Valuation: capital & discount rate (Cost Benefit Analysis DEC 51304) R. Jongeneel Z&D Ch.3 and 13

Lecture Plan  Interest rate in 1st best world  The present value criterion  Ethical basis for discounting  Economic growth rate  Discount rate in 2nd best world  Shadow price-approach

Interest rate in 1st best world C0C0 C2C2 Cons in P 0 Cons in P 1 Opportunity cost of cons - today is loss of available cons next year (MRT)

Interest rate in 1st best world Transformation curve (PPC) MRT = P0/P1 = MOCR + 1

Interest rate in 1st best world Transformation curve (PPC) MRT = MRS MRTP = MOCR C0 C1 Indifference curve

Interest in 1st best world  MRT is equal to marginal opportunity costs of capital (MOCR) plus 1  Efficiency: MRTPs for all consumers equal  social rate of time preference (SRTP)  SRTP=SOCR (social opp.cst of capital)

Interest rate in a 1st best world  Relevant interest rate = called discount rate  In 1st best world economy the correct discount rate for B/C-analysis is just the market rate

The Present Value-criterion Thus: Discounting: calculate the equivalent of C 1 in period 0 (C 0 ) (calculated along indifference curve: i.e. consumer is indifferent)

The Present Value-criterion  cons.  project rule

Ethical basis for discounting  “Veil of ignorance”-principle  choose a discount rate before knowing to what generation you will belong to  positive discount rate implies placing more value on 1 euro in the present generation than 1 euro in a future generation

Economic Growth Rate  Discount rate effects investment level  Investment level determines economic growth rate  What proportion of GNP should be saved?  Optimal growth path (max cons): marginal return to capital should equal the growth rate of the economy due to technical change

Discount rate in 2nd best world  Economy is economy with taxes  Assume: corporate profit tax 36% marginal income tax 27% MRTP 8%  Before-tax rate should be 10,9% to end up with 8% after (8 / (1 – 0.27) = 10.9)  Corporation must earn 17% before taxes

Discount rate in a 2nd best world  In a 2nd best world (tax) the choice for a discount rate is no longer obvious  Wedge between rate of return and MRTP causes biases (underinvestment, favors short-term projects)  Debate: MRTP-rate: trade present cons. for future cons. OCR-rate: public investment displaces private investment

Discount rate in 2nd best world But…. SRTP (or MRTP)-approach not yet takes into account displacement of private investment Solution: adjust for OCR-effect NEW: shadow price approach

Shadow Price of Capital Trick: express both benefits and costs of an investment in consumption terms Total capital: K(t)=K(0)e srt sr: growth factor s: fraction of proceeds reinvested r: private rate of return (OCR) i: social rage of time preference (SRTP)

Shadow Price of Capital Consumption: (1-s)* net capital income Present value (general rule) Thus:

Shadow Price of Capital Total cons. stream with s. r < i (necessary cond.) Simplifies to Present value of the consumption from €1 of private investment Shadow price of private capital

Shadow Price of Capital Shadow price (SPC): In 1st best world: i=r and V t =1 Rationale: convert all benefits and costs to consumption equivalents and discount by the social rate of time preference (shadow price of private capital SPC)

Shadow Price of Capital (optional) : fraction of public spending that displaces private spending costs benefits

Shadow Price of Capital (optional) Fundamental present value equation for B/C-A in a 2nd best world with F B and F C conversion terms

Shadow Price of Capital (optional) Case 1: (multiplier affects size but not sign) Case 2: (all benefits go to private capital) Case 3: (all costs from private capital)

Shadow Price of Capital SRTP still good choice for case 1 and when relying on global capital market Empirical estimates  SPC or V t [ ]  SRTP [ ] Reasonable approx: rate on government bonds of the same length as project