Narrative and Numbers - Aswath Damodaran on investment analysis

In his book, Narratives and Numbers: The Value of Stories in Business, NYU finance professor Aswath Damodaran suggests that plausible valuation of companies and investments requires meaningful financial models and compelling narratives.

We review some of the considerations and diagnostics that Damodaran believes are important to discounted cash flow analysis in this post.

If you missed it, our first post summarised Damodaran’s observations on business stories, and how the combination of numbers and narratives can inform investment analysis.

The second post summarises his views on the relationship between narratives, numbers and the intrinsic value of a company; and the questions investors can ask to inform their analysis.

Considerations to investment analysis

While the overarching narrative and key valuation drivers will form the backbone of your analysis, several nuances to discounted cash flow analysis can sometimes have significant impact on your final conclusions. Damodaran discusses several valuation considerations, refinements and diagnostics to be aware of when undertaking DCF analysis.

Debt and cash (net debt)

Debt should include interest bearing liabilities and other contractual commitments such as leases. Cash may also require nuanced considerations. For example, US companies may see cash holdings trapped overseas as they seek to avoid corporate tax associated with repatriation of foreign income. Another common example is that cash balances that are invested in risky securities may deviate significantly from current book value.

Cross holdings

When possible, the parent company and its subsidiaries should be valued separately. Each holding should then be added back proportionately. Otherwise, you risk miscalculation of total intrinsic value. Majority holdings for instance are consolidated into financial statements as if the company owns the subsidiary fully (incl. revenue, operating income, etc.).

Accountants estimate the unowned value of the subsidiary and lists it as a liability (i.e. minority or noncontrolling interest). For minority holdings, adjustments to net income are made to reflect the share of earnings obtained from the subsidiary. On the balance sheet, only the original book value of the investment is included.

Stock based compensation

Many companies issue restricted shares or options as a form of employee compensation. This should be treated as an operating expense. While this is standard accounting practice, some companies may add these expenses back for a variety of reasons (e.g. attempts to boost reported cash flows, treatment as unusual expense treatments, etc.). Options that are still outstanding is a claim on equity. They should be subtracted from equity value per share.

Currency invariance

Valuations need to keep assumptions about inflation, cash flows and discount rates consistent. Companies in low-inflation currency countries should expect lower discount rates and expected growth rates. Conversely, countries in high-inflation currency countries should expect a higher discount rate and growth rate to reflect inflation.

Dynamic discount rates

A company’s growth rate, debt-to-equity mix, and business mix may change over time. This may change the discount rate that is most appropriate for the company during that period.

Investment diagnostics and tools

In Narrative and Numbers, Aswath Damodaran also discusses several diagnostics and simple tools that we can use to help interpret the consistency and plausibility of your valuation and corresponding narrative.

Terminal value

The terminal value is likely to be an important determinant of an investment’s value when using a DCF valuation method. Investments generate cash flows in the form of dividends and cash payouts, but most returns are likely to come from price appreciation. The terminal value here represents the price appreciation.

The long run growth rate must be less than or equal to the nominal growth rate of the domestic or global economy that the company operates in. The risk-free rate may be a good proxy for nominal growth. This would also bring the currency choice into the growth estimate. The risk-free rate and expected growth rate in perpetuity would be higher in a high-inflation environment.

Growth, reinvestment and investment quality

A sensible valuation requires some balance between growth, reinvestment and risk. A helpful check for consistency is to sum the change in operating income during its high growth phase divided by the reinvestment required over that same period. This marginal return on invested capital can be compared to the company’s cost of capital, historical return on capital and industry averages to determine whether assumptions around growth and reinvestment are sensible.

Marginal return on capital = Change in operating income / Reinvestment

Risk and the time value of money

Cash flows are discounted to reflect the time value (or opportunity cost) of money, and the operating risk of the company as a going concern. In risky or high-inflation settings, waiting for positive cash flows can diminish the present value of an investment very quickly.

Free cash flows may also be negative. This is often the case for young, high-growth companies whose earnings are low in early years and because reinvestment is needed to achieve even further growth.

Negative cash flows are useful for capturing the dilution effect since further equity issues could be needed to cover negative cash flows. The dilution effect is captured by the present value of negative cash flows. Hence, adjustments for share issuances in DCF valuations are not needed.

Negative value for equity

The value of operating assets is equal to the present value of expected cash flows. The difference between this value and net debt is the value of equity. While theoretical valuations of a company can be fall below zero, market prices cannot. Some companies with prospects for a turnaround can achieve prices beyond the value of its operating assets. Equity in these companies exhibit characteristics of an option and could be treated or valued as such.

Return on capital under stable growth

Companies will need to reinvest to deliver their stable or long run growth rate, implicit in the terminal value. One way to approximate this is to estimate the return on capital that the company might generate under stable growth. You can use this rate to determine the reinvestment rate.

For example, if the company achieves an ROIC of 12% in new projects, the company would need to reinvest 25% of after-tax operating income in perpetuity to grow at 3% per annum. If the company’s return on capital is equal to its cost of capital, growth becomes a ‘neutral’ variable and does not affect the company’s terminal value.

Going concern terminal value t = E(Cash flow n+1) / (Stable growth cost of capital – Growth rate)

Terminal reinvestment rate = Stable growth rate / Return on invested capital

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Fighting hubris when investing

Remember that valuations and narratives are point in time estimates. Assumptions for growth, margins, cost of capitals, etc. come from a probability distribution of many possibilities. We should consider the use of what-if analysis, scenario analysis, decision trees and/or simulations to understand how the valuation and story might change under different circumstances.

We should also tell our stories and valuations to people who are most likely to disagree; be open about areas of uncertainty and explain how it might affect our estimates; separate facts from assumptions that are just beliefs; avoid covering our mistakes when new information debunks our work (simply review and change as necessary).

References

Damodaran, D. (2017). Narrative and Numbers: The Value of Stories in Business.

Damodaran, D. (2019). Musings on Markets. Accessed at <http://aswathdamodaran.blogspot.com/ >

Narrative and Numbers – Aswath Damodaran on investment analysis