Research Seminar Archive
Mark Freeman (Bradford School of Management): Far horizon discount rates
Economics and Finance Research Seminar.Abstract
The UK Treasury’s guidance on capital budgeting for the public sector recommends that lower social discount rates should be applied at very far horizons compared to shorter maturities. This is consistent with the low cost of capital applied in the Stern Review on the economics climate change. This paper extends this analysis by demonstrating that, when logarithmic returns are independently and identically normally distributed, very far horizon costs of equity capital should also below their short-term equivalent counterparts. I prove that, for any horizon the appropriate equity discount rate can be expressed as a weighted mean of the arithmetic and geometric averages of historic returns. The algebraic expressions for the weights are surprisingly complex functions of the length of available historical data, T, and the cash flow horizon, H. By calibrating the model using UK and broader international data I show that for maturities under a century, the appropriate cost of capital is only marginally dependent on the cash flow horizon. However, for very long-term projects, such as nuclear decommissioning and certain environmental programmes, the effects are of economic significance. The resulting discount rate term premia are of similar magnitudes to those recommended by the Treasury.