The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

Present Value

  • Stephen F. LeRoy
Living reference work entry

Later version available View entry history

First Online:
Received:
Accepted:
DOI: https://doi.org/10.1057/978-1-349-95121-5_1387-1
How to cite

Abstract

The present-value relation says that, under certainty, the value of a capital good or financial asset equals the summed discounted value of the stream of revenues which that asset generates. The discount factor will be that determined by the interest rate over the relevant period. The justification for the present-value relation lies in the fact that (in perfect capital markets) an asset must earn a rate of return exactly equal to the interest rate; otherwise arbitrage opportunities emerge, which is inconsistent with equilibrium. Thus if r t is the one-period interest rate at t, p t is the (ex-dividend) price of an asset and d t is its dividend, it must be true that
$$ {r}_t=\left({d}_{t+1}+{p}_{t+1}\right)/{p}_t-1 $$
since the right-hand side equals the rate of return on the asset. Solving for p t ,
$$ {p}_t=\left({d}_{t+1}+{p}_{t+1}\right)/\left(1+{r}_t\right). $$
Replacing t by t + 1, (2) becomes an equation expressing p t+1 as a function of r t+1, d t+2 and p t+2.

Keywords

Interest Rate Asset Price Discount Factor Mutual Fund Spot Price 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Bibliography

  1. Fama, E.F. 1970. Efficient capital markets: A review of theory and empirical work. Journal of Finance 25: 383–417.CrossRefGoogle Scholar
  2. Fama, E.F. 1976. Reply. Journal of Finance 31: 143–145.Google Scholar
  3. Krouse, C.G. 1985. Competition and unanimity revisited, again. American Economic Review 75: 109–114.Google Scholar
  4. LeRoy, S.F. 1973. Risk aversion and the martingale property of stock prices. International Economic Review 14: 436–446.CrossRefGoogle Scholar
  5. LeRoy, S.F. 1976. Efficient capital markets: Comment. Journal of Finance 3: 139–141.CrossRefGoogle Scholar
  6. LeRoy, S.F. 1982. Expectations models of asset prices: A survey of theory. Journal of Finance 37: 185–217.CrossRefGoogle Scholar
  7. LeRoy, S.F. 1984. Efficiency and the variability of asset prices. American Economic Review 74: 183–187.Google Scholar
  8. LeRoy, S.F., and R.D. Porter. 1981. The present-value relation: Tests based on implied variance bounds. Econometrica 49: 555–574.CrossRefGoogle Scholar
  9. Lucas Jr., R.E. 1978. Asset prices in an exchange economy. Econometrica 46: 1429–1445.CrossRefGoogle Scholar
  10. Ohlson, J. 1977. Risk aversion and the martingale property of stock prices: Comment. International Economic Review 18: 229–234.CrossRefGoogle Scholar
  11. Samuelson, P.A. 1965. Proof that properly anticipated prices fluctuate randomly. In Collected scientific papers of Paul A. Samuelson, vol. 3, ed. R.C. Merton, 782–790. Cambridge, MA: MIT Press, 1972.Google Scholar
  12. Samuelson, P.A. 1973. Proof that properly discounted present values of assets vibrate randomly. Bell Journal of Economics and Management Science 2: 894–896.Google Scholar
  13. Shiller, R.J. 1979. The volatility of long-term interest rates and expectations models of the term structure. Journal of Political Economy 87: 1190–1219.CrossRefGoogle Scholar
  14. Tirole, J. 1985. Asset bubbles and overlapping generations. Econometrica 53: 1071–1100.CrossRefGoogle Scholar

Copyright information

© The Author(s) 1987

Authors and Affiliations

  • Stephen F. LeRoy
    • 1
  1. 1.