Question

Purchased a one year treasury bill that offers an effective annual yield of 12 percent. You are confident that there will be 6 percent rate inflation. The tax rate is 33.33 percent, i.e, the tax rate is exactly one-third. What after tax real return are you expecting?

Answer 1

By definition, The after-tax real rate of return is the actual financial benefit of an investment after accounting for inflation and taxes.

Effective annual yield or rate of return = 12%. This is nominal rate of return.

We first need to calculate the aftr tax nominal rate of return here:

After tax nominal rate of return = Nominal rate of Return * (1 - tax rate) = 12% * (1 - 33.33%) = 8%

Inflation = 6%.

By the exact formula of Fisher's effect,

(1 + Nominal rate of Return) = (1 + Real rate of return) * (1 + Inflation)

(1 + Real rate of return) = (1.08)/(1.06) = 1.01887

Real rate of Return = 0.01887 = 1.89%. After tax Real rate of Return.

{Some text also mention the mathematical relation between nominal and real rate of return as "Nominal rate = Real rate + Inflation". This is an approximation formula, derived from the above relation itself. If this was applied. After tax real rate of return would have been 2%}