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

2. 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

3. 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

4. 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?

5. Herby Builds a Cash Flow $650 Rent $650 Deposit $650 Rent$730 Rent $650 Deposit Refund 0 1 2 3 4 5 6 7 854 55 56 57 58 59 60 61 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?

6. 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

7. 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

8. 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?

9. 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?

10. 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 = 0.00667  Plug and Crank  { 1.00667 180 * 0.00667}/{1.00667 180 -1} = 0.009559  $25,200 * 0.009559 = $240.88/month

11. 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 * 0.015 = $378  Loan amount is $25,578

12. Get Our Monthly Payments  What is n (30 year loan) n= 360  Watch out for i compounding period mismatch trick  6.25%/12 = 0.0052083  Plug and Crunch  A/P 0.0052083, 360 = 0.006157  $25,578 * 0.006157 = $157.49

13. Some Initial Statistics  Action Up Front Cost Monthly Cost  Rent $1,300 $650  Buy with US $3,535 $240.88  Buy with IYP $4,060 $157.49  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?

14. Building some cash flows ………………………... 0 1 2 3 4 5 6 7 8 9 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)