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

$700,000

0 1 2 3 4 5 6 7

Initial Value for Tax and Insurance

$600,000 inYear 2

$500,000 inYear 3

$100,000 inYear 7

Note that average value is not middle valueof $350,000 which occurs at time 3.5 years(taxes and insurance are based on value atthe beginning of the year)

($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

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