Question

Two firms, Firm X and Firm Y, are both considering investing in Project Z, which has an IRR of 10.60%
and a beta of 0.9. Firm X has an asset beta of 0.7 and Firm Y’s asset beta is 1.2. The risk-free rate is 3.00%
and the expected return on the market is 11.00%. Explain clearly and concisely whether each firm should
take the project, being sure to justify your reasoning.

Answer 1

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Correct Answer: Only firm X must accept the project Z

Working:

Parameters provided in the question,

Project Z has an IRR of 10.60 %

The risk-free rate, RF= 3 %

The expected market return E(RM) = 11 %

Beta for firm X,Beta X = 0.7

Beta for firm Y,Beta Y = 1.2

Calculating the expected return for each firm and comparing it with the project Z's IRR.Firms with lower expected returns than IRR of the project must take the project as it is more viable for them. Firms with the expected return greater than IRR must reject the same as the value created by the project will be less and must look for other projects.

Expected Return can be calculated using CAPM

CAPM(Capital Asset Pricing Model ),

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

• Now for expected return for FIRM X,

E(RX) = Risk-free rate + Beta X ( Expected market return - Risk-free rate )

= 3 + 0.7 (11- 3)

= 3 + 0.7 (8) = 3+ 5.6

E(RX )= 8.6

Thus expected return of firm X is 8.6 %

• Now expected return for FIRM Y,

E(RY) = Risk-free rate + Beta Y ( Expected market return - Risk-free rate )

= 3 + 1.2 (11- 3)

= 3 + 1.2 (8) = 3+ 9.6

E(RY )= 12.6 %

Thus expected return of firm Y is 12.6 %

Therefore, only firm X must accept the project as its expected return(8.6 %) is less than the IRR of project z(10.6 %). However, project Y must not accept project Z as its expected returns(12.6%) are greater than the project.