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Annuities and Present Value Continuing our analysis of the time value of money. Revised by DBH 1/2006

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Scenario You are age 35 today and you start to think for the first time about retirement. You calculate a careful budget and find you have only $100 per month you can set aside for retirement savings. Is it even worth it? Suppose we can invest in an investment fund that historically pays an average rate of 8% Let’s do the math

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Do the Math (#1) With disciplined investing, you could accumulate a fund of $149,000+ depositing only $100 per month at 8%. (Many securities funds have historically done better than 8%)

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How much do I need now for later? Suppose you’ve done that for 30 years and have accumulated your fund. You determine you need $1,200 per month over your Social Security to survive in retirement. If you expect to live 20 more years (to age 85) can you do it on your little fund?

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Do the Math #2 You should have little trouble living for 20 years with your retirement fund provided you are a disciplined investor and spender.

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Net Present Value Businesses must make the same kinds of decisions we look at as individuals. They decide whether or not to invest in a project that will pay off gradually, over a period of years. But often, in these analyses, the cash flows from these investments are not always equal—they may increase or decrease as time passes This can be measured using a tool called Net Present Value (NPV function in Excel)—this is explored in ch. 9.

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A Simple Illustration of NPV Let’s assume a new project costs $1 million in initial capital investment on a given date (we’ll call this Year 0). Over the next five years (Years 1 through 5), the project is projected to produce $280 K in annual new cash flow to the firm ($1.4 mil. over its life) Our “hurdle rate” (cost of capital) is 12%--we must earn at least 12% on any new investment to satisfy our stockholders Should we do the project?

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Excel NPV calculation Year 1$280,000 Year 2$280,000 Year 3$280,000 Year 4$280,000 Year 5$280,000 NPV at 12%$1,009,337 Less Initial Inv. (Year 0)-$1,000,000 Net Present Value$9,337 The NPV function in Excel calculates the present value today of the cash flows for the next five years (discounted at 12%) Result= the project has a small positive NPV and can be approved. (It will earn at least 12%)

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Suppose cash flows are uneven? Suppose the cash flows were “uneven” but did better later in the project? Total cash flows are identical ( $1.4 million) Still a good idea? Not necessarily—in the case at right the NPV is negative—it won’t earn 12% over its life. The earlier we can recover our cost, the more likely we’ll meet our hurdle rate. Year 1$200,000 Year 2$250,000 Year 3$300,000 Year 4$300,000 Year 5$350,000 NPV$980,659 Less Initial Inv. (Year 0)-$1,000,000 Net Present Value-$19,341

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More to come We’ll explore this concept a bit more in Chapter Nine and also illustrate a method of estimating the projected rate of return for a given project (Internal Rate of Return or IRR) The present value calculations would be a challenge to do by hand, but are easy using computerized financial functions.

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Chapter 4 The Time Value of Money

Chapter 4 The Time Value of Money

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