Transcript FE Review

FE Review
Engineering Economics
Things to Expect
• Multiple Choice Test
• Need to Pick off Answers fast
– Narrowing field by knowing what to expect will help
– Don’t have to get it right, just close enough to pick.
• Restricted to only certain calculators
– Is a financial or two available
– Can’t have preprogrammed formulas
– No “Class Assistant” on your laptop
Resources
• You will have a list of Formulas including
for 6 magic numbers (F/P, P/F, A/P, P/A,
A/F, F/A)
• Few other Formulas
• Interest Tables, Modified ACRS factors
• Problems are designed for fast solution
– If you know what to do a few quick
multiplications of divisions will “take out” the
problem
Using Tables
• Tables are designed for only one rate of
interest given at the top of table
Approach
• I’ll try to review
• Then I’ll give you a problem that tests that
• Well time to see who can kill it in 3
minutes
• We’ll check the answer
• See if anyone needs to see how they got
that.
Interest Rates
• Interest is reported annually but often
compounds more often
– Result is that money sitting for a year will
accumulate more interest than indicated by
the annual rate
• To Find a Yield
– Caution – Interest rates are in % orally and
decimals in calculations
– Step 1 – get a period interest rate
Annual Rate
# of Compounding Periods in a Year
To Get A Yield
• Use the F/P formula (1+i)^n
– Where n is number of compounding periods
• Can substitute period interest rate into F/P
formula
m
r
i  (1 )
m
e
Let r be the annual interest
Rate
m is the number of
Compounding periods in a year
Note yield is always higher than annual rate but usually not by a large amount
Remember the 1 is there to preserve principle so its you’ll get 1+interest in
Decimal form
Your Turn
• What is the effective annual rate of interest
(yield) for money invested at 5% interest
compounded quarterly
–A
–B
–C
–D
1.3%
5.0%
5.1%
20%
The Answer
• How Many had C - 5.1%
How Did I Do That
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Ie= ( 1 + (0.05/4))^4 = 1.050495
The 1 preserves my original investment
-1
0.0509495
Convert back to %
5.09495 – very close to 5.1%
Another Interest Application
• Test writers like continuous compounding
– Have all sorts of functions in books that no one uses
• You can use same old formula and just make m
something big
m
r

i (1 )
m
e
A Bank advertises 4.6%
Interest with continuous
Compounding – What is the
Effective rate of interest
(A) – 4.62%
(B) – 4.71%
(C) – 4.89%
(D) - 4.94%
The Answer
• How Many Picked (B) – 4.71%
How Did I Do That?
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Make m some big number – say 1000
=(1+ (0.046/1000))^1000 = 1.047073
Get rid of the 1
0.047073
Convert back to %
4.7073% which is about 4.71%
The “Magic Numbers”
• Two most important questions
– How much do I get
– When do I get it
• I can add only money at the same point in
time
The Annuity
How much is that equal to right now if interest is 6%
$5,700 per year for 5 years
0
1
I can’t just add up $5,700 * 5 because the money is at different
Points in time
5
My Magic Number Friend
• P/A
• Present Value = P/A*amount of one annuity
payment
• P/A is a function of interest rate and number of
payments (6% interest, 5 payments)
4.212
Finish Up
• $5700 * 4.212 = $2408.4
Can Do That in Reverse
Have $24,000 right now
Want to know an annuity of 5 equal annual payments
Present Amount * A/P = Annuity
Try It You’ll Like It.
Do $24,000 * A/P (for 6% interest and 5 payments)
The Answer
• Did you get A/P = 0.2374
• And the Annuity is $5,698 per year
The Total Life Cycle Cost
• Often want to know what is most cost
effective
– A cheaper short lived good
– Or a longer lived but more expensive good
Move All the Money to Time ZeroIe Get an NPV
Recover $5,000
0
3
6
9
12
Spend $18,000
Spend $70,000
NPV = $70,000 + P/F(6%,3)*$18,000
+P/F(6%,6)*$18,000
+P/F(6%,9)*$18,000
+P/F(6%,12)*$13,000
Get the P/F Values from the Table
• You need for 3, 6, 9,
and 12 years
Move All the Money to Time ZeroIe Get an NPV
Recover $5,000
0
3
6
9
12
Spend $18,000
Spend $70,000
NPV = $70,000 + P/F(6%,3)*$18,000
+P/F(6%,6)*$18,000
+P/F(6%,9)*$18,000
+P/F(6%,12)*$13,000
Now Convert to An Annuity Over
the Service Life
Get the Cost Per Year for 12 years
NPV * A/P(6%,12)
Ok You Couldn’t Read it
Get A/P(6%,12)
Now Get the Total Life Cycle Cost
• NPV * A/P(6%,12) =
Now Try This
• Warehouse A cost $100,000 now and has a
salvage value of $10,000 after 10 years.
• Warehouse B costs $70,000 now, needs
$18,000 of service every 3 years and is
salvaged after 12 years for $5,000
• Warehousing is needed forever. Which
warehouse is the better deal
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–
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(A)A by $140 per year
(B) A by $190 per year
(C) B by $190 per year
(D) A by $880 per year
The Answer
• How Many Got (D) A by $880/per year
Can Have Limiting Cases To
• What if the annuity goes forever?
A
P
i
Annuity Issues
• An annuity has to be a repeating payment
that occurs at the compounding interval
• Suppose I have an event that occurs every
5 years
– I can convert that to an annual equivilent
– 5 year amount * A/P for 5 years = annual
amount
– Now I have made an infrequently occurring
event equal to a regularly occurring one
Try This
• A Tractor Manufacture signs a long term contract
with a farm consortium to provide a new tractor
for $24,000 every 5 years indefinitely. At a 6%
interest rate what is the capitalized cost (present
value of the contract)
(A)- $950
(B)- $5700
(C)- $80,000
(D)- $95,000
The Answer
• How Many Got (D)- $95,000
How Did I Do That?
• Convert 24,000 to an annual annuity
– 24,000 * A/P(5,6%)
– $24,000 * 0.2374 = $5698
• Now just plug into the forever annuity
formula
– NPV = $5,698 / 0.06 = $94,967
– About equal $95,000
Depreciation
• Things wear out with time or use
• In taxes or book keeping we spread the
cost of a long lived asset over its useful life
• There are different ways of doing that but
the simplest is straight line depreciation
• I have an asset that cost $700,000
• It lasts 7 years
• Each Year I use up $700,000/7 = $100,000
Book Values with Depreciation
• Book Value is Original Value –
Depreciation taken to date
• My $700,000 truck has a book value of
$200,000 after 5 years of depreciation
• $700,000 – 5*100,000 = $200,000
Salvage Value
• Not Everything depreciates to zero value
• Suppose my truck cost $710,000.
• When its all worn out I can still get
$10,000 out of scrap metal or salvage
• My Annual Depreciation is
– (Cost – Salvage)/years of life
– (710,000 – 10,000)/ 7 = 100,000
Book Value with Salvage
• Original Cost – Depreciation to Date =
Book Value
• My Truck after 5 years
• $710,000 – 5*100,000 = $210,000
Now You Try It
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A $100,000 Asset
It lasts 7 years
It has a salvage value of $15,000
What is its book value after 3 years of
depreciation
– (A) 12,100
– (B) 36,400
– (C) 57,100
– (D) 63,100
What Answer Did You Get
• (D) 63,100
How Did I Do That?
• Get Annual Depreciation
– (100,000 – 15,000)/ 7 = $12,173
• Get Book Value
– $100,000 – 3*$12,173 = $63,571
– Close to $63,600 which is answer D