Question

# Steve "The Chef" Smith decided to invest in LittleGive Bank in a \$10,000 certificate of deposit...

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.

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%