Question

Choose values of r=4%, i=3%, p=1.5%, a=0.4 and b=0.2 and provide an estimation of the weighted opportunity of capital. When would you choose this discount rate?

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Answer 1

Well, looking at the components in the question, I can say one thing for sure that this is the question for calculating Weighted Social Opportunity Cost of Capital. However, it seems like the word 'social' has been missed out on. This is anote for clarification. I have solved the question for you below:

Weighted opportunity of capital, also called Weighted Social Opportunity Cost of Capital (WSOC) - It calculates the social discount rate as weighted average of r_z, p_z, and i. It can be calculated using the following formula:

WSOC = ar_z + bp_z + (1 - a - b)i

where, a = the proportion of a project's resources that displace private domestic investment
          b = the proportion of the resources that displace domestic consumption
   (1-a-b) = the proportion of the resources that are financed by borrowing from foreigners
          i = government’s real long-term borrowing rate
          r_z = represents the marginal rate of return on private investment (This is the sacrificing consumption this year to yield more income next year)
          p_z = represents the marginal rate of time preference (It is the proportion of additional consumption that an individual requires in order to be willing to postpone consumption for one year)

Therefore,

r_z = 4%
i = 3%
p_z = 1.5%
a = 0.4
b = 0.2

WSOC = ar_z + bp_z + (1 - a - b)i    
           = 0.4(.04) + 0.2(0.015) +(1-0.4-0.2)*0.03
           = 0.031
           = 3.1%

This is useful for Least Developed Countries who are resorting to foreign borrowings. This is because - resources can come from foreign borrowings, domestic investment or government investment and economists have proposed that the social discount rate should be calculated in terms of social opportunity cost of different sources according to the relative contribution of each source.