CIIA Exam Preparation: Corporate Finance – Implicit ROE calculation according to the Gordon-Shapiro model

I found the explanation in the solution to one of the past CIIA exam questions on implicit ROE calculation insufficient to fully understand at first, so I thought I’d provide the full solution here including question;

Question: The PE ratio of Zurb Company is 15. Using a discount rate of 10% and knowing that the retention rate of earnings is 70%, the implicit ROE according to the Gordon-Shapiro model, is

Formula from Foundation:
kE = (EPS · p/P0) + (1 – p) · ROE

Solution: Step 1: [ -(EPS · p/P0)] Step 2: [ / (1 – p)]

ROE = (kE – EPS · p/P0) / (1 – p)                               Step 4: P0= (EPS · PE ratio)
= (kE – EPS · p/ EPS · PE ratio) / (1 – p)                    Step 5: EPS divided by EPS
= (kE – p / PE ratio) / (1 – p)
= (0.1 – 0.3/15) / 0.7 = 11.43%

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