ENGR Decision Making Flashcards
Gradient
Payment Increased over multiple periods
Arithmetic Gradient
Constant dollar value increase
Geometric Gradient
Percentage increase over terms
Arithmetic increase future value calculation
F = G(P/G, i, n) * P(F/P, i, n)
Geometric increase future value calculation
P = A[(1-(1+g)^n * (1+i)^-n)/(i-g)]
Present Worth Analysis
Single project/product
Multiple Alternatives
- equal life
- different life
- infinite life
PW and bond pricing
What does MARR stand for?
Minimum Acceptable Rate of Return
What is MARR exactly?
The minimum percentage of interest that is personally acceptable for a purchase of an asset. Includes profits, liability, inflation, etc.
If the present worth with MARR calculation is zero, did you meet your MARR?
Yes
If the present worth is zero when using MARR, did you make a profit?
Yes
If the present worth is less than 0 in your MARR calculation, does it mean you’re losing money?
Not necessarily, it just means you are not profiting as much. If the number is too far in the negative then there is a possibility you have no profit at all and are losing money.
What year does Gradient start on?
The year after the initial ‘A’ payment
Capitalized investment formula
P = A/i
Present worth formula
Compound table - (P/F,i,n)
(P/A,i,n)
Sinking fund formula
(A/F, i, n)
Another name for present worth is?
Net Present Value
Equal Service comparisons
Comparing two assets or investments with differing useful lives.
How do you compare two investments with differing investment lives?
You need to find the least common multiple of each and adjust the cash flow diagram to this new timeline. Keep in mind that useful life remains the same and it may be necessary to repeat the first cost of a new investment at the end of the useful life.
How do you compare two investments with different timelines when it doesn’t make sense to find a least common multiple (for example if the least common multiple is 35 and one of the items has a use-life of 5 years)
Bring the present worth of the longer timeline to match the end time of the shorter timeline. Keep in mind that you must calculate the depreciation rate for that item to figure out what the new salvage value is.
The CFD below represents the information given in this problem. From the CFD, we see that
year 1 is $20,000 and it decreases by $2,000 every year. This suggests a negative Arithmetic
gradient series with A = 20000, G = -2000, i = 7% and n = 10.
P can therefore be calculated as:
𝐴 = 85048(𝐴 𝑃⁄ , 7%, 10) = 85048(0.1424) = $12,110.84
Initial borrowed amount, P = $10,000 at 5% simple interest for 5 years.
After five years, the loan pay off amount (loan balance) = 𝐹 = 10000 + 10000 x 0.05 x 5 =
$12,500
The amount borrowed at in year 5 at 6% compound interest for for five more years is $12,500.
The lump sum due at the end of the 10-year loan period is the loan balance borrowed at year 5
for 5 additional years. This can be calculated as
𝐹 = 12500(1.06)^5 = $16,727.82
A diesel manufacturer is considering the two alternative production machines with the
following estimates:
Alternative A Alternative B
Initial Cost ($) 55,000
Salvage value ($) 10000
Useful Life (years) 6
70,000
Salvage value ($) 10000 18000
Useful Life (years) 6 7
For such machines, the manufacturer uses an analysis period of 10 years and estimates the
following salvage values: four-year-old alternative A machine as $25,000 and a three-year-old
alternative B machine as $40,000. Using present worth analysis, which of the machines will the
company buy? MARR = 12%
A chemical engineering firm installed a chemical plant at a cost of $1.2 million. This plant
will be used for ten years and then sold for $250,000. The company uses a Minimum
Attractive Rate of Return (MARR) of 20% per year for all of its business operations. As a
student doing an internship with this company, you are asked to determine the minimum
revenue required each year to realize the expected recovery and return. What is your
answer?
$276,628.10
The firm you work for was presented with an opportunity to invest in a project. The
following are the data on the project:
Initial investment: 60 million
Salvage Value: 1.2 million
Life: 10 years
Annual Income: 15,500,000
The project is expected to operate for ten years. If your management expects to make 25% on its
investment before taxes, would you recommend this project using the present worth analysis?
