1. Discounting Intro/Refresher H. Scott Matthews 12-706 / 19-702 / 73-359 Lecture 2a

2. Project Financing zRecall - will only be skimming this material in lecture - it is straightforward and mechanical yEspecially with excel, calculators, etc. yShould know theory regardless yShould look at problems in Schaum or Au and ensure you can do them all on your own by hand before doing them in Excel

3. Common Monetary Units zOften face problems where benefits and costs occur at different times zNeed to adjust values to common units to compare them

4. Compounding (Future Value Method) zBuy painting for $10,000 yWill be worth $11,000 in one year (sure) yNeed to consider ‘opportunity cost’ yMake table or diagram of streams of benefits and costs over time zHave several analysis options yPut $10,000 in savings, would earn simple interest (8% annual rate): so $10,000*(1.08)=$10,800 ySo should you buy the painting?

5. Decision Rules zAs always, should choose option that maximizes net benefits yNow we are using that same rule with values adjusted for time value of money yStill choose option that gives us the highest value yIn this case it is ‘buying the painting’ yCalled ‘future value’ when you compound current value to future

6. Alternative - Present Value zDo the problem in reverse yTime - line representation (see Schaum or Au) yHow much money you would need to invest in savings to get $11,000 in 1 year yFV=$10,000*(1+i) : $10,000 was ‘present’ y ySince greater, should buy painting xHas lower investment cost of $10k yLast option - convert all to present value

7. Net Present Value Method zCurrent investment of $10,000 for painting represented as -$10,000 zReceipt of $11,000 in a year as = $10,185 zSo NPV= -$10,000 + $10,185 = $185 zSince NPV positive, should buy painting (it has positive net benefits)

8. General Terms zThree methods: PV, FV, NPV zFuture Value: F = $P (1+i) n y P : present value, i:interest rate and n is number of periods (eg years) of interest yUsually referred to as (F|P,i,n) yRule of 72 zPresent Value: yUsually referred to as (P|F,i,n) zNPV=NPV(B) - NPV(C) (over time)

9. Rates to Use for Analysis zIn example, investments vs. savings yWe assumed an actual option for rate zBut can use any rate to discount FV! yCalled a “discount rate” - may be set for us zMARR: opportunity cost of funds zAssume all values ‘real’ unless stated otherwise

10. Minimum Attractive Rate of Return zMARR usually resolved by top management in view of numerous considerations. Among these are: yAmount of money available for investment, and the source and cost of these funds (i.e., equity or borrowed funds). yNumber of projects available for investment and purpose (i.e., whether they sustain present operations and are essential, or expand present operations)

11. MARR part 2 yThe amount of perceived risk associated with investment opportunities available to the firm and the estimated cost of administering projects over short planning horizons versus long planning horizons. yThe type of organization involved (i.e., government, public utility, or competitive industry) zIn the end, we are usually given MARR zCompanies: maybe 20% zPublic: usually more like 5%

12. Other Issues zInflation hard to predict yTend to use historical trends/estimates zTerminal or residual values yValue of equipment at end of investment zTiming - typically assume beginning of period values, not end of period

13. Ex: The Value of Money (pt 1) zWhen did it stop becoming worth it for the avg American to pick up a penny? zTwo parts: time to pick up money? yAssume 5 seconds to do this - what fraction of an hour is this? 1/12 of min =.0014 hr zAnd value of penny over time? Assume avg American makes $30,000 / yr yAbout $14.4 per hour, so.0014hr = $0.02 yThus ‘opportunity cost’ of picking up a penny is 2 cents in today’s terms

14. Ex: The Value of Money (pt 2) zIf ‘time value’ of 5 seconds is $0.02 now yAssuming 5% long-term inflation, we can work problem in reverse to determine when 5 seconds of work ‘cost’ less than a penny zUsing Excel (penny.xls file): yAdjusting per year back by factor 1.05 yValue of 5 seconds in 1993 was 1 cent zBetter method would use ‘actual’ CPI for each year..

15. Annuities zConsider the PV (aka P) of getting the same amount ($1) for many years yLottery pays $A / yr for n yrs at i=5% y----- Subtract above 2 equations.. ------- ya.k.a “annuity factor”; usually listed as (P|A,i,n)

16. Perpetuity (money forever) zCan we calculate PV of $A received per year forever at i=5%? z zP*(1+i)-P=A zP*(i)=A => P/A = 1/i zE.g. PV of $2000/yr at 8% = $25,000 zWhen can/should we use this?

17. Reciprocal Nature of Capital Factors

18. Sample Problems zExample: know how to do these problems without calculators, if given factors.