7 PFK plc is an undiversified and ungeared company operating in the cardboard packaging industry. The Beta coefficient of its ordinary shares is 1.05. It now contemplates diversification into making plastic containers.

After evaluation of the proposed investment, it considers that the expected cash flows can be described by the following probability distribution:

The overall risk (standard deviation) of parent company returns is 20 per cent and the risk of the market return is 12 per cent. The risk-free rate is 5 per cent and the FTSE-100 Index is expected to offer an overall return of 10 per cent per annum in the foreseeable future.
The new project will increase the value of PFK’s assets by 33 per cent.
Required

(a) Calculate the risk–return characteristics of PFK’s proposed diversification.

(b) It is believed that the plastic cartons activity has a covariance value of 40 with the company’s existing activity.
(i) Calculate the total risk of the company after undertaking the diversification.
(ii) Calculate the new Beta value for PFK, given that the diversification lowers its overall covariance with the market portfolio to 120.
(iii) Deduce the Beta value for the new activity.
(iv) What appears to be the required return on this new activity?

(c) Discuss the desirability, from the shareholders’ point of view, of the proposed diversification.
You may ignore taxes.

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State of economy Probability Internal rate of return (%) Recession 0.2 -5 No growth 0.3 Steady growth 0.3 12 Rapid growth 0.2 5828 30