The All Cost Alternatives Problem ©2002 Dr. Bradley C. Paul

Types of Problems  We’ve met Invest and Earn  Objective is to find whether a single cash flow meets an earnings of objective  Usually is Rate of Return high enough - do NPV  Sometimes concerned about a future accumulation of money - do NFV  Some Problems require expenditures  Decision is already made to do something  Objective becomes to find most cost effective

All Cost Alternatives  Engineers design something - sales markets  engineers see only cost side  Environmental Laws  an investment is required as a condition of doing business  In Personal Life you have basic needs  must meet them as a condition of being able to function productively

Some Events in Both Personal and Business Life are Measured by the Cost of Something Needed, Rather than by Profit  Example - Herby Housing needs a place for his family to live while he goes to school at SIU. Herby is debating whether to rent an apartment or buy a house (he has military benefits and his wife Hanna will be working). Herby finds that the cost of renting will be $650/month. Herby does some house shopping and finds he can get a house in DeSoto for $28,000. Herby expects to take 5 years for school and wants to know what his housing is really going to cost?

Herby Builds a Cash Flow $650 Rent $650 Deposit $650 Rent$730 Rent $650 Deposit Refund Cash Flow for Renting Scenario Herby assumes rent will go up $20/year with inflation The NPV of this cash flow will surely be negative - does that mean no go?

Herby Studies Buying  The house will cost Herby $28,000. (Herby will finance that)  Herby needs a 10% down payment $2,800  Herby discovers that there are “Closing Costs” when you buy a house  Appraisal fee $250  Flood Determination Letter $150  Credit Report $25  Dead Registration $15  Mortgage Registration $15  Private Mortgage Insurance $280

Herby’s first time home buyers adventure continues  Herby will need to get Home Owners Insurance $600/year  Herby discovers that banks also like to charge their little “fees” for starting up a loan  Herby can get a local loan from Union Shafters Bank  Union Shafters will simply recover closing costs  Union Shafters will charge 8% annual interest compounded monthly over 15 years  Herby could also get a loan over the internet from Inter Your Pocket Mortgage Lenders  5% of face amount loan initiation - covers all closing costs  1.5 points (rolled into the mortgage)  6.25% annual interest compounded monthly over 30 years

Herby Compares Loans  Union Shafters  Closing Costs $735  Down Payment $2,800  Needs $3,535 now  Mortgage Payments  Loan Amount $28,000 - $2,800 (down payment) = $25,200  Loan over 15 years at 8% interest - How do I get the Payments?

Enter Our Super Hero  I need to convert a present value amount into an annuity  A/P * Present Loan = Annuity of Loan Payments  cancellation of units checks out  What is the value of n?  15 years * 12 months/year = 180  What is the value of i?

Oh NO You Don’t We is smart students. We know that interest rate did not match the compounding period.  Annual interest is 8%  But it is compounded monthly  Get the monthly rate  8%/12 =  Plug and Crank  { * }/{ } =  $25,200 * = $240.88/month

Now Check Out the Internet Bank  Loan Amount $25,200  5% initiation fee $25,200*0.05 = $1,260  Whats this point business  Lenders discount interest rate on the loan for an up front payment of a percentage of the loan amount. A point is a catchy way of saying what percent of the loan amount they will charge (they often roll it into the loan)  $25,200 * = $378  Loan amount is $25,578

Get Our Monthly Payments  What is n (30 year loan) n= 360  Watch out for i compounding period mismatch trick  6.25%/12 =  Plug and Crunch  A/P , 360 =  $25,578 * = $157.49

Some Initial Statistics  Action Up Front Cost Monthly Cost  Rent $1,300 $650  Buy with US $3,535 $  Buy with IYP $4,060 $  Buying is looking really good right now except for those scary up front costs.  Which loan should Herby get if he does buy the house?

Building some cash flows ……………………… Resell the House Interest is tax deductible but the loans have different interest rates Loans have different terms so one loan will be more paid-off when the house sells (they will build “equity” faster) 69 months (assumed takes 9 months to sell house)