IF FCFps & Eps Growth-Clean Discount Factor Spread approaches Zero AND Remaining Life Runway Years Equals to CROIC & ROIC Respectively
Assignment :
IF FCFps Growth-Clean Discount Spread approaching Zero & Remaining Life Runway Years Equals to CROIC, kindly simplify the DCF equation.
.
Solution :
.
When
FCFps Growth-Clean Discount Spread
= Gfcfps - Clean Discount
—> 0
Then,
Gfcfps —> Clean Discount
.
Therefore,
Gfcfps Factor ÷Clean Discount Factor approaches 1 :
Gfcfps Factor ÷ Clean Discount Factor —> 1
Where
Gfcfps Factor = 1 + Gfcfps Ratio
Clean Discount Factor = 1 + Clean Discount Ratio
.
Let’s say CROIC = 25
.
DCF
(Remaining Life Runway Years = CROIC 25, discounted each year, Gfcfps—>Clean Discount)
= FCFps × Gfcfps Factor ÷ Clean Discount Factor × [ 1 - {Gfcfps Factor ÷Clean Discount Factor}^croic ] × [ 1 - {Gfcfps Factor ÷ Clean Discount Factor} ]
=>
DCF
= FCFps×1.01×(1-1.01^25)÷(1-1.01)
= FCFps × 28.5256314967
.
DCF
= FCFps×1.0001×(1-1.0001^25)÷(1-1.0001)
= FCFps × 25.032526015
.
DCF
= FCFps×1.000001×(1-1.000001^25)÷(1-1.000001)
= FCFps × 25.0003250026
.
DCF
= FCFps×1.00000000001×(1−1.00000000001^25)÷(1−1.00000000001)
= FCFps × 25.000000003250
.
Continue eternally …
DCF —> FCFps × 25.0000000 (upto 7 significant decimals)
DCF = FCFps × CROIC
.
Thus, When
Gfcfps Factor ÷ Clean Discount Factor —> 1
we have
.
DCF
(Remaining Life Runway Years = CROIC, discounted each year, Gfcfps—>Clean Discount)
= FCFps × Gfcfps Factor ÷ Clean Discount Factor × [ 1 - {Gfcfps Factor ÷Clean Discount Factor}^croic ] × [ 1 - {Gfcfps Factor ÷ Clean Discount Factor} ]
DCF = FCFps × CROIC
.
The same goes for :
Discounted Earning Flow, DEF
(Remaining Life, Runway Years = ROIC, discounted each year, Geps—>Clean Discount)
= Eps × Geps Factor ÷ Clean Discount Factor × [ 1 - {Geps Factor ÷Clean Discount Factor}^roic ] × [ 1 - {Geps Factor ÷Clean Discount Factor} ]
DEF = EPS × ROIC
.
Summary :
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When Geps—>Clean Discount :
Intrinsic value (EPS & ROIC Based)
= DEF
= EPS × ROIC
.
When Gfcfps—>Clean Discount :
Intrinsic value (FCFps & CROIC Based)
= DCF
= FCFps × CROIC
.
Infrinsic Value (DEF)
= EPS × ROIC
Intrinsic value (DEF) /EPS ÷ ROIC = 1
Intrinsic P/E ÷ ROIC = 1
Intrinsic P/E to ROIC Weight Ratio = 1
Intrinsic PEROIC Weight Ratio = 1
.
Compared to Peter Lynch’s PEG:
Intrinsic PEG Weight Ratio = 1
Intrinsic P/E ÷ G = 1
.
For Clean Discount Factor, kindly refer to :