The growing perpetuity calculation in DCF

Hey, guys. I am a pre-MBA student. I studied one corporate finance class in law school so my question may seem too plain and simple. I was reading the DCF and noted that the calculation of the terminal value is different from the formula I learned from class. The formula taught in our class is to divide the year 10 cash flow by the discount rate minus the growth rate but the formula I found on the wso guide is to multiply cash flow by 1 plus the growth rate and divide that by the discount rate minus the growth rate. Could anyone explain why there is a difference? Or I completely misunderstood what the prof had taught us. Thank you!

 

No. By calculating the value of the perpetuity from years 6 (year after last forecasted year) to infinity, you have the FUTURE VALUE of a perpetuity starting at the beginning of year 6/end of year 5. To determine the PRESENT VALUE of this perpetuity, you must discount it back 5 five years to the present day, a.k.a. time 0. Before you discount 5 years, you have what its value WILL BE at the end of 5 years. What you want to discover is its value NOW.

 
gimmeshelter43:
thanks jhoratio - but why is that value a future value if the discount rate is included? what is the point of the discount rate in the calculation of the perpetuity value?

CF / (k-g) is the value of the perpetuity at a given point in time. When you're valuing the perpetuity in year 5, that tells you what its worth in 2015 for example. But you need to know what its worth TODAY. So you discount it from Year 5 to now.

 
Best Response

Gimme,

It's a future value because the perpetuity is being expressed as a single lump sum in year five. Is year 5 today? No. Year 5 is in the future. Any cash flow assigned to a future year is a future value.

In the context of your question, the perpetuity terminal value and the FCF in year 5 are both cash flows in year five. It doesn't matter that one is a normal cash flow as a result of business operations and the other is an lump sum equivalent to the value of a stream of cash from that time foward. Once they are expressed as single lump sum cash flows in year 5, they can be added, subtracted, moved foward and backwards through time just like any other cash flow. Forget what you did before to make the perpetuity into a single cash event in year 5. All that matters now is getting all the year 5 cash flows to time zero, which is accomplished by discounting.

 

it goes on forever. eventually the discount factor erodes the marginal years worth of cash flow to almost zero in present value terms.

Remember that Cf(n)/r = value of an infinite perpetuity (they call it a consol in finance classes sometimes). Try applying the long formula over 100 years and compare it.

Also why are you assuming zero growth in that cash flow?

 

The funny thing is that the assumptions regarding terminal value will often tell you whether the investment is worthwhile. Meanwhile, everyone is overly focused on next year's earnings. This is what I like to call "time horizon arbitrage", and you can make a ton of money buying up companies with excellent terminal values but that are currently out of favor (solar comes to mind as a current example, sector's out of favor because subsidies won't be there short-term, but long-term, there will be huge energy demand and fossil fuels are coming up short...so the terminal value is potentially very large).

 
alexpasch:
...short-term, but long-term, there will be huge energy demand and fossil fuels are coming up short...so the terminal value is potentially very large).

Dude no offense and I know you just broke out on your own but if you think you can invest without identifying near term catalysts then I think you are in for a world of hurt. I'm a long term buyside investor also but you can't disrespect near term technicals ( not talking about resistance and m a c d bs)

 

^Is that "time horizon arbitrage?" Or is it just going long a risky asset class? I always thought that time horizon arbitrage involved taking advantage of certain investors' short time horizons in order to acquire investments at levels that appear attractive in the long run. For instance, a private equity investor aquiring a company from shareholders for a 25% premium today and selling it in 5 years for a multiple of their investment (ignoring the effect of leverage).

 

The easiest way to do this and see how it works is to go into excel and go 100 years or so. Have one column for the CF, one for the PV factor, one for the PV. Also, if the perp starts in year 5 you don't include r in your PV formula because it isn't growing from years 0-4.

This to all my hatin' folks seeing me getting guac right now..
 

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