## 11.6 Examples of Valuation

Many considerations and estimates enter into a business valuation. It is more art than science, with the skill and insight of the valuation expert playing an important role.

To illustrate some of the effects of the estimates and assumptions involved, consider a new business venture, Ron’s Business Valuation Services, with the first-year cash flow estimates as shown in Table 11.4 "First-year Projected Cash Flow".

The first question is the expected growth of the business. Consider first an assumption of 6% annual growth. We assume that collections and all expenses will grow at that rate, though other assumptions could be made. A 5-year cash flow projection for Ron’s Business Valuation Services, with 6% growth, would be as shown in Table 11.5 "Five-year Cash Flow Projection, 6% Growth Rate".

A discount rate needs to be chosen. Since growth is already built into the cash flow assumptions, the discount rate reflects only the riskiness of this business. If we believed that the business had relatively little risk, we might choose a discount rate of 10%. This would give a present value for the 5 years of cash flow of \$76,080. If we believed the risk was high, we might choose a discount rate of 30%, which would give a present value of \$47,968. Clearly, the choice of discount rate has a major influence on the calculated present value.

Instead of estimating the cash flow of each of the first 5 years, suppose we simply estimated that the average annual cash flow over 5 years would be \$20,293. This would not make a big difference in the present-value calculations, giving \$76,926 at a 10% discount rate and \$49,425 at a 30% discount rate. These amounts are somewhat higher than shown earlier, because using an average in this case attributes somewhat higher cash flows to earlier years and somewhat lower cash flows to later years, thus increasing the present value.

Table 11.4 First-year Projected Cash Flow

 Cash receipts (\$) Cash collections from clients 200,000 Cash payments (\$) Payroll 80,000 Marketing and customer service 16,000 Rent 30,000 Office supplies and equipment 20,000 Taxes and licenses 36,000 Total cash payments (\$) 182,000 Net cash flow (\$) 18,000

Table 11.5 Five-year Cash Flow Projection, 6% Growth Rate

Year 1 Year 2 Year 3 Year 4 Year 5
Cash collections (\$) 200,000 212,000 224,720 238,203 252,495
Cash payments (\$)
Payroll 80,000 84,800 89,888 95,281 100,998
Marketing and customer service 16,000 16,960 17,978 19,056 20,200
Rent 30,000 31,800 33,708 35,730 37,874
Office supplies and equipment 20,000 21,200 22,472 23,820 25,250
Taxes and licenses 36,000 38,160 40,450 42,877 45,449
Total cash payments (\$) 182,000 192,920 204,496 216,764 229,771
Net cash flow (\$) 18,000 19,080 20,224 21,439 22,724

This example considered only 5 years; what about subsequent years? One approach would be to continue the growth projections for more years, although the confidence in our estimates decreases as we go further out in time. At the other extreme, we could assign zero value beyond 5 years, on the basis that the survival of the business beyond that time is too uncertain. A third possibility is to assume that the average cash flows calculated above would continue indefinitely; the present value of that perpetuity would be \$202,930 (=\$20,293/0.10) at a 10% discount rate or \$67,643 (=\$20,293/0.30) at a 30% discount rate. As can be seen, the value of this business depends heavily upon the assumptions used in our calculations.

Consider next an assumption of 16% annual growth. Again, we assume that collections and all expenses will grow at that rate, though other assumptions could be made. A 5-year cash flow projection for Ron’s Business Valuation Services, with 16% growth, would be as shown in Table 11.6 "Five-year Cash Flow Projection, 16% Growth Rate".

Here the present value of the 5 years of projected cash flows is \$91,244 at a 10% discount rate and \$55,836 at a 30% discount rate. These present values are 20% and 16% higher, respectively, than those calculated under the 6% growth assumption. Average 5-year cash flow for this scenario is \$24,758; the present value based on the 5-year average is \$93,842 at 10%, and \$60,300 at 30%, both 22% higher than the corresponding figures for the 6% growth scenario. Perpetuity values are \$247,580 (=\$24,578/0.10) at 10% and \$81,927 (=\$24,578/0.30) at 30%.

Table 11.6 Five-year Cash Flow Projection, 16% Growth Rate

Year 1 Year 2 Year 3 Year 4 Year 5
Cash collections (\$) 200,000 232,000 269,120 312,179 362,128
Cash payments (\$)
Payroll 80,000 92,800 107,648 124,872 144,851
Marketing and customer service 16,000 18,560 21,530 24,974 28,970
Rent 30,000 34,800 40,368 46,827 54,319
Office supplies and equipment 20,000 23,200 26,912 31,218 36,213
Taxes and licenses 36,000 41,760 48,442 56,192 65,183
Total cash payments (\$) 182,000 211,120 244,899 284,083 329,536
Net cash flow (\$) 18,000 20,880 24,211 28,096 32,592

These comparisons represent the importance of sensitivity analysisAddresses the question of how much difference in the outcome results from different assumptions. in performing business valuation calculations. Sensitivity analysis addresses the question of how much difference in the outcome results from different assumptions. The more sensitive the outcome, the less confidence we should place in the result.