8.19 Calculating the Present Value of Residual Earnings
Stage 1 Growth Phase
The cost of equity capital equals the
investors’ required rate of return.
In turn this equals the discount rate for computing the
present value of the residual earnings over the Stage 1 growth
phase. You
can verify the above as follows:
Present Value Stage 1 phase
Residual Income = 30.7233 = 7.0771/(1.0837) + 7.3656/(1.0837^2)
+ 7.7769/(1.0837^3) + 8.2312/(1.0837^4) + 8.7328/(1.0837^5)
Stage 2: Calculating the Present Value of Going Concern
At the end of the Stage 1 growth phase we
make the simplifying assumption that the firm is a going concern.
As such it’s residual income will continue to grow at its
estimated normal growth rate in perpetuity.
Recall from above that in 2014 the
residual income is projected to be $8.7328.
To compute the continuing value of the firm we use Gordon’s
constant growth model:
Continuing Value of the Stock at
the beginning of 2015 = ($8.7328*1.045)/(0.0837 – 0.045) =
$235.8075
Finally, we need to discount this
back to the present:
PV = $235.8075/(1.0837^5) =
$157.7656
Calculating the Intrinsic Value of the Stock
Intrinsic Value for IBM = Book
Value2009 + PV of Stage 1 Phase Residual Income + PV
of Going Concern
Intrinsic Value for IBM = 16.881 +
30.7233 + 157.7656 = $205.36
Calculating Price Ratios
Suppose the current price is 125.28 and
as calculated earlier the ROCE = 50.29:
Price/Book Ratio = 125.28/16.881 = 7.42
Price/E(Book Ratio) = 125.28/22.968 =
5.45
Price/CEPS Ratio = 125.28/7.543 = 16.61
Price/E(CEPS) Ratio = 125.28/8.49 = 14.76
(Price/E(CEPS))/Stage 1 Growth =
14.76/10.43 = 1.41