Question

# A tax-exempt investment (X) offers annual return of 7.5%, a taxable investment (Y) offers annual return...

1. A tax-exempt investment (X) offers annual return of 7.5%, a taxable investment (Y) offers annual return of 9%. Which investment will you choose if your marginal tax rate is 30%? At what marginal tax rate will you be indifferent between the two investment alternatives?

a) Marginal tax rate = 30%

The after-tax annual return on investment Y = 9% * (1 - 0.30)

The after-tax annual return on investment Y = 9% * 0.70

The after-tax annual return on investment Y = 0.063

The after-tax annual return on investment Y = 6.3%

We will choose the tax-exempt investment X, because it has a higher annual return of 7.5% as compared to the after-tax annual return on investment Y of 6.3%

b) Now, we need to find the tax rate such that the after-tax return on investment Y is equal to the annual return on investment X.

That is,

7.5% = 9% * (1 - tax rate)

0.075 = 0.09 - 0.09 * tax rate

0.09 * tax rate = 0.09 - 0.075

0.09 * tax rate = 0.015

tax rate = 0.015/0.09

tax rate = 0.1666666667

At the marginal tax rate of 16.66666667% we will be indifferent between the two investment alternatives.

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