BUSI 534 Week 2 Discussion Board Forum 1 Example

Discussion Board Forum 1: The Income Approach and the Cost of Capital

BUSI 534 Business Valuation, Discussion Board Forum 1 Thread and Replies

Thread by [Student Name]

The forum prompt, the two classmates and the machine shop in the thread are composites standing in for the course's own prompt; the textbook and the research cited are real, and the requirements follow Liberty's public course guide for BUSI 534.

Thread

When I build a discount rate for a small private company with the build-up method Hitchner (2017) describes, the first two pieces are uncontroversial: a risk-free rate and an equity risk premium. The third, a size premium, often adds several percentage points, and it is the piece I find hardest to defend. My position is that a size premium is justified, but only when the analyst can connect it to risks the company actually has, rather than adding it automatically because the company is small.

The evidence has had a strange history. Banz (1981) found that from 1936 to 1975 small New York Stock Exchange companies earned higher returns than their betas predicted. That finding helped create the size premium used in practice today. But the effect was weaker in the decades after it was published. Van Dijk (2011), reviewing the research, concluded that the size effect in U.S. stocks had largely disappeared after the early 1980s and that much of what remained came from the very smallest stocks and from the month of January.

Then the premium came back in an unexpected way. Asness et al. (2018) argued that small companies include many low-quality ones, with weak profits, unstable earnings and high risk of distress, whose poor returns hide the premium earned by small companies of good quality. Once they controlled for quality, a significant and stable size premium appeared across 30 industries and 24 international markets. If the premium belongs to small companies of good quality, the case for adding it is strongest exactly where appraisers usually feel least comfortable adding it.

Consider a composite machine shop with $8 million in revenue, steady customers and twenty years of profits. A mechanical build-up might add a size premium and then a company-specific premium for customer concentration and key-person risk, counting some of the same risks twice. A more careful approach would treat the size premium as compensation for the risks small companies share, thin access to capital, few products and limited management depth, and then add a company-specific premium only for risks beyond those. Hitchner (2017) warns that the build-up method invites this kind of double counting, and the research gives an appraiser a reason to look for it.

The practical rule I would follow is to state the source of each premium, explain what risk it covers and confirm that no risk is counted twice. For the machine shop, that might mean a size premium drawn from published data for the smallest decile of public companies, reduced or left unadjusted after comparing the shop's profit stability with the low-quality firms that drag down small-company averages, and a modest company-specific premium for its reliance on three large customers. Each number would carry a sentence explaining it. A reader, whether a lender, a judge or a buyer, could then disagree with a specific premium instead of having to accept or reject the whole rate. That transparency matters more than the precise figure, because the evidence on size will keep shifting and the report has to stand up after it does.

Reply to Jamal

Jamal, your thread built a clear discounted cash flow model for a regional landscaping company, and I agreed with your choice of a capitalized cash flow at the end of the five-year forecast. My question is about the 5 percent long-term growth rate you used in the terminal value, because that single assumption probably drives most of your value. When the terminal value accounts for 70 or 80 percent of the total, as it often does for a stable business, a one-point change in perpetual growth can move the conclusion more than every year of the detailed forecast combined.

Hitchner (2017) explains that the long-term growth rate in a capitalization model must be sustainable forever, which in practice means it should not exceed the expected long-run growth of the economy in which the company operates. For the U.S. economy, long-term nominal growth of roughly 4 percent is a common reference point, and a mature landscaping business serving one region would usually be expected to grow more slowly than the economy, not faster. A 5 percent rate implies that the company will eventually become a larger share of the economy every year, forever.

Research on corporate growth supports caution. When Chan et al. (2003) tracked how U.S. companies' operating performance grew over long horizons, fast growth turned out to repeat hardly more often than a coin toss would predict: a strong five years told them little about the next five, and analysts' long-term growth forecasts ran consistently too high. If that is true of public companies with professional management and access to capital, it is likely to be even more true of a small regional business.

I would suggest two changes. First, if your forecast shows strong growth in the next five years, consider extending the forecast period until growth settles to a sustainable rate, rather than carrying a high rate into perpetuity. Second, test the sensitivity of your conclusion to the growth rate. Showing the value at 2, 3 and 4 percent would let a reader see how much of the conclusion depends on that assumption, and it would protect the report if it were ever challenged. Hitchner stresses that the growth rate and the discount rate must be estimated consistently, so if you lower growth you should also check that the cash flow in the final year reflects only the reinvestment that slower growth requires.

It may also help to look at what buyers of similar businesses have paid. If the transaction multiples for landscaping companies imply growth well below 5 percent, the market is telling you something your model should reflect. Would your company's history support 5 percent if you looked at its revenue over the past ten years rather than the past three?

Reply to Priya

Priya, I learned a great deal from your thread on valuing the Mexican subsidiary of a U.S. auto parts supplier, especially your explanation of the different ways to add country risk to a cost of capital. You argued for adding a premium equal to the yield gap between Mexican government dollar bonds and U.S. Treasuries, which is one of the most common methods Hitchner (2017) describes in the chapter on international cost of capital.

I want to add a consideration that might change the size of that premium. Whether investors demand extra return for country risk depends on whether the country's capital market is integrated with world markets or segmented from them. Where a market is integrated, investors holding portfolios across many countries are largely insulated from any single country's troubles, so what they require depends mainly on how the investment moves with the world market. In a segmented market, local investors bear the country's risk without that diversification, and required returns are higher. Bekaert and Harvey (1995) developed a way to measure integration over time and found that several emerging markets moved from segmentation toward integration, while others remained segmented even when foreigners could invest freely. They also found that integration does not always increase over time, as many people assume.

For your subsidiary, that research suggests two questions. First, how integrated is the Mexican market today for the kind of investor who would buy this business? A U.S. parent with operations in many countries is diversified in a way that a local buyer is not, which matters when the standard of value assumes a hypothetical buyer. Second, is the bond spread measuring risk that equity investors actually face? Sovereign default risk and the business risk of an auto parts plant overlap but are not identical, and the plant's exports to the United States may make it less exposed to Mexican conditions than a company selling only within Mexico.

Hitchner also stresses consistency between the cash flows and the rate, a principle that applies with special force across borders, where inflation and currency expectations differ. If your projections are in U.S. dollars, the discount rate should be a dollar rate; if they are in pesos, the rate should reflect expected peso inflation. Pairing peso cash flows with a dollar rate, or the reverse, is a frequent mistake in cross-border work, and it can swamp the effect of any country premium.

One way to test the premium is to compare the implied cost of equity with the returns that local buyers of similar Mexican manufacturers appear to require, if transaction data are available. Did you consider whether the subsidiary's export sales would justify a smaller premium than one based on the government bond spread alone?

References

Asness, C., Frazzini, A., Israel, R., Moskowitz, T. J., & Pedersen, L. H. (2018). Size matters, if you control your junk. Journal of Financial Economics, 129(3), 479-509. https://doi.org/10.1016/j.jfineco.2018.05.006

Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9(1), 3-18. https://doi.org/10.1016/0304-405X(81)90018-0

Bekaert, G., & Harvey, C. R. (1995). Time-varying world market integration. The Journal of Finance, 50(2), 403-444. https://doi.org/10.1111/j.1540-6261.1995.tb04790.x

Chan, L. K. C., Karceski, J., & Lakonishok, J. (2003). The level and persistence of growth rates. The Journal of Finance, 58(2), 643-684. https://doi.org/10.1111/1540-6261.00540

Hitchner, J. R. (Ed.). (2017). Financial valuation: Applications and models (4th ed.). Wiley.

van Dijk, M. A. (2011). Is size dead? A review of the size effect in equity returns. Journal of Banking & Finance, 35(12), 3263-3274. https://doi.org/10.1016/j.jbankfin.2011.05.009