Just yesterday I posted a key question as to why the statelottery might hypothetically offer you an upfront lump-sum paymentof $50 million or an ongoing annuity of a $5 million check eachyear for 20 years (totaling $100 million in checks). Remember thatthis was just my simplified hypothetical example. A few peopleattempted the answer to this further above, but here's what'sreally going on...it has to do with Net Present Value (NPV). It'sbecause future-year dollars are worth less, and the further you gointo the future, the less those dollars are worth in terms oftoday's dollars. And that is why, when financial analysts look at adecision involving multi-year cash flows, they will use discountfactors to convert all of the future-year dollars to present value(i.e., this year's dollars) and add them up to yield the NPV of allof the amounts to put a final answer in terms of today's value.Where do these discount factors come from? They're derived from thereciprocal of the famous compound interest formula, but you justneed to go and look at two tables in your textbook in Chapter 12,Appendix 12A, Table A (present value of $1 due in n periods) andTable B (present value of an annuity of $1 per period). Class, Icannot stress to you enough how widely-used this concept is, andthe importance of understanding how these discount factors areapplied to solve for net present value (NPV) and a related metric,internal rate of return (IRR). You will likely need to read, andreread, Chapter 12 and closely walk through some textbook exampleswhere each year's cash flows are multiplied by the appropriatediscount factor to convert all of that money into this year'sdollars (present value). We are surrounded by this financialanalysis methodology when faced with a decision on a lotterypayout, a retirement payout (lump sum versus annuity), and many ofour states and cities right now are dealing with issues relating tothe calculation of NPV in assessing whether they currently haveenough money in the appropriate accounts to meet the futureretirement payment obligations they've made to their publicemployees. This is an economic issue that has been on the brink ofexploding for a long time (don't take my word for it, it's beendiscussed in multiple articles in the NY Times, Wall StreetJournal, The Economist), but I'm not going to add all of that intothis discussion here. Let's learn to walk before we try to run.Would you like to see how the lottery payouts I described would bemultiplied by each year's financial discount factor? Just take alook at my attached Excel workbook, and note that there are threetabs: the first assumed a 0% cost of capital (no financialdiscounting done), the second assumed a 5% cost of capital, and thethird sheet inserted a 10% cost of capital. You'll see how thesedifferent interest rates changed the discount factor multipliersand ultimately changed the NPV of each alternative (the value ofthe lump sum or the annuity, all shown in present value). Also,this example just shows money moving one way (i.e., to the state,it's cash out of their pocket...to the lottery winner, it's cashinto their pocket). In many NPV and IRR examples, money will moveboth ways over multiple years...cash flows that are expenses orinvestments are outflows and are shown as negative, while revenuesor other incoming money are inflows and are shown as positive.Please look closely at my attached Excel workbook (all three tabs)and also walk through all of the examples in the chapter showinghow to do NPV and IRR problems. There are also examples in the textof simpler metrics including payback period and accounting rate ofreturn. It's typically very hard stuff for students to master. Now,for those of you who've looked at the chapter examples, maybeyou've figured this out already:
1. What is the key difference between Tables A and B in Chapter12, Appendix 12A, and how and when are each of them used in ananalysis?
2. What do we mean by âYear 0â in a financial analysis? Whatvalue do we use for the discount factor or multiplier for the cashflow in Year 0 of a financial analysis?
