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Valuation: capital & discount rate

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.

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Valuation: capital & discount rate

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

  2. 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

  3. Cons in P1 C2 C0 Cons in P0 Interest rate in 1st best world Opportunity cost of cons - today is loss of available cons next year (MRT)

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

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

  6. 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)

  7. 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

  8. The Present Value-criterion Thus: Discounting: calculate the equivalent of C1 in period 0 (C0) (calculated along indifference curve: i.e. consumer is indifferent)

  9. The Present Value-criterion • cons. • project rule

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

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

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

  17. 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

  18. Shadow Price of Capital Shadow price (SPC): In 1st best world: i=r and Vt=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)

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

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

  21. 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)

  22. Shadow Price of Capital SRTP still good choice for case 1 and when relying on global capital market Empirical estimates • SPC or Vt [ 2.5 - 3.5 ] • SRTP [ 2.0 - 5.5 ] Reasonable approx: rate on government bonds of the same length as project

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