(I) Discounted EPS ROA_CTAC Value Formula — PDD Case Study (II) Discounted EPS NetROIC_CICC Value Formula — PDD Case Study
(I) Discounted EPS ROA_CTAC Value Formula — PDD Case Study
(II) Discounted EPS NetROIC_CICC Value Formula — PDD Case Study
.
The LIMITED LIFETIME is defined to be equal to the respective ROA or NetROIC based discounted valuations.
.
LIMITED LIFETIME is breaking into the 2 parts : Front Lifetime & Rear Lifetime
.
(A)
Design 1 :
LIMITED LIFETIME (Years)
= Respective ROA or NetROIC
=
Front Lifetime (Survival Growth Period)
+
Rear Lifetime (Zero Growth is assumed For the Period From After Front Lifetime to the End of LIMITED LIFETIME )
= Clean Total Assets Cost + (ROA - Clean Total Assets Cost)
= CTAC + (ROA - CTAC)
Or
= Clean Invested Capital Cost + (NetROIC - Clean Invested Capital Cost)
= CICC + (NetROIC - CICC)
.
In Short :
Front Lifetime
= CTAC or CICC
.
Rear Lifetime
= (ROA - CTAC) or (NetROIC - CICC)
.
Design 2 :
In order for a business to survive, the Survival Growth during the Front Lifetime must be equal to the respective Discount.
.
Gfront_Lifetime Factor
= DISCOUNT FACTOR
.
Design 3 :
DISCOUNT FACTOR
= CTAC Factor or CICC Factor
.
Therefore,
Gfront_Lifetime Factor
= DISCOUNT FACTOR
= CTAC Factor or CICC Factor
.
In short :
Gfront_Lifetime Factor = CTAC Factor or CICC Factor
DISCOUNT Factor = CTAC Factor or CICC Factor
Front Lifetime = CTAC or CICC
.
(I)
Discounted EPS ROA_CTAC Value
=
Discounted Front Lifetime Value
+
Discounted Rear Lifetime Value
=
EPS × (Gfront_lifetime Factor ÷ Discount Factor)×(1-(Gfront_lifetime Factor ÷ Discount Factor)^front_lifetime)÷(1-Gfront_lifetime Factor ÷ Discount Factor)
+
EPS × (1÷Discount Factor)×(1-(1÷Discount Factor)^rear_lifetime)÷(1-1÷Discount Factor)
=
EPS × (Discount Factor ÷ Discount Factor)×(1-(Discount Factor ÷ Discount Factor)^front_lifetime)÷(1-Discount Factor ÷ Discount Factor)
+
EPS × (1÷Discount Factor)×(1-(1÷Discount Factor)^rear_lifetime)÷(1-1÷Discount Factor)
=
EPS × Front Lifetime
+
EPS × (1÷Discount Factor)×(1-(1÷Discount Factor)^rear_lifetime)÷(1-1÷Discount Factor)
=
EPS × CTAC
+
EPS × (1÷CTAC Factor)×(1-(1÷CTAC Factor)^(roa-ctac))÷(1-1÷CTAC Factor)
.
(II)
Discounted EPS NetROIC_CICC Value
= Discounted Front Lifetime Value + Discounted Rear Lifetime Value
=
EPS × CICC
+
EPS × (1÷CICC Factor)×(1-(1÷CICC Factor)^(netroic-cicc))÷(1-1÷CICC Factor)
.
As you can see, mathematically, when the growth rate equals the discount rate, the Non-Linear Exponential Power is transformed into Linear.
.
(B)
CASE STUDY
.
PDD
(Non_Gaap_Financial.2025.Dec.Q4.TTM)
.
Non-Gaap EPS (Diluted)
= (99,364,469+7,936,971)÷6.9931÷(5,929,576÷4)
= USD 10.3507581966
.
Non-Gaap NetROIC
= 100 × Non-Gaap Net Income ÷ (Total Equity + Total Debts)
= 25.5305840264
.
Non-Gaap ROA
= 100×107,301,440÷630,044,327
= 17.0307763123
.
CTAC Factor ttm
= Clean Total Assets Cost Factor ttm
= 30Y Government Bond Yield Factor × (1 + Total Liabilities/Total Equity × (1 + 2 × 30Y Government Bond Yield Ratio)) ÷ (1 + Total Liabilities/Total Equity)
= 1.04982×(1+0.5185190812×(1+0.04982×2))÷(1+0.5185190812)
= 1.085538486
.
CTAC
= 100 × (CTAC Factor - 1)
= 8.5538486
.
CICC Factor
= Clean Invested Capital Cost Factor
= 30Y Government Bond Yield Factor × ( 1 + D/E × (1 + 2 x 30Y Government Bond Yield Ratio) ) ÷ (1 + D/E)
= 1.04982×(1+0.0129638543×(1+2×0.04982))÷(1+0.0129638543)
= 1.0511587169
.
CICC
= 5.11587169
.
Gfront_lifetime Factor
= CTAC Factor or CICC Factor
= 1.085538486 or 1.0511587169
.
Front Lifetime
= CTAC or CICC
= 8.5538486 or 5.11587169
.
Rear Lifetime
= Non-Gaap ROA - CTAC
= 17.0307763123 - 8.5538486
= 8.4769277123
or
=
Non-Gaap NetROIC - CICC
= 25.5305840264 - 5.11587169
= 20.4147123364
.
(I)
Discounted EPS ROA_CTAC Value
=
EPS × CTAC
+
EPS × (1÷CTAC Factor)×(1-(1÷CTAC Factor)^(roa-ctac))÷(1-1÷CTAC Factor)
=
10.3507581966×8.5538486
+
10.3507581966×(1÷1.085538486)×(1-(1÷1.085538486)^(17.0307763123 - 8.5538486))÷(1-1÷1.085538486)
= 88.5388185089 + 60.6610142837
= USD 149.1998327926
=
Or
=
10.3507581966×(1.08553848600001÷1.085538486)×(1−(1.08553848600001÷1.085538486)^(8.5538486))÷(1−1.08553848600001÷1.085538486)
+
10.3507581966×(1÷1.085538486)×(1-(1÷1.085538486)^(17.0307763123 - 8.5538486))÷(1-1÷1.085538486))
= 88.5388185089 + 60.6610142837
= USD 149.1998327926
.
As you can see, mathematically, when the growth rate equals the discount rate, the Non-Linear Exponential Power is transformed into Linear.
.
(II)
Discounted EPS NetROIC_CICC Value
=
EPS × CICC
+
EPS × (1÷CICC Factor)×(1-(1÷CICC Factor)^(netroic-cicc))÷(1-1÷CICC Factor)
=
10.3507581966×5.11587169
+
10.3507581966×(1÷1.0511587169)×(1-(1÷1.0511587169)^(25.5305840264 - 5.11587169))÷(1-1÷1.0511587169)
= 52.953150828 + 129.2628813874
= USD 182.2160322154
.
Remark:
Compared to Graham’s Overvalued Formula, EPS×(7+2G), what’s your take?