5 Annual Worth

ANNUAL WORTH COMPARISON
Why Annual Worth Comparison?

• Many economic decision are assisted by determining the
costs, expenditures, and net worth on the basis of annual
or periodic timings.
• Manufacturing manager is often required to justify the

operations on , monthly or annual basis.
• Annual goals are frequently set.

Procedure
In this method all the receipts and

disbursements occurring over a
period are converted to an
equivalent uniform yearly amount.
Advantages
• It is possible to view an years gains and losses as a
milestone for progress.
• Cost accounting procedures, depreciation expenses, tax
calculations and other summary reports are annual.
• The major tool used in annual worth calculations is the
capital recovery factor that converts a lumpsum into
annuity.
EXAMPLE 1
A food beverage company is planning expansion of its cold storage
facility. Three alternative site design proposals are being considered
that uses an interest rate of 10%. Plan A and B require an
expenditure of Rs.35,00,000 for land and which will retain its value
in 10 years, while plan C requires Rs.45,00,000 for land, which will
also retain its value in 10 years. The estimated income increase due
to facility available is annualized at Rs.24,80,000 per year. the
company requires that a life of 10 years be used for analysis. Data
pertaining to the project are given below,

In Rs. Proposal A Proposal B Proposal C
Building and installation 60,00,000 70,00,000 40,00,000
Compressor 10,00,000 13,50,000 8,50,000
Expected energy cost 1 year 6,50,000 4,80,000 6,50,000
Energy cost increase for each 30,000 20,000 35,000
additional year
Annual maintenance cost 2,00,000 1,50,000 5,00,000
Estimated salvage value 3,50,000 4,30,000 1,80,000
Proposal A: -168673.3
Proposal B: -126114.2
Proposal C: -310808.6
Cash Flow Diagram 3,50,000
A (Income)= 24,80,000
0 1
10
A= 2,00,000
35,00,000
6,50,000
60,00,000 G= 30,000
10,00,000
Situations for Equivalent Annual Worth
Comparison
Negative cash flows that is costs or disbursements

are more than receipts. But alternative should be
selected.
Ex- safety measures

Consolidation of cash flows
A consulting firm proposes to provide “self inspection” training for clerks who
work with insurance claims. The program lasts one year, costs Rs. 20,000 per
month, and professes to improve quality while reducing clerical time. A
potential user of the program estimates that savings in the first month should
amount to Rs. 8000 and should increase by Rs. 4000 per month for the rest of
the year. however . Operational confusion and work interference are expected
to boost clerical costs by Rs.12,000 the first month but this amount should
subsequently decline in equal increments at the rate of Rs.1000 per month. If
the required rate of return on money is 12% compounded monthly and there is
a stipulation that the program must pay for itself within 1 year, should the
Case A:
Two machines models A and B perform the same function. Type A
machine has a low initial cost of Rs. 95000, relatively high operating cost
of Rs.19,000 per year more than those of type B machine, and a short life
of 4 years. Type B machine costs Rs. 2,51,000 and can be used for 8 years.
The scrap value from either machine at the end of the life will barely
cover its removal cost. Which is preferred when the minimum attractive
rate of return is 8%? [47680;43680]
Case B:
If machine A will produce refinements within 4 years with the availability
of a modified one at a cost of Rs. 1,15,000 but reducing the operating
costs to Rs.4000, then find the annual worth? [43890]
Note: if the future conditions can be estimated in confidence, excluding inflation
Case A
Type B
Type A
Case B
Type A Type B
Capital Recovery Method
F
0 @i%
n
Let, P= first cost of the asset, F= estimated salvage value,
n= estimated service life in years, CR(i)= capital recovery with
return.
CR(i)= P(A/P, i, n) – F(A/F, i, n)
But since, (A/F, i, n)=(A/P, i, n) – i
CR(i)= P(A/P, i, n) – F[(A/P, i, n) – i]
CR(i)= (P-F) (A/P, i, n) + F.i

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ANNUAL WORTH COMPARISON

Why Annual Worth Comparison?

• Manufacturing manager is often required to justify the

• Annual goals are frequently set.

In this method all the receipts and

A food beverage company is planning expansion of its cold storage

facility. Three alternative site design proposals are being considered

that uses an interest rate of 10%. Plan A and B require an

in 10 years, while plan C requires Rs.45,00,000 for land, which will

to facility available is annualized at Rs.24,80,000 per year. the

company requires that a life of 10 years be used for analysis. Data

pertaining to the project are given below,

Negative cash flows that is costs or disbursements

Ex- safety measures

month, and professes to improve quality while reducing clerical time. A

subsequently decline in equal increments at the rate of Rs.1000 per month. If

Let, P= first cost of the asset, F= estimated salvage value,

n= estimated service life in years, CR(i)= capital recovery with

CR(i)= P(A/P, i, n) – F(A/F, i, n)

But since, (A/F, i, n)=(A/P, i, n) – i

CR(i)= P(A/P, i, n) – F[(A/P, i, n) – i]

CR(i)= (P-F) (A/P, i, n) + F.i

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