Public Policy Analysis MPA 404 Lecture 13

Previous Lecture  A practical example of policy formulation, application and refinement.  The Madrassa Reform Program (MRP).  The initiation, implementation and its poor results.  Policy redesign, new survey and random sample selection.  Conclusions or interpretations from the gathered data.

The IRR calculation- An example  In one of the previous lectures, we went through definitions of PV, IRR, Cost-Benefit ratio’s. Let us go through a stepwise calculation of the IRR, which involves calculation of other variables like the PV.  A few basics: IRR is a useful yard stick for measuring the feasibility of investments. Notice though that this kind of measure works best when the future income and expenditure streams are well known. For example, in the case of a bank account paying a specific fixed percentage on deposit, the income stream is well known. But in cases where future income goes through variations, calculating IRR is not that easy. For example, the returns from education or training do not follow a straightforward trajectory.  Now consider that an individual decides to put Rs. 1,000/- in a bank account for 6 years that pays 5% interest rate yearly (its not necessary that the interests is yearly; interest could be monthly). What this means is that for 5 years, there will be annual interest payment, and in the 6 th year we can withdraw the principal plus the interest. The calculation is as follows:

 Years Return  Return at 5 percent=1000*5%=1000*5/100=50  Now consider any alternative investment of buying a machine, that pays Rs. 200/- for 6 years investment of Rs. 1,000/-. Difference from the first investment: there is no lump sum amount waiting at the end (meaning principal plus profit). It looks like this:  Years Return  The comparative returns are tabulated as follows: Year123456Total Bank Machine200

 You may be wondering why the total income in case of the bank is 300 while its 200 in the case of alternative investment. Note here that I am only talking about ‘returns’ or income from two different investments. The Rs.1000/- of bank investment is the principal amount, while the Rs. 1,000/- of alternative investment (buying machine) is purely an expenditure which wouldn’t be retrieved (not in full at least).  So it would seem a straightforward decision, right? Bank account income is more than income from machine (in total), therefore it seems a more profitable investment. But to arrive at an answer, we need to calculate the PV’s of both income streams. The difference from above calculation here is that we will consider the initial Rs.1000/-, as an expenditure (remember in calculations like cost-benefit ratio, we consider both income and expenditure adjusted for PV). The discounted values are as follows: Year123456Total Bank PV Machine200 PV

 Two questions here: why 5 percent was chosen as discount rate for PV calculation, and how did we get the end total after PV calculations? a) Why 5 percent: It’s the rate of investment at bank account, and represents the opportunity cost of investing in machine. In valuation of projects or analysis of a proposed public policy, the opportunity cost of capital is needed for PV calculations. In this case, while comparing two investments (bank and machine), the opportunity cost of capital is the option we forgo (the bank option and thus its 5 percent rate). b) The discounted PV total: The total at the end of PV discounted calculations is arrived at after subtracting it from total expenditure (Rs. 1,000/-). In deciding about investment decisions, discounted numbers of income in lieu of expenditures made is what really counts.  So strictly speaking in terms of PV calculations, the machine represents a better payoff in the end as an investment option. Remember though that these are mostly used for large scale projects and investments. Outside of the investment world or the world of projects, it is not PV or like calculations

that matter but rather the preferences of individuals. A person might be perfectly happy with receiving Rs. 50/- as income for 5 years from the bank account option, and then collect Rs. 1,050/- at the end without giving any thought to PV or IRR.  What the calculations using PV have done is that it has told us the option that is better in terms of a discounted future income stream. Now that we have chosen an investment option, the next step is to calculate an IRR for that investment. Put simply, IRR is the discount rate that makes the present value of the machine's income stream total to zero. For any question about why zero, refer to the lecture about discounting and IRR.  We already know about the 5 percent number, which gives us Rs /- as return. We want to know the number that makes this return equal to zero. The logical step is to try a higher percentage, i-e, 6 percent. However, if we make the discounted calculations (as we did above), we will get a number les than zero, which is not acceptable (it should be a positive number). Logically this implies that the rate that we are looking for is somewhere between these two numbers.

 Try making the calculation at 5.5 percent and likewise. In the end, the rate at which discounted returns reach zero (or very near zero) turns out to be 5.47 percent. This is our IRR. Again, notice that 5.47 percent IRR is higher than 5 percent of the bank account return, which makes the comparative return on machine more attractive.  Applications : 1. Bond sale at a discount  What’s a bond? Its basically a debt instrument (or a way of acquiring debt). Through bond sales, what the issuer does is that it is promising to pay the principal amount plus a certain percentage in profit (monthly, bi-annually or annually). These can be issued by a government or a corporation/private entity.  This example is of a common type of bond known as discounted bond (which sells at a discount). Suppose there is this offer of Rs. 1,000/- bond with a return of 10% for 5 years, selling at a discount for Rs. 900/-. Is it a good investment? To answer this, we need to come up with PV’s and IRR for comparison to other investments.

 Let’s first make the table that shows the future income streams and the discounted values, as we did before.  Notice again that the total of the PV is gained after subtracting the original amount (Rs. 900/-). The discounted PV of future income stream turns out to be exactly the same as the discount (i-e, Rs. 100/-). So the companies offer the discount in order to attract bond investors. Without a discount, when the investors figure out that the PV of future income stream is equal to price today, they perhaps won’t find any incentive to buy a bond. This is a bit different from project calculations because the element of offering an incentive is not that strong as far as government run projects are concerned. But when it comes to private investors, the bond offerer needs to offer an incentive to the private investor. The discount on buying price is the incentive. Year 12345Total Income PV

 The next step is finding the IRR, which will make the future income stream near zero. Just like above, tinker with the percentages (or the interest rates). It turns out that the rate at which the future income stream nears zero is 12.8%. This 12.8% is our IRR, and it is this rate which the investor will use to compare with other investments to see whether it is worthwhile to go ahead with buying bonds. In case of bonds, this IRR is also known as Yield to Maturity.