# 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%

# TI BA II Plus: Calculating Duration, Modified Duration, Price Impact for change in YTM by +50bp

Exam Question: At the end of May 2013, one of your clients wants to invest 10’000 EUR in the bond market to diversify his fixed income portfolio. You will propose a bond 3,5% Italy 31.05.2016 (annual coupon). The yield to maturity of this bond is 2,7%. In case of an increase of 50 basis points, what will be the impact on the bond’s price?

Step 1: Calulate Bond Price with YTM 2.7%

a. use N, I/Y, PMT, FV to calulate current bond price

N = 3 (3 years), I/Y = 2,7 (YTM), PMT = 3,5 FV= 100   –> compute CPT PV = 102,276

Step 2: Calculate Duration of Bond

a. CF Menu: (leave CFO empty) CF1 = 1 * 3,5  N=1  / CF2 = 2 * 3,5  N=1 / CF3 = 3 * 103,50 N =1

b. use NPV key: I = 2,7   CPT NPV = 296,69365

c. Duration =  NPV / PV    so step 2b value divided by step 1a value    =  2,9009   or ~2,901

Step 3: Calculate Modified Duration (MD)

a. MD = D / 1+Y        2,901 / 1,027 = 2,8246 ~2.825

Step 4: Calculate Price Impact of a 50bp (0.005) increase in interest rates using Modified Duration (MD)

= – MD * change in interest rate  = -2.825 * 0.005 = -0.0141 = -1.41% solution: It will lower the bond price by 1,41%

Note: There are other ways to arrive at this solution. I intentionally used the duration example to be able to demonstrate using the Texas Instruments BA II Plus calculator.

Formula: Maculay Duration (Step 2)

Forumla: Modified Duration , Price Duration (Step 3)

Forumla: Price change approximated with Modified Duration (Step 4)

Numbers as in CIIA Exam 2003; Fo2-September2003-English-MCQ-8