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10 5
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19 14
20 15
21 16
22 17
23 18
24 19
25 20
26 21
036 006 005 004 004 003 003 003 002 002 700 618 552 498 453 416 001 001 000 000 000 001 001 001 000 000 000 000 384 002 001 001 000 000 000 002 001 001 000 000 000 002 001 001 001 000 000 000 000 000 000 000 357 002 002 001 001 000 000 000 003 002 001 001 001 000 000 003 002 002 001 001 000 000 004 003 002 001 001 001 000 000 000 000 000 000 000 000 000 000 333
27 22
28 23
29 24
30 25
31 26
32 27
33 28
34 29
35 30
36 Total
38 Years
39 1-10
772 141 038 700 618 552 498 025 016 011 110 086 068 054 007 453
Present Value of $1 per Year for each 10-Year Period 522 483 449 419 392 368 043 005 416
346 034 003 384
327 028 002 357
309 022 002 333
40 11-20
41 21-30
42 Total
45 Years
46 1-10
50% 20% 5% 100% 100% 4% 18%
Percentage of Present Value for each 10-Year Period 74% 78% 81% 84% 87% 89% 16% 3% 100% 14% 2% 100% 12% 2% 100% 10% 1% 100%
90% 9% 1% 100%
92% 8% 1% 100%
93% 7% 0% 100%
47 11-20
48 21-30
49 Total
100%
100%
100%
PART ONE Business Valuation
stocks, and publicly traded firms to privately owned firms unless they are compensated for the additional risk in the form of a higher expected return That is what happens at least on average over the long run Now let s understand the table At a 5 percent rate of return, you should be willing to pay $95 (cell B6) today for the right to receive $100 in one year Why Because you can take the $95, invest it at 5 percent, making $05 interest, and end up with $100 in one year13 Moving one column to the right, you should be willing to pay only $93 (C6) today for the promise of $100 in one year if you require an 8 percent rate of return Again, you can invest the $93 for one year at 8 percent, earn $07 interest ($93 08 $07), and end up with $100 Of course, as you move to the right in the table, the discount rate rises which means the risk also increases and the amount you should be willing to pay for each dollar of cash in one year decreases This is consistent with the intuitive explanation of Ardath Bigbucks versus Johnny Middlebucks Now let s move down a column to see how the present value factor behaves over time We will use the 20 percent discount rate (column H), since that is a reasonable discount rate for midsize privately held businesses, and the mathematics are easy Assuming a 20 percent rate of return is appropriate, you should be willing to pay $83 (H6) for the expectation of receiving $100 in one year, $69 (H7) for the expectation of receiving $100 in two years, and $58 (H8) for the expectation of receiving $100 in three years If you take the $58 today and invest it and receive an annual return of 20 percent, you will have $69 at the end of Year One ($58 20% $11, plus the original $58, equals $69),14 $83 at the end of Year Two ($69 20% $14, plus the $69, equals $83), and $100 at the end of Year Three ($83 20% $17, plus the $83, equals $100) Thus, if 20 percent is
13 There is some apparent but not real rounding error in this process If Table 52 were shown to three or four decimal points, that problem would disappear I chose two decimal points because it is simpler and most people are not familiar with fractions of a cent 14 Again, there is an apparent but not real rounding error that would go away with more decimal points
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