Rate of Return (ROR) : Engineering Economic

Rate of Return
(ROR)
Engineering Economic
Annisa Uswatun Khasanah
1
Introduction
• For any investment to be profitable, the
investor (corporate or individual) expects
to receive more money than the amount of
capital invested.
• In other words, a fair rate of return (ROR),
or return on investment, must be
realizable
2
Definition
• Rate of return (ROR) is the rate paid on the
unpaid balance of borrowed money, or the
rate earned on the unrecovered balance of an
investment, so that the final payment or receipt
brings the balance to exactly zero with
interest considered.
• Tingkat bunga yang menyebabkan terjadinya
keseimbangan antara semua pengeluaran
dan semua pemasukan pada suatu periode
tertentu.
3
Introduction
• The Minimum Attractive Rate of Return
(MARR) is a reasonable rate of return
established for the evaluation and
selection of alternatives.
• A project is not economically viable unless
it is expected to return at least the MARR.
• MARR is also referred to as the hurdle
rate, cutoff rate, benchmark rate, and
minimum acceptable rate of return.
4
Illustration
• To get started in a new telecommuting position with AB
Hammond Engineers, Jane took out a $1000 loan at i
=10% per year for 4 years to buy home office equipment.
From the lender’s perspective, the investment in this
young engineer is expected to produce an equivalent net
cash flow of $315.47 for each of 4 years. This represents
a 10% per year rate of return on the unrecovered
balance
5
Illustration
lender’s perspective
Rate of return is the interest rate at which the benefits are equivalent to
the costs
6
Rate of Return Calculation Using a PW
or AW Relation
• The rate of return is the interest rate that makes
the present worth or annual worth of a cash
flow series exactly equal to 0.
• To determine the rate of return, develop the
ROR equation using either a PW or AW relation,
set it equal to 0, and solve for the interest rate
• The i value that makes these equations
numerically correct is called i* . It is the root of
the ROR relation.
7
or AW Relation
• To determine if the investment project’s
cash flow series is viable, compare i *
with the established MARR
8
or AW Relation
• The purpose of engineering economy
calculations is equivalence in PW or AW
terms for a stated i ≥ 0%.
• In rate of return calculations, the objective
is to find the interest rate i* at which the
cash flows are equivalent.
• The calculations are the reverse of those
made in previous chapters, where the
interest rate was known
9
Example
For example, if you deposit $1000 now and are
promised payments of $500 three years from now
and $1500 five years from now
10
• The equation is solved for i* =16.9% by
hand using trial and error or using a
spreadsheet function
• The rate of return will always be greater
than zero if the total amount of cash inflow
is greater than the total amount of outflow,
when the time value of money is
considered
11
Determine i*
1. trial and error by hand
2. using a programmable calculator

3. spreadsheet function
When cash flows vary from year to year (period to

period), the best way to find i* is to enter the net cash
flows into contiguous cells (including any $0 amounts)
and apply the IRR function in any cell.
12
Example
• Applications of green, lean manufacturing techniques coupled with value
stream mapping can make large financial differences over future years while
placing greater emphasis on environmental factors. Engineers with Monarch
Paints have recommended to management an investment of $200,000 now
in novel methods that will reduce the amount of wastewater, packaging
materials, and other solid waste in their consumer paint manufacturing
facility. Estimated savings are $15,000 per year for each of the next 10
years and an additional savings of $300,000 at the end of 10 years in facility
and equipment upgrade costs. Determine the rate of return using hand and
spreadsheet solutions.
13
Trial and Error
14
Using Spread Sheet
• n = 10 year
• A = $15000
• P = $ 200000
• F = $ 300000
• ROR = 11%
15
Using Spread Sheet
Year CF
0 $ (200,000.00)
1 $ 15,000.00
2 $ 15,000.00
3 $ 15,000.00
4 $ 15,000.00
5 $ 15,000.00
6 $ 15,000.00
7 $ 15,000.00
8 $ 15,000.00
9 $ 15,000.00
10 $ 315,000.00
IRR 11%
16
Trial error using spread sheet
Year CF trial NPV
0 $ (200,000.00)
1 $ 15,000.00 8% $39,609.27
2 $ 15,000.00 9% $ 22,988.11
3 $ 15,000.00 10% $ 7,831.49
4 $ 15,000.00 11% $ (6,006.18)
5 $ 15,000.00
6 $ 15,000.00
7 $ 15,000.00
8 $ 15,000.00
9 $ 15,000.00
10 $ 315,000.00
17
Exercise (assignment 7)
1. Assume you borrow $50,000 at 10% per
year interest and you agree to repay the
loan in five equal annual payments. What
is the amount of the unrecovered balance
immediately after you make the third
payment
18
Exercise
2. Determine the Rate of return of this cash
flow!
19
Exercise
3. Given the cash flow below, calculate the
rate of return on the investment!
Year Cash flow
0 ($100)
1 $20
2 $30
3 $20
4 $40
5 $40
20
Exercise
4. Given the cash flow below, calculate the
rate of return on the investment!
Year Cash flow
0 $125
1 ($10)
2 ($20)
3 ($30)
4 ($40)
5 ($50)
6 ($60)
21

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2. using a programmable calculator

When cash ﬂows vary from year to year (period to

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