Learning Objectives. The Economic Justification of Telecommunications Projects. Describe these concepts

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1 Copyrght 200 Martn B.H. Wess Lecture otes The Economc Justfcaton of Telecommuncatons Projects Martn B.H. Wess Telecommuncatons Program Unversty of Pttsburgh Learnng Objectves Descrbe these concepts Present value Future value Interest Perform smple computatons nvolvng these concepts

2 Copyrght 200 Martn B.H. Wess Lecture otes Defnton Types of cost Cost of a resource s the decrease n wealth that results from commttng ths resource to a partcular alternatve (before benefts from the alternatve are computed) Past vs. future costs Jont costs Drect and ndrect Fxed and ncremental Long and short run Opportunty costs Sunk costs Postponable cost Replacement cost

3 Copyrght 200 Martn B.H. Wess Lecture otes Mathematcs of Money Formulaton Value of money changes wth tme Inflaton causes future dollars to be worth less than today s dollars Investment rsk devalues future dollars proportonately to the rsk Elements Future value (F) Present value (P) Rate () nnuty () - sequence of unform payments If an amount of money (P) were nvested such that t grew at precsely the rate of nflaton () for one tme perod, then F P P P( ) That s, F s the equvalent future value of P For n tme perods, F P() P() P()() Generalzng, F P() n Ths s referred to as the future worth of a present amount

4 Copyrght 200 Martn B.H. Wess Lecture otes Cash Flow Dagrams Cash Flow Seres % % F dollars n future P dollars deposted F P F P P F P F ( ) ( %, ) ( %, ) P dollars deposted F dollars n future

5 Lecture otes Copyrght 200 Martn B.H. Wess Cash Flow Seres Payments of made at regular ntervals Compute [ ] ( ) F F F %, ; / ) ( ) ( ) ( ) ( 2 K Cash Flow Seres Computng P ( ) ( ) P P F F ) ( ) ( and ) (

6 Copyrght 200 Martn B.H. Wess Lecture otes Other Formulatons Present worth of a future amount nnuty of a future amount Future worth of an annuty F n ( ) Spreadsheet Present worth of an annuty P n ( ) n ( ) Spreadsheet nnuty from a present amount n ( ) n ( ) P Spreadsheet ( ) n P F F ( ) n Project Justfcaton Technques et future value (FV) The dfference between the future value of your project and the future value of alternatve nvestments FV F - F * F - P( * ) * s the rate of return of an alternatve nvestment Use money market rates, bond rates, return on equty Internal Rate of Return Rato of the value change and the present value IRR F P P Ths s useful when a mnmum RoR s requred

7 Copyrght 200 Martn B.H. Wess Lecture otes pplcaton of these Concepts Deprecaton Compare the fnancal mplcatons of mplementng the project to not mplementng the project Case : P conssts of The cost of mplementng the project The PV of mantenance costs over the lfe of the project Case 2: Compute the PV of an annuty, where the annuty s the estmated cost of watng, retry behavor, and other productvty decreasng factors Compare PVs Defntons of Deprecaton System of ccountng whch ms to Dstrbute Cost or Other Basc Value of Tangble Captal ssets, Less Salvage Value, Over the Estmated Useful Lfe of a Unt n a Systematc and Ratonal Manner for the Purpose of llocaton (Paraphrased from ICP) Loss n Servce Value ot Restored by Mantenance Due to ormal Wear and Tear, Exposure and Decay, Technologcal Obsolescence, etc. Deprecaton Does ot Involve ctual Cash Outlays

8 Copyrght 200 Martn B.H. Wess Lecture otes Computng Deprecaton Expense Orgnal Cost of Equpment Estmated Servce Lfe of Equpment Estmated et Salvage Value of the Equpment Remanng Value at the End of the Servce Lfe Can Include the Cost of Removal Deprecaton Method Retrement/Replacement ge-lfe Retrement/Replacement Methods ot Wdely Used Because Operatng Expenses Vary Wdely from Year to Year Retrement ccountng Carrys Orgnal Cost untl the Equpment s Retred Full Cost s Charged as an Operatng Expense at Retrement Replacement ccountng Smlar to Retrement ccountng Replacements and Retrements Wthout Replacements are Charged to Operatng Expense

9 Copyrght 200 Martn B.H. Wess Lecture otes ge-lfe Methods ge-lfe Methods Desgned to Provde More Consstent Expense ccounts from Year to Year Straght-Lne Deprecaton Deprecaton Charge s Computed for Each Retrement Perod Draw a Straght Lne Between Orgnal Cost and Salvage Value, and llocate the Dfference over Servce Lfe Deprecaton Charge Orgnal Cost - Salvage Value Servce Lfe ccelerated deprecaton allows hgher deprecaton early n the equpment lfe than straght lne method Sum-of-the-Year s-dgts # Years Remanng at Begnnng of Year Deprecaton Expense x (Orgnal Cost - Salvage Value) Total of the Dgts of the Year s Lfe Subtract from current value (undeprecated value) Repeat next year Double declnng balance Double the deprecaton rate of straght lne Subtract from current value Deprecate remanng balance by straght lne

10 Copyrght 200 Martn B.H. Wess Lecture otes Deprecaton Concepts Cost ($) Comparson of Deprecaton pproaches Cost ($) Orgnal Cost ccrued Deprecaton nnual Deprecaton Charge Orgnal Cost $2M $2M -$00K $.9M $.8M Straght-Lne Sum of the Year s Dgts Double Declnng Balance Current Value Salvage Value Servce Lfe Tme (Years) Salvage Value $500, Servce Lfe Tme (Years)

11 Copyrght 200 Martn B.H. Wess Lecture otes Comments on Deprecaton Revew Sze of deprecaton charge depends on Servce Lfe Salvage value Estmatng both parameters n advance s dffcult Servce lfe must take technologcal and usage factors nto account ctual salvage value depends on costs and prces at the tme of decommssonng Money has tme value Ths value s called nterest Smple nterest Interest s not earned/pad on nterest Compound nterest Interest s computed on prncple as well as accrued nterest

12 Copyrght 200 Martn B.H. Wess Lecture otes Types of Cash Flows Sngle Unform seres Lnear gradent seres Geometrc gradent seres Irregular seres Sngle Studed earler F P(;) FP() % P dollars deposted

13 Copyrght 200 Martn B.H. Wess Lecture otes Unform Constant seres of payments ( ) F F ( F / ; ; [ ] ) pplcatons Snkng Fund- Interest bearng account nto whch money s pad on a regular bass, usually for replacng a fxed asset Captal recovery F dollars n future

14 Copyrght 200 Martn B.H. Wess Lecture otes Lnear Gradent Payment ncreases (or decreases) by a constant amount from perod to perod n (n-)g G 2G 3G 2 3 G Lnear Gradent P 0 n G 2 2 G 3 L ( ) ( ) ( n ) G( ) ( ) G 2 ( ) n ( ) G ( ) G( P / G; ; )

15 Lecture otes Copyrght 200 Martn B.H. Wess Lnear Gradent What s the equvalent unform payment? lso [ ] ) ; ; / ( ) ( ) ( G G G ) ; ; / ( ) ( G F G G F Geometrc Gradent Seres Payments change by a constant percentage over tme, where g s the percent change Ths s also called compound growth Thus, n (g) n- [ ] g g g P P g g ) ( ) ( ) ( ),,, / (

16 Copyrght 200 Martn B.H. Wess Lecture otes Irregular Payments Effectve Interest Rates Brng each payment to the present (or future) dd the values at the same pont n tme omnal nterest rate the rate that s used n computatons Effectve nterest rate nterest rate that s actually experenced Equvalence a ( r M ) M Where r s the nomnal rate and M s the number of compoundng perods

17 Copyrght 200 Martn B.H. Wess Lecture otes Comparng Projects et Present Value (PV) Rate of Return Payback perod et Present Value Data needed Frst cost nnual costs nnual recepts Salvage value Compute the present value of these streams

18 Copyrght 200 Martn B.H. Wess Lecture otes PV Example Whch s Better? Item Swtch Swtch B Consder 8% Frst cost $0,000 $5,000 Item Swtch Swtch B Lfe Salvage nn. Recepts 5 years $2,000 $5,000 0 years $0 $7,000 PV of rcpts PV of salvage Cost Frst cost $5K(P/;8;0) $2K(P/F;8;0) -$2.2K(P/;8;0) -$0,000 $7K(P/;8;0) $0 -$4K(P/;8;0) -$5,000 nnual Costs $2,200 $4,000 Replacement -(0K-2K) (P/F;8;5)

19 Copyrght 200 Martn B.H. Wess Lecture otes Results Rate of Return Item PV of rcpts PV of salvage Cost Frst cost Swtch $33,55 $926 -$4,762 -$0,000 Swtch B $46,970 $0 -$-26,840 -$5,000 Internal Rate of Return What s the nterest rate at whch the PV of the cash nflow equals the PV of the cash outflow? Compare ths to the Mnmum ttractve Rate of Return (MRR) External RR Replacement TOTL -$5,445 $4,270 $5,30 What s the nterest rate that equates the future worth of nvestments to the accumulaton of renvested returns?

20 Copyrght 200 Martn B.H. Wess Lecture otes Example usng IRR Example usng IRR Year Swtch -0,000 2,800 2,800-8,000 4,800 Swtch 2-5,000 3,000 3,000 3,000 Dfference -5, , K PV for the dfference n cash flows: - 5K 200 (P/,,0) 8K (P/F,,5) - 2K (P/F,,0) What s the value of for whch ths equals zero? 2.% Ths s greater than MRR (0%), so the larger nvestment (swtch B) s justfed

21 Copyrght 200 Martn B.H. Wess Lecture otes Rsk n Projects n nvestment project where the cash flows are not known wth certanty Project rsk s varablty n et Preset Worth (or IRR) Rsk s the consequence of uncertanty, and usually mples a potental for loss nalytcal pproaches Senstvty analyss Break-even analyss Scenaro analyss

22 Copyrght 200 Martn B.H. Wess Lecture otes Senstvty nalyss n approach that can be used when some assumptons are questonable Useful n all branches of analyss, not just engneerng economcs Basc pproach Vary model parameters Observe the outcome of the model Determne at what parameter values the dfference n the model outcome becomes sgnfcant ssess whether ths crtcal parameter value s possble or lkely

23 Copyrght 200 Martn B.H. Wess Lecture otes Example Example Postal Servce s consderng purchasng a 4,000 lb forklft truck Fuel alternatves Gasolne LPG Desel Electrc (battery) Whch power source s the better value? ssume 7 year lfe 0% nterest One shft 8 hrs operaton 200 to 260 shfts per year

24 Copyrght 200 Martn B.H. Wess Lecture otes Example Example Fuels Gasolne:. gal per shft, $.20/gal LPG: gal/shft, $.02/gal Intal Salv. Gas` $20,07 $2000 LPG $2,200 $2000 Desel $22,263 $2200 Elec. $29,739 $3000 Desel: 7.2 gal/shft, $.3/gal Electrc: 3.25kWh, $0.05/kWh Fuel/shft Fuel cost. gal $.20 gal $ gal $ kwh $0.05 Fuel/shft $3.32 $.22 $8.4 $.56 Mant./yr $000 $000 $000 $500 Var./shft $7 $7 $7 $4.5

25 Copyrght 200 Martn B.H. Wess Lecture otes Computatons Fnd annual costs for each alternatve: Gasolne: $20,70(/P,0%,7)- $2000(/F,0%,7) $3,99 LPG: $2,200(/P,0%,7)- $2000(/F,0%,7) $4,44 Desel: $22,263(/P,0%,7)- $2200(/F,0%,7) $4,34 Electrc: $29,739(/P,0%,7)- $3000(/F,0%,7) $5,792 Computatons nnual operatng costs Gasolne: $000 (3.327)M LPG:$000 (.227)M Desel: $000 (8.47)M Electrc: $500 (.564.5)M

26 Copyrght 200 Martn B.H. Wess Lecture otes Computatons Total Equvalent nnual Costs Gasolne: $499$20.32M LPG:$544$8.22M Desel:$534$5.4M Electrc: $6292$5.06M Plot the Lnes $ umber Of Shfts