Lecture # Cost-Benefit Analysis

Transcription

1 Lecture # Cst-Benefit Analysis I. Steps t Cst-Benefit Analysis (cntinued) 4. Discunting The csts and benefits will ccur at different times. T cmpare them fairly, it is imprtant t discunt csts and benefits that ccur in the future. The idea is t cmpare a flw f benefits and csts int a single value. The present value f a future amunt f mney is the maximum amunt yu wuld be willing t pay tday fr the right t receive that mney in the future. Present value accunts fr the pprtunity cst f nt investing the mney elsewhere. Example: Yu have $100 nw If yu put it in the bank, yu will get 5% interest Next year, that mney is wrth ( )x100 = $105 After tw years, it is wrth (1.05)(1.05)(100) = (1.05) 2 (100) = $ General rule: PV = present value (the principal that yu invest) r = interest rate Future Value = FV = PV(1 + r) t As a result, yu wuldn t give up $100 nw fr $100 next year, because yu culd invest the mney and get $105 next year. The present value f $100 next year is the mst yu wuld give up tday t get $100 next year FV = $100 = PV(1.05) = $100 PV = 100/1.05 = $95.24 General rule PV = FV/(1 + r) Fr a stream f payments: PV = FV + FV/(1+r) + FV/(1+r) FV/(1+r) t Fr payments frever: PV = FV/r

2 What abut inflatin? When we are discunting csts & benefits, we must remember that inflatin affects the interpretatin. The key is t be cnsistent. If all the dllar values are real dllars already adjusted fr inflatin use a real rate f interest. If all the dllar values are nminal dllars we need t adjust fr inflatin. We use a nminal rate f interest. Recall ur example frm befre. Suppse inflatin is 3%. Then, $105 next year is nly wrth 105/1.03 = $ tday. The present value nw is 100(1 + r) = $ This implies a rate f return f apprximately 2%. Inflatin lwers the real return n ur investment. Fr thse interested in the derivatin f the real rate f return, define the fllwing terms: r = real rate f interest γ = rate f inflatin m = nminal rate f interest the nminal return (1 + m) = (1 + r)(1 + γ) = 1 + r + rγ + γ => m = r + rγ + γ r r = (m - γ)/(1 + γ) In practice, rγ is very small, s a useful apprximatin is: m = r + γ r r = m - γ E.g. nminal rate = 5%, inflatin = 3% => real rate = 2% Key pint: if nminal prices are used, discunt using a nminal rate f interest, s that inflatin is accunted fr. If real prices are used, inflatin has already cnsidered. A nminal rate wuld duble cunt inflatin. Therefre, use a real rate f interest. In general, the real rate f interest will be arund 3-5%. In the next class we will discuss mre carefully hw t select the discunt rate. What abut capital? Since we are discunting, the cst f capital shuld be included in the year the capital is purchased. Depreciatin is nt necessary. The full cst is already cnsidered when the cst f purchasing the capital is recrded. Adding depreciatin wuld lead t duble cunting. Hwever, if the capital is nt cmpletely used, the salvage value shuld be added as a benefit at the end f the prgram.

3 5. Interpreting the Results Once ur calculatins are cmplete, hw d we interpret the final results? There are several alternative criteria. 1. Net present value (NPV) the present value f benefits minus the present value f csts If NPV is psitive, the prject is wrth ding. If several prjects are under cnsideratin, chse the ne with the highest NPV. Advantage: nt sensitive t whether smething is recrded as a cst r a benefit. 2. Benefit cst rati the rati f the present value f a stream f benefits t the present value f the stream f csts. A prject is acceptable if BC rati > 1. Prblems Sensitive t whether items are recrded as csts r benefits. Des nt take the scale f the prject int accunt. 3. Internal Rate f Return the discunt rate that wuld make a prject s net present value equal zer. A prject is wrthwhile if the IRR is greater than the pprtunity cst f funds fr the cmmunity (that is, the apprpriate discunt rate). Prblem: Desn t accunt fr the size f the prject As a result f all f this, NPV is the best methd t use. The interpretatin f net present value (NPV) depends n the situatin. Key questins: 1. Are there several prjects being cnsidered? If nt, the prject is acceptable if the NPV is psitive. If there are several alternative prjects, chse the ne with the highest NPV.

4 2. Des the cmmunity budget limit the size f the prject? If s, chse the cmbinatin f prjects that maximize net benefits, given the cmmunity's budget cnstraints. Example: Csts Benefits Net Benefits Benefits/Csts Prject A Prject B Prject C Prject D Prject E In this case, if there is n cnstraint, chse A, B, C & D If there is a cnstraint, find the best cmbinatin Fr example, cnsider a $10 budget Chsing A, C, & D give a net benefit f $15, whereas B alne nly gives net benefit f $12. A nte n the benefit-cst rati This is an example f hw the benefit/cst rati desn't select the prject with the highest NPV. NPV is highest fr B, but the benefit/cst rati is highest fr A. Hwever, when we face a budget cnstraint, the benefit/cst rati helps us identify the prject that has the mst "bang fr the buck." 3. Can the scale f the prject be varied? If s, chse the size where marginal benefits = marginal csts.

5 II. Which Discunt Rate t Use? We didn't cver all f this material tday, s I'll spent a few minutes n this at the start f class n Wednesday. My cmplete ntes n the subject are belw. The discunt rate reflects the relative value a persn places n future cnsumptin cmpared t current cnsumptin. Lwer values shw a greater preference fr future cnsumptin. If yur discunt rate is greater than the interest rate, yu will be willing t brrw mney. A high discunt rate says that current cnsumptin is imprtant t yu. If yur discunt rate is lwer than the interest rate, yu will be willing t lan mney. A lw discunt rate says that future cnsumptin is imprtant t yu. Since the market interest rate reflects an equilibrium f lenders and brrwers, we can use the market interest rate as a measure f the discunt rate. Why the discunt rate matters Discunting affects the value placed n future benefits and csts. Higher discunt rates place less imprtance n future returns. In particular, discunting can affect the desirability f lng-term prjects As a practical matter, this is nt a big issue fr shrt-term prjects (e.g years). Hwever, fr prjects with benefits ver several generatins, such as climate change, discunting will place very little weight n future benefits. Hwever, there are several market interest rates. Which shuld we use? Typically, ecnmists use a risk-free rate. Investrs lking fr a safe return invest in U.S. Treasury bills. Thus, the return n T-bills is a measure f the nminal risk-free rate. After subtracting inflatin, the real risk-free rate is typically arund 3%. T purchase assets that are riskier, investrs need t be cmpensated with a higher rate f return. This additinal return is knwn as a risk premium. Anther alternative is t use a market rate f return. If the funds cme frm firms, the befre tax rate f return is the pprtunity cst. Hwever, if the funds cme frm private investrs, the after-tax rate f return is the pprtunity cst. In the U.S., this is typically arund 7%. Nte that this rate varies by cuntry, and may be higher in cuntries with riskier investment climates. Since gvernment prjects use bth types f funds, an alternative is t use an average f bth rates.

6 Might the scial discunt rate deviate frm the market rate? The abve estimates use market data t determine the discunt rate. Are their reasns t believe that the market rate is flawed? Sme ecnmists argue that the pprtunity cst f fregne future cnsumptin might differ frm the pprtunity cst revealed in the markets. Fr example, lng term prjects invlve benefits r csts fr future generatins. Hwever, future generatins are nt represented in the market. In this case, it might make sense t use a scial discunt rate which is lwer than the rates bserved in the marketplace. What des the gvernment d? Occasinally n discunting is used. Ex. Cngressinal budget planning Risk-free rate (T-bill rate) This is the mst cmmnly used discunt rate by gvernment ecnmists. Because it is a lw rate, its use tends t favr gvernment spending. A prblem ccurs if, when cmparing tw ptins, ne is riskier. Using a risk-free rate favrs the riskier prject. Market rates Federal agencies are required t perfrm CBA in justificatins fr prpsed public investments and regulatins. The Office f Management and Budget directs agencies t use a 7% real discunt rate. This rate apprximates the marginal pre-tax rate f return in the private sectr. Scial discunt rate A lwer, scial discunt rate is used fr scial plicy analysis ver lng perids f time. Used because high rates place little weight n the utility f future generatins. General Accunting Office recmmends using lw discunt rates when analyzing plicies with large intergeneratinal effects invlving human life.