Question

We discussed some of the theoretical aspects of the social discount rate (r) in class. The benchmark for cost-bene t analysis by the public sector was set by the O ce of Management & Budget (OMB) in 1992 to 7%. However, Obama's Council of Economic Advisers questioned this (see the policy paper posted under additional reading). In the 1970s, the OMB used 10%, and then lowered it in the 1980s to 8%. In the 1950s, the Army Corps of Engineers used a discount rate of 2.5%.

In 1965, the economist Kenneth Boulding testi ed before the Congressional Subcommittee on Irrigation & Reclamation and recited a poem regarding the issue:

The long-term interest rate
Determines any project's fate:
At 2 percent the case is clear,
At 3 percent some sneaking doubts appear, At 4 percent it draws its nal breath, While 5 percent is certain death.

4

Boulding's lyrics suggest that the discount rate (r) a ects whether a project will be approved that is, whether P V (B) > P V (C) or not. Answer the following questions about the discount rate and its a ects on cost-bene t calculations.

(a) Consider a project that costs $12 million initially, but then after 10 years (t = 10), it has a (one-time) bene t of $24 million. Use three of the above-mentioned discount factors 2.5%, 7%, and 10% to demonstrate Boulding's point. Under which discount factors would the project be approved?

(b) Since the costs of projects are typically incurred in the earlier years of a project (while the bene ts typically last into the future), how might an increase in the discount rate a ect NPV calculations? Demonstrate your reasoning using the project values in Table 2 and the three discount rates used in the previous question (2.5%, 7%, and 10%). How do the P V (B) and P V (C) change with over the three di erent discount rates?

Table 2: Project Costs and Benefits

(c) As noted in class, the bene t-cost B/C ratio is really the ratio (PV (B)/PV (C)). When it is greater than 1, NPV > 0. There is an easily deciphered relationship between the internal rate of return (IRR) and the B/C ratio when the PV(B) is a perpetuity. In the case where PV(B) is a perpetuity, the bene t amount (B) is constant each year and continues inde nitely. (It is used frequently in examples in the textbook.) The perpetuity formulation is P V (B) = (B/r). Since the IRR is the discount rate (r) that makes PV (B) = PV (C), we can say that the IRR is when

0 = (B/r)?PV(C) = (B/IRR)?PV(C)
What is the IRR for the project described by Table 2? What is the value of the B/C

ratio if the discount rate (r) is equal to the IRR?

Answer 1

Answer to question No. a)

To select the appropriate social discount rate to use in evaluating public sector investment projects, which option one will choose is the debate. It depends on the government of that country by looking the situation. If someone assume that the project funds from private sector investment or consumption or some combination of the two then the discout rate will higher than the govt funding because for govt fund the interest rate is lower than private fund. As irate of interest in govt fund is lower than the discount rate will be lower. But cost of other expenses is higher in govt projects only for the less control and private investment will give better return than the govt project though govt funding rate is less.

So for considering social discount rate govt will calculate by taking the cost of funds of own govt not by considering the private investment. But it is better to follow the private investment or consumption or both. So private funding rate should be the more healthy option.

b) It is sure that govt will look the cost of fund of own fund and private funding methord is in theory. Govt principle is giving some social benefits to govt for co-relation between govt and private. Why govt follow the own methord of funding it has also certain meaning. Govt wants equilibrium the economy. If govt follow the private approach then the poorer will be more poor and richer will be more reach. But in certain cases also govt follow the private methord where the govt faced many problem and condition is bad. So it depends on the situation and position.

Other issue is govt for the people and by the people and one govt will continue if that govt listen the majority of the voice of public.

Other situation may be in a country most of the people are rich and developed economic at that time Govt follow private mode of funding.

It is definite that private option is only in theory and govt cost of fund approach is always practical.