Question

Ingrid Ilyasova is considering the purchase of the common stock of the Irish Indigo Inc. The most recent dividend paid by the company was $3.78 per share. This dividend is expected to increase at a constant rate of 5.25% indefinitely. Ingrid uses the CAPM to calculate her required rate of return. The current rate on U.S. Treasury securities is 2.78% and the expected rate of return on the stock market going forward is 16.22%. If the beta of the company is 1.17, what is the maximum amount that Ingrid would pay for a share of stock for this company ?

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Answer 1

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Correct Answer: $ 30.04

Working :

Since the dividend of Irish Indigo Inc is expected to grow at a constant rate after 1 year, we will use the Gordon Growth model to find the required rate of return.

Gordon Growth Model is given by

P = D1 / ( R - G )

Here,

• P= Current Selling price of the stock
• D1= Dividend for the next year
• G = Constant growth rate
• R = Required return on stock

Parameters provided in the question=

• P=?
• D0(Most recent dividened)= $ 3.78
• G = 5.25 % or 0.0525
• R =?

First Calculating D1

D1 = Do(1+g)

D1 = 3.78 (1.0525)

D1 = $ 3.9784

Now Calculating the required return on the stock using CAPM,

CAPM(Capital Asset Pricing Model ),

R = Risk-free rate + Beta (Expected market return - Risk-free rate )

Here

Risk-free rate = 2.78 % as the U.S treasury is considered to be risk-free since they are backed by the US government.

Beta = 1.17

Expected market return = 16.22 %

Substituting these values to find the expected return

R = Risk-free rate + Beta (Expected market return - Risk-free rate )

R = 2.78 + 1.17 (16.22 - 2.78)

R = 2.78 + 1.17 (13.44)

R = 2.78 + 15.7248

R= 18.50 %

Now using the Gordan growth model to find the price of Indigo Inc,

Substituting the values in the formula.

P = D1 / ( R - G )

=> P = 3.98 / (0.1850 - 0.0525)

=> P = 3.98 / 0.1325

=> P = $ 30.04

Therefore, the maximum amount that Ingrid would pay for a share of stock of for Irish indigo inc is $ 30.04