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Chapter 4

Chapter 4. Time Value and Relations between returns. Up Until Now. Up to this point we have discussed who runs a company, potential purposes of a company, the goals of a company, and how a company accounts for its wealth.

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Chapter 4

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  1. Chapter 4 Time Value and Relations between returns

  2. Up Until Now • Up to this point we have discussed who runs a company, potential purposes of a company, the goals of a company, and how a company accounts for its wealth. • As we discussed earlier, a company has to deal with multiple cash flows, occurring and being recognized at different times. • Is a dollar received tomorrow worth the same as a dollar received today to a company?

  3. Properly Measuring Average Rates of Return • Financial decisions often require proper recognition of rates of return resulting from different cash flow streams. • Cumulative ROR represents the percentage change in wealth between two periods regardless of how much time elapses. Notice this can be re-written in many different ways.

  4. Average Rates of Return • Consider the following example: • Today you buy a stock for $100; in one year the security price is $50. In two years you sell the security for $100. What are our annual RORs and what is the Average Annual ROR? • ROR1 = ($50-$100)/$100 = -50% • ROR2 = ($100 - $50)/$50= 100% • We can find the average ROR one of two ways:

  5. Average Rates of Return You should recognize this as a simple average: Add them all up and divide by the number of items. (-50% + 100%)/2 = 25% Notice the investor starts and ends with the same wealth yet realizes a return of %25. This curiosity motives the introduction of the geometric average. Check to see that this Average gives us an ROR of 0.0%

  6. Lump-Sum time Value • Using our earlier formula we can solve for beginning wealth giving our resulting wealth and the ROR we earn. This allows for us to create the lump-sum time value relation: • Note: The above has new names for variables but it represents the same idea. • PV = present value, FV = future value, r = ROR, and N equals the number of periods in the future that the cash flow is recognized.

  7. Periodic Components in Time Value Formula 4.7 computes the periodic interest that an asset earns or that a liability owes by multiplying the periodic interest rate by the BOP balance. Formula 4.8 computes the total accumulated market interest as the difference between the account balance and the total contributed principal. (Think savings account.) Formula 4.9 computes total acc. market interest as the sum of total IOI and IOP Not only does the principal earn interest but so too does the interest accumulated during a previous period!

  8. Calculator HELP • Looking at your BAII Plus: • 90% of the problems faced in this class revolve around five buttons, of which you will either know directly or be able to solve for four of them. Hit “CPT” and the fifth button to find the answer asked for. • See calculators clues on pages 114 and 115. Consider the Lump-Sum valuation formula appearing earlier – we may have to solve for any of the variables within the formula. Let’s try a few examples.

  9. Basis Points • Suppose our rate of return chance from %50 to %51. Does our ROR change by %1 or %.02? • We use the concept of the basis point as a unit for measuring change in rates so that the above confusion is avoided. • So %50 -> %51 = 100 BP • %50 -> %50.25 = 25 BP • %50 -> %50.05 = 5 BP • A single BP may not seem like much but when you are dealing with millions of dollars in wealth it is certainly significant.

  10. Rule of 72 • What if we don’t have a calculator to do the math? Or what if we would like to check our work? Can we do the work in our head? • There is a simple rule that can allow us to calculate the length of time it will take to double our wealth given a particular rate of return. Given a 10% ROR wealth doubles every 7.2 years

  11. Intraperiod Compounding of interest • Up until now we have dealt with “annual interest,” that is our interest is compounded annually or once per year. Suppose we have monthly compounding, daily compounding, continuous compounding? • We still use the same lump-sum time value formula: • But now R = i/m where i equals the Annual Percentage Rate, “APR”, and m is the number of compounding periods per years (E.g. monthly -> N = 12) • Does compounding frequency matter? ABSOLUTELY • consider in-class example.

  12. APR vs. EAR • Our discussion about APR gives rise to differing amounts of annual interest. Consider EAR: • We can compute the EAR given APR as follows: We can use this number, for example, to calculate how expensive a loan will actually be: Consider two loans with different interest rates compounded differently. Which is more expensive?

  13. Inflation and Time Value • Please read pages 132-133 on your own.

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