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Question 9.S-TQ9: One-third of the total market value of Johnson plc consists ...

One-third of the total market value of Johnson plc consists of bonds with a cost of 10 per cent. York plc is identical in every respect to Johnson except that it is financed by equity alone. York’s cost of equity is 16 per cent. According to Modigliani and Miller, if taxation and tax relief on interest are ignored, what is Johnson plc’s cost of equity?

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Here we are assuming that the world of Miller and Modigliani’s first paper exists. Therefore the two companies should have identical WACCs. Because York is all-equity financed, its WACC is the same as its cost of equity finance, i.e. 16 per cent. It follows that Johnson must have a WACC equal to 16 per cent also.

Therefore: (1/3 × 10%) + (2/3 × K_e ) = 16%

Hence: K_e = 19%

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