Question

Steve "The Chef" Smith decided to invest in LittleGive Bank in a
$10,000 certificate of deposit for 5

year that pays an interest rate of 3.5% annually (single interest).
Suppose that the interest payment

they send it annually in a check to your home and that this money
is taxable. When the

certificate, he will receive his $10,000 return (non-taxable
amount). The marginal tax rate of

"The Chef" is 24% and overall inflation is expected to be 2% per
year.

Determine for this investment instrument:

(a) The rate of return before taxes, ignoring inflation.

(b) The rate of after-tax return, ignoring inflation

(c) The rate of return after tax, considering inflation.

Answer #1

a. For this we calculate the IRR directly.

-10000 + 350/(1+r) + 350/(1+r)^2 + 350/(1+r)^3 + 350/(1+r)^4 + 10350/(1+r)^5 = 0

r= 3.5%.

b. Since it's after-tax, we will just deduct the tax amount. Hence, the $350 amount becomes 0.76 x 350 = $266

-10000 + 266/(1+r) + 266/(1+r)^2 + 266/(1+r)^3 + 266/(1+r)^4 + 10266/(1+r)^5 = 0

r = 2.66%.

c. Similarly, here we apply tax and divide the cashflows by 1.02% (inflation)

-10000 + 266/1.02(1+r) + 266/(1.02^2)(1+r)^2 + 266/(1.02^3)(1+r)^3 + 266/(1.02^4)(1+r)^4 + 10266/(1.02^5)(1+r)^5 = 0

r = 0.647%

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