2007年5月7日

如何選擇折現率?(十)

巴菲特本人是如何選擇折現率呢?基本上他是用長期的國庫券利率做為折現率。但如利率水準太低時--例如低到3%,他會用比較高的折現率,原則上不會低於6%。因為長期而言,暫時的低利率會逐漸回歸到長期的正常利率水平。

“For our discount rate, we basically think in terms of the long-term government rate. We don't think we're any good at predicting interest rates. But in times of what seem like very low rates, we might use a little higher rate.”---Warren Buffett, 1996 Annual Meeting.

但他也提醒投資人,不管用什麼折現率,對同時間所有的投資案評估都應該用相同的利率,這樣才能相互比較。他說:

Only want one variable to compare in order to access the viability of an investment – price versus value. If we allowed discount rates to change it would lead to more than one variable. ---Warren Buffett

We want to stick with businesses we think we understand quite well and not try to have the whole panoply with all different kinds of risk rates because, frankly, we think that would just be playing games with numbers. ---Warren Buffett, 1996 Annual Meeting

另外,他建議投資人在選擇折現率時要考慮到投資持有的期間多長,如果你的投資期間是十五年,那你應該選擇十五年期的正常化(Normalized)國庫券利率做為折現率。

因此歸納起來,巴菲特對選擇折現率的建議是:
  • 如果是長期投資,應該用長期的國庫券利率做為折現率。
  • 不管用什麼數字,對所有的投資案應該都用相同的折現率,才可以比較。
  • 關鍵不在折現率是多少,而在於預估的未來現金流量是否相當保守且確定。如果你無法很確定所估計的未來現金流量被達成的機率,折現就失去意義了。

Munger則從另個角度來看待折現率,他認為應該用機會成本(Opportunity Cost)做為折現率。他說:

“Finding a single investment that will return 20% per year for 40 years tends to happen only in dreamland. In the real world, you uncover an opportunity, then you compare other opportunities with that. And you only invest in the most attractive opportunities. It’s all about opportunity cost. The game hasn’t changed at all. That’s why modern portfolio theory is so asinine.”--- Charlie Munger, 2006 shareholders meeting.


Seth Klarman則依據不同的風險採用不同的折現率。

看來即使是大師或專家也沒有一致的看法,也可以說如何選擇折現率並沒有一個所謂正確的方法,即使是巴菲特的做法也不見得讓每一位投資人都同意。

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