Cash Flow Problems are 5 Types
• Invest and Earn
– solve with NPV, maybe IRR or tweeked IRR or
ERR
• All Cost Investment Alternatives
– develop cash flows for alternatives
– subtract other choices from favorite choice
– Evaluate comparison problem using an invest
and earn technique - especially NPV
– Run a basket-ball elimination tournament to
pick the best
Five Types of Cash Flow
Problems
• Incremental Investment Problem
– Write cash flow for basic investment
– Write cash flow with the add on being
evaluated
– Subtract the basic cash flow from the one with
the add on - get a cash flow for value of the add
on
– Do an NPV or IRR/ERR/Tweeked IRR on the
new cash flow
Five Types of Cash Flow
Problems
• Competing Investments Problem
– Is no one right answer
– Have to choose what strategy you are using to
pursue wealth and then choose your analysis
technique
• Last Type of Problem is the Unit Cost
Problem
Unit Cost Problems
• It costs a certain amount to produce a unit
of something your business handles
• Cost to get equipment to produce something
is divided into two types of costs
– Ownership costs (have to buy the equipment)
– Operating costs (have to run it)
• These costs are put on an annual basis and
divided by units produced to get a cost/unit
Example
• Earnest does mine planning for Crader
Mining
• Operating Costs
–
–
–
–
–
Each Truck uses $60,000 in diesel fuel
$10,000 in lubricants
$20,000 in repairs
$10,000 in tires
$40,000 for operator
Unit Cost Problem
• Total Operating Cost/Year
– $60,000+$10,000+$20,000+$10,000+$40,000
= $140,000 / Year
– Annual tonnage produced is 700,000 tons
– Operating Cost/Unit is $140,000/700,000 =
$0.2/ton
• Ownership consists of
– Purchase
– Taxes and Insurance
– Tax Benefits
Purchase Cost
• In order to get cost per ton, ownership costs
must be put on an annual basis so it can be
divided by annual production
• Earnest’s trucks cost $700,000 each
– Can make it a series of annual payments
– Maybe in life it is - Maybe the share holders
paid
– Break it up as if it were annual payments at
interest rate for loan of shareholders rate
Need the Life of Equipment or
Loan
• Mining trucks are often 7 years
• Assume shareholders pay and want 15%
rate of return
• A/P0.15,7 = 0.2404
• $700,000 * 0.2404 = $168,280 / Year
Depreciation
• Truck is used up by working it in
production
– Already said life was 7 years
• Simple Way to Depreciate is called
“Straight Line”
–
–
–
–
Truck was worth $700,000
Is used up over 7 years
$700,000 / 7 = $100,000 per year used up
Per unit cost analysis uses straight line
More Depreciation
• In practice things depreciate faster at first
– New car dropping $2000 when drive it off the
lot
• Other Depreciation Methods such as Sum of
Years Digits
– Income tax has schedule IRS developed called
ACRS (Accelerated Cost Recovery Schedule)
– Not going to cover right now
Depreciation and Tax Advantage
• Earnest’s trucks can be depreciated on
Federal and State Income Tax
– Government taxes business income just like
yours
– Government allows you to deduct from your
income
• If self employed you can deduct business expenses
• Only pay tax on what you actually cleared
– Crader Mining has to buy trucks - it’s a
business expense taken by depreciation
The Tax Advantage
• Straight Line Depreciation give
$100,000/year
• Crader will deduct $100,000 from their
reported earnings
– Saves them money on taxes - should be
considered in per unit cost
• some analysis are done before taxes
• some are done after taxes
– Large businesses pay was about 36% Federal
and 3% state - now 32% Federal 3% State
Calculating Tax Advantage
• $100,000 deduction
– 35% tax rate
– $100,000 * 0.35 = $35,000
– $35,000 in income tax that don’t have to pay
Property Tax and Insurance
• Property Tax is about 2%, Insurance is
about 2%
• Problem is 2% of what?
• Insurance and Property Tax are on the value
of the property - which is changing
• We need an annual cost but its different
every year
• Use what is called “Average Annual
Investment”
Depreciation and Average Annual
Investment
Initial Value for Tax and Insurance
$700,000
$600,000 in
Year 2
Note that average value is not middle value
of $350,000 which occurs at time 3.5 years
(taxes and insurance are based on value at
the beginning of the year)
$500,000 in
Year 3
($700,000 + 600,000 + $500,000 + $400,000 + $300,000+
$200,000 + 100,000)/7 = $400,000
General Formula
(n+1)/2n * Initial Value =
Average Annual Investment
$100,000 in
Year 7
0
1
2
3
4
5
6
7
Apply
(7 + 1)/ (2*7) * $700,000 = $400,000 Average Annual Investment
Taxes Are 2% of Average Annual Investment
$400,000 * 0.02 = $8,000
Insurance is 2% of Average Annual Investment
$400,000 * 0.02 = $8,000
Summing Annual Ownership
Cost
•
•
•
•
•
$168,400 / year from purchase
$16,000 /year in taxes and insurance
-$35,000 / year in tax savings
$149,400 / year in Ownership Cost
$149,400 / 700,000 tons / year = $0.2134
Finishing the Problem
• Ownership Cost/ton = 21.34 cents
• Operating Cost/ton = 20.00 cents
• Total Cost per ton to move rock with the
haul truck is 41.34 cents/ton
• Most Engineering Applications can do a per
unit cost the same way
– Often an analysis of choice in trying to justify
or explain new equipment purchases