ENGR Decision Making

Question 1

Gradient

Answer 1

Payment Increased over multiple periods

Question 2

Arithmetic Gradient

Answer 2

Constant dollar value increase

Question 3

Geometric Gradient

Answer 3

Percentage increase over terms

Question 4

Arithmetic increase future value calculation

Answer 4

F = G(P/G, i, n) * P(F/P, i, n)

Question 5

Geometric increase future value calculation

Answer 5

P = A[(1-(1+g)^n * (1+i)^-n)/(i-g)]

Question 6

Present Worth Analysis

Answer 6

Single project/product
Multiple Alternatives
- equal life
- different life
- infinite life
PW and bond pricing

Question 7

What does MARR stand for?

Answer 7

Minimum Acceptable Rate of Return

Question 8

What is MARR exactly?

Answer 8

The minimum percentage of interest that is personally acceptable for a purchase of an asset. Includes profits, liability, inflation, etc.

Question 9

If the present worth with MARR calculation is zero, did you meet your MARR?

Answer 9

Yes

Question 10

If the present worth is zero when using MARR, did you make a profit?

Answer 10

Yes

Question 11

If the present worth is less than 0 in your MARR calculation, does it mean you’re losing money?

Answer 11

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.

Question 12

What year does Gradient start on?

Answer 12

The year after the initial ‘A’ payment

Question 13

Capitalized investment formula

Answer 13

P = A/i

Question 14

Present worth formula

Answer 14

Compound table - (P/F,i,n)
(P/A,i,n)

Question 15

Sinking fund formula

Answer 15

(A/F, i, n)

Question 16

Another name for present worth is?

Answer 16

Net Present Value

Question 17

Equal Service comparisons

Answer 17

Comparing two assets or investments with differing useful lives.

Question 18

How do you compare two investments with differing investment lives?

Answer 18

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.

Question 19

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)

Answer 19

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.

Question 20

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:

Answer 20

𝐴 = 85048(𝐴 𝑃⁄ , 7%, 10) = 85048(0.1424) = $12,110.84

Question 21

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

Answer 21

𝐹 = 12500(1.06)^5 = $16,727.82

Question 22

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%

Question 23

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?

Answer 23

$276,628.10

Question 24

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?