This problem set will help illustrate how the timing of taxable income$/$deductions and taxes paid affects the present value of cash flows.

Please see this separate google doc for guidance on calculating present values.

Instructions:

Please calculate the present value of the following series of cash flow transactions.

Hint: if the pretax cash flow and the tax cash flows are in different time periods, you will want to calculate their present values separately and then add them together.

Assumptions:

Calculate present values using whole years. You do not need to prorate by days, months, etc.

While taxes are paid throughout the year $($as the income becomes taxable$)$ you can assume to simplify the calculations that all taxable income and tax payments are made$/$received at the same time at the end of the period.

The discount rate is $10\%.$

The tax rate is $30\%.$

n is the number of years in the future when the cash flow transpires.

Cash flow transactions:

$1.$ Calculate present value of taxable income of $$100,000$ received in the current taxable year $($n$=0).$

$2.$ Calculate the present value of taxable income and cash flow of $$100,000$ that is not received until the next taxable year $($n$=1).$

$3.$ Calculate the present value of a cash inflow of $$100,000$ received this taxable year $($n $=0)$ but that is not taxable until next year $($n $=1).$

$4.$ A business incurs a $$100,000$ expense in the current taxable year. Calculate the present value of the after$-$tax cash outflow using three scenarios:

The expense is fully deductible in the current taxable year $($n$=0).$

a$.$ The expense is deductive evenly over the course of five years. Hint: think of the annual tax savings as an annuity.

The expense is eligible for a tax credit that is equal to $20\%$ of the cost in year t$.$ The credit reduces the tax basis of the asset $($i$.$e$.,$ the amount that can be depreciated$).$ The remaining tax basis $($the $100$k minus the credit$)$ can be depreciated evenly over five years. Hint: think of the annual tax savings from depreciation deductions as an annuity.

$5.$ Now that we have an idea of how to calculate the NPV of a business expense, what other information do we need to evaluate whether to invest in the asset?