 5) + 5(300)(A/F,10%, 5) = - $
  • A = - 5(4600)(A/P,10%, 5) - 650 + 5(300)(A/F,10%, 5) - 50 (A/G,10%, 5)
  • A = - 5(4600)(0.2638) - 650 +5(300)(0.1638) - 50 (1.8101) =
    • $6562. A = - capital recovery + equivalent net income
  • ( b ) The owner conservatively estimates increased income of $1200 per

year for all five systems. Is this project financially viable at the MARR?

  • The financial viability can be determined without calculating the AW

value. The $1200 in new income is substantially lower than the CR of

$5822 that does not yet include the annual costs. The purchase is

clearly not economically justified.

  • The annual operating costs and incomes form an arithmetic gradient

series with a base of $550 ($1200 – $650) in year 1, decreasing by $

per year for 5 years. The AW relation is:

A = - capital recovery + equivalent net income

= - 5822 + 550 - 50( A/G ,10%,5) = - $

This is the equivalent 5-year net amount needed to return the investment and recover the estimated operating costs at a 10% per year return. This shows, that the alternative is clearly not financially viable at MARR = 10%. Note that the estimated extra $1200 per year income, offset by the operating costs, has reduced the required annual amount from $5822 to $5362. 19 Annual Worth of a Permanent Investment

  • This section discusses the annual worth equivalent of the capitalized

cost.

  • Evaluation of public sector projects (flood control dams, irrigation

canals, bridges, or other large-scale projects), requires the comparison

of alternatives that have such long lives that they may be considered

infinite in economic analysis terms.

  • For this type of analysis, the annual worth of the initial investment is the

perpetual annual interest earned on the initial investment, that is,

CR = A = Pi.

  • This is Equation [5.3]; however, the A value is also the capital recovery

amount.

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