Discount rates for long-term projects: the cost of capital and social discount rate compared

Abstract

Research on the cost of capital and on the social discount rate (SDR) has developed largely along separate paths. This paper offers an overview and comparison of both concepts. The consumption-based theory of discount rates is common to both, but there are striking differences in how the cost of capital and SDR are estimated. A project's cost of capital is inferred in practice from market data, by a well-established package of techniques, and project risk makes a large difference. In contrast, the SDR is estimated by applying judgement about the welfare of future generations, in the setting of consumption-based theory. Project risk has tended to be ignored under the SDR approach.

Keywords:

• cost of capital
• social discount rate
• consumption-based theory
• risk premium
• declining discount rate

JEL Codes:

• G31
• H43
• G12

Acknowledgements

I am grateful to Mark Freeman, Ian Hirst, Angelica Gonzalez, seminar participants at Heriot-Watt University and the University of Glasgow, and, especially, two anonymous referees and the Editor, Chris Adcock, for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. See Armitage (2005), Danthine and Donaldson (2005), or Gollier (2013), for fuller expositions, all relatively accessible in terms of mathematics.

2. See Ramsey's Equations (3) and (9); also Dasgupta (1982). Ramsey assumes non-increasing marginal utility, but does not specify a utility function.

3. In the derivation of the standard CAPM, the individual's existing consumption at date t comes entirely from the payoff from her holding of the market portfolio, so risk means positive covariance with the market portfolio.

4. Lind's (1982) review of the SDR draws attention to this question, but the question has since been somewhat ignored in both the finance and SDR literatures.

5. In fact, the correlation between returns on the stock market and growth of consumption per head is 0.2 at most, and the standard deviation of annual returns on the market is about 17% (US data; Cochrane 1997). This gives cov(r_j, g) = (0.2)(0.17)(0.02) = 0.07% instead of σ² = (0.02)² = 0.04%.

6. In addition, Weitzman (2007a, 2007b) shows that, if g_τ is assumed to have a distribution with fatter tails than the normal distribution, the possibility of ‘disaster states of the world’ is increased, which reduces the implied risk-free rate.

7. See, for example, Graham and Harvey (2001), for survey evidence of company practice. For much more detail about implementation than appears here or in a textbook, see the documentation published by utility regulators and their advisers (for example, NERA 2009).

8. The judgement involves ethics in that it directly involves taking an explicit view about how much the welfare of people in the future matters compared with the welfare of people today. The finance approach is to accept the ‘view’ about intergenerational welfare that is implicit in market data.

9. Dasgupta (2008) and others argue that, in the absence of ‘market imperfections’, society will maximise its lifetime utility and the social discount rate will be equal to the market rate of return on investment (ROI). His conception of market imperfections includes the existence of externalities which are not reflected in the rate of ROI. There are more conventional types of market imperfection which might also make it difficult to infer from market data the revealed preferences of the current population regarding social decisions, including taxes and poor information on the part of the population.

10. Assuming a constant ROI. The trust would reduce the interest rate if there were diminishing returns on investment. With a constant ROI, r_F = ROI, otherwise the rate of saving would not be optimal. The growth rate in the Ramsey model is then g = (ROI − δ)/η. The trust's activities imply a lower δ or η for society than would prevail without the trust, and a higher saving rate and growth rate.

11. There is no established method of estimation from private sector data, that is, no equivalent to the practical finance package. Earlier literature does consider which private sector rate of return, or average of such rates, to use in estimating the SDR. The main issue was not risk, but the fact that the (pre-taxes) rate of return on private investment is higher than the (after-taxes) rate on individual saving. Recent reviews, for example, Gollier (2013), Dasgupta (2008), and Weitzman (2007a), almost ignore tax.

12. Stern (2008, 13–14) does argue that a close-to-risk-free rate is relevant for projects to reduce carbon emissions, but on the questionable grounds that they are ‘likely to be financed via the diversion of resources from consumption (via pricing) rather than from investment’.

13. Aspects of the implementation of the Gollier (2002a) and Weitzman (1998) models are reviewed in Groom et al. (2005).