Skip to content

FRM Part I · FRM Exam Part I · How Do Firms Manage Financial Risk?

A firm faces a progressive corporate tax schedule in which taxable income below USD 10 million is taxed at 20% and income above that level at 40%. Its pre-tax income is equally likely to be USD 4 million or USD 16 million in a year if unhedged. Which statement best describes why hedging to stabilize pre-tax income at USD 10 million could add value?

Hedging can add value because a progressive tax schedule is convex. Stabilizing income at USD 10 million gives tax of 2.0 million versus an expected 2.6 million unhedged, so expected taxes fall even though expected pre-tax income is unchanged.

  1. AExpected tax paid falls because the tax function is convex and smoothing income reduces expected taxesCorrect
  2. BExpected tax paid rises because stable income is taxed at the higher marginal rate
  3. CExpected pre-tax income rises because hedging eliminates the risk premium on operating assets
  4. DExpected tax is unchanged because the expected pre-tax income is the same

Explanation

Unhedged: income 4m taxed 0.8m; income 16m taxed 2.0m+2.4m=4.4m? Correcting: 10m×20%=2m plus 6m×40%=2.4m gives 4.4m; expected tax = (0.8+4.4)/2 = 2.6m. Hedged at 10m: tax = 2.0m. Expected tax falls by 0.6m because the tax schedule is convex. Option D ignores convexity.

Did you get it right without looking?

One question tells you little. A timed set on How Do Firms Manage Financial Risk? shows your real accuracy, how long you take and where you lose marks.

Practise How Do Firms Manage Financial Risk?Free diagnostic mock

More How Do Firms Manage Financial Risk? questions