Wednesday, February 23, 2011

CHOICE OF NUMERAIRE

All benefits and costs have to be converted into a common unit of account or numeraire. The traditional approach is to take consumption measured at domestic market prices as numeraire. By contrast, Little and Mirrlees take the savings contribution of the project as the objective and accordingly take as numeraire what they call ' uncommitted social income , measured at border prices (or free foreign exchange in the hands of government). Clearly the numeraire taken will have a bearing on the estimation of the Net Present Value formula.
To evaluate NPV we first find the value of benefit flow Vt as shown from the  equation (1). Conventional approach is considered (as UNIDO guidelines). Annual flow of social benefit is measured in consumption stream in domestic currency. If Little Mirrlees approach is considered we take the value of benefit as the projects cash flow valued at world price with future consumption revalued in terms of saving. Both the approaches give the same result as to the price of investment in terms of consumption.
Since income and consumption are expected to rise over the time we discount future benefits and costs with their aggregates as;
Bt = B0 + V1 B1 + ... +VT BT   ...         ...         ...         (2)
Where the weights attached to future consumption streams, V1 , ...   ...  ..., VT  , decline over time. The weights V1 , ...   ...  ..., VT   are discount factors.
If weights decline over time at a constant percentage rate (r), then it can be shown as,
B* = [Bt / (1+ r)t]            ...         ...         ...         (3)

Where r = social discount rate.
If the Little-Mirrlees approach is taken future benefits and costs should not be discounted by the so-called consumption rate of interest (CRI) but by the rate at which the marginal utility of public saving falls, since public saving expressed in foreign exchange is the numeraire and this rate is called accounting rate of interest (ARI) which is equal to rate of return on public money. Hence project with positive net present value at this rate should be chosen. In Little-Mirrlees ARI is determined by a process of trial and error such that its value does not pass more projects as profitable than the investment budget allows.
If investment is totally done on consumption the social investment cost is measured by the current sacrifice of consumption, if it is numeraire.
If investment of one project is partly of another then a part of cost of the sacrifice of consumption is deferred until the time displaced investment would itself have yielded consumption.

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