Question

A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,000 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Company B pays corporate taxes at a rate of 21% and can claim 100% bonus depreciation on the investment. Suppose the opportunity cost of capital is 8%. Ignore inflation.

a. Calculate project NPV for each company. (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)

b. What is the IRR of the after-tax cash flows for each company? (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal places.)

Answer 1

To calculate the NPV, we will first need to compute future values of our cash inflows.

In the below calculation, our formula to calculate Present value factor is

1 / (1+ (R/100))ⁿ

Where R is rate of interest and N is no of years discounting is done.

So for first year it would be: 1 / (1+0.08)

= 0.9259

Similarly, we will do for rest 4 years. Below table shows the calculation for NPV for Company A. And note that no tax is applicable on Company A.

For NPV of Company B, they have a tax rate of 21%, which is to be charged on the inflows of the company, as a deduction from the inflow. Also, they have a 100 % Depreciation bonus, it means they can claim 20000 (Cost of Investment <100000>/ No of Years<5> ) amount as depreciation over the next five years. Tax saved on depreciation each year would be 20000 @ 21% = 4200, as tax is saved due to depreciation.

The calculations of NPV are shown below.

For company B, this project has Negative NPV

a. NPV for Each

Company A: $3810

Company B: -$1220

For calculating the IRR the formula is as under. The IRR is that rate of Discounting where the PV of Inflow of the Project is equal to the present value of the outflow.

Outflow of Project = Inflow 1 / (1+IRR/100)¹+ .....+ Inflow N / (1+IRR/100)ⁿ

^{(Where N is year in which cashflow is received, and IRR is the required return)}

Putting in values we get for Company A

100000 = 26000 / (1+IRR/100) + 26000 / (1+IRR/100)² + 26000 / (1+IRR/100)³ + 26000 / (1+IRR/100)⁴ + 26000 / (1+IRR/100)⁵

Solving for IRR we get

IRR = 9.44% Approx for Project A

Similarly for Project B:

100000 = 24740 / (1+IRR/100) + 24740 / (1+IRR/100)² + 24740 / (1+IRR/100)³ + 24740 / (1+IRR/100)⁴ + 24740 / (1+IRR/100)⁵

Solving for IRR we get

IRR = 7.54% Approx for Project B