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ACCA Strategic Professional · Advanced Financial Management · Impact of financing on investment decisions and adjusted present values

A company with a constant debt-to-equity ratio of 1:2 (by market value) has a geared cost of equity of 12%. Its pre-tax cost of debt is 5% and the corporate tax rate is 20%. Using the Modigliani and Miller with-tax relationship, Keg = Keu + (Keu − Kd)(1 − t)(D/E), what is the ungeared cost of equity (Keu) to use in an APV calculation?

The ungeared cost of equity is 10.0%. Setting 12 = Keu + (Keu − 5) × 0.8 × 0.5 gives 12 = 1.4Keu − 2, so Keu = 10%. Leaving out the (1 − t) factor would wrongly give 9.67%.

  1. A12.0%
  2. B9.67%
  3. C10.0%Correct
  4. D8.0%

Explanation

12 = Keu + (Keu − 5)(0.8)(0.5) = Keu + 0.4Keu − 2 = 1.4Keu − 2, so Keu = 10%. Check: 10 + 5 × 0.4 = 12. Ignoring tax (using factor 0.5 instead of 0.4) gives 9.67%, which is wrong because the relationship must include (1 − t).

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