The stock market crash has reduced the confidence of our estimates of the cost of equity capital. Historical build-ups using Ibbotson or Duff & Phelps data show lower 2008 risk-free rates and equity premiums than in 2007. But uncertainty is higher, so the cost of equity capital has to be higher. (Seen an IPO lately?) Regardless of how we handle this – for example, with a higher company-specific equity risk premium – our cost of equity capital estimates are not as reliable used to be.
To compensate, I now include in my reports a sensitivity analysis of Income Approach value indications to the discount (or capitalization) rate. This shows by how much the value falls if the discount rate rises by 1%. Obviously, a higher discount rate lowers the value, but by how much? This is easy to do in Excel.
Bond market analysts call the percentage change in bond value due only to a percentage change in interest rates its duration, volatility, or price elasticity with respect to interest rates. Wikipedia has a great explanation of “Bond Duration”. It can also be expressed as the present-value weighted average of cash flows by time of receipt. At one extreme, a payment received now has zero duration. At the other, a zero coupon bond of 10 years’ maturity has a duration of 10 years. Duration rises as interest rates fall, as coupon yields fall, and as maturity rises. Duration concerns only interest rate sensitivity, and ignores factors like income and capital gains taxes, default risk (on both principal and interest), and (in its simplest form) call and put options. (Microsoft Excel’s Analysis Toolpak add-in has Duration and Mduration functions to calculate it.) Translated to stock valuation, the same limitations apply. Only sensitivity to a change in the discount rate is calculated. Uncertainty regarding enterprise or shareholder cash flows (dividends and lack of control), marketability, calls and puts are not considered.
I worked two examples of duration or stock value volatility relative to the discount rate:
A “Lease” yields $100 annual cash flows for 10 consecutive years. Valued at a 10% discount rate, its present value is $614. If the discount rate rises 1% to 11%, the present value falls to $589. This is a 4% decline is value due to a 1% increase in the discount rate.
A “Startup” yields no cash flows for nine years, then $1,000 (i.e., an exit sale). Valued at a 40% discount rate, its present value is $35. If the discount rate rises 1% to 41%, the present value falls to $32.  This is a 7% decline in value due to a 1% increase in the discount rate.
All other things being equal, the Startup is more sensitive to the discount rate than is the Lease, which makes sense given their respective cash flow patterns. Â You can play with the assumed discount rates, maturities, and cash flows to further explore this. Â I hope it helps you better defend your value conclusions!