Question

A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $27,500 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 10%. Ignore inflation. a. Calculate project NPV for each company. (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.) NPV Company A Company B 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.) IRR Company A % Company B

Answer 1

a. Calculating NPV for company A

Initial investment = $100000, Before tax cash inflow flows for year 1 to 5 = $27500

Since the company does not pay any taxes, therefore before tax cash inflow for year 1 to 5 = After tax cash flow for company A for year 1 to 5 = 27500

NPV of Company A = - Initial Investment + Sum present values of after tax cash flows for year 1 to 5 discounted at opportunity cost of 10%

NPV of Company A = -100000 + 27500 / (1 + 10%) + 27500 / (1 + 10%)² + 27500 / (1 + 10%)³ +27500 / (1+10%)⁴ + 27500 / (1 + 10%)⁵   = -100000 + 25000 + 22727.2727 + 20661.1570 + 18782.8700 + 17075.3363 = 4246.6360 = 4246.64 (Rounded to two decimal places)

NPV for company A = 4246.64

Calculating NPV for company B

Initial investment = $100000, Before tax cash inflow flows for year 1 to 5 = $27500

Since the company qualifies for 100% bonus depreciation, hence depreciation in year 1 = 100% of initial investment = 100% x 100000 = 100000

Depreciation for year 2 to 5 = 0

After tax cash flow for year 1 = Cash inflow(1-tax rate) + Tax rate x depreciation =27500(1-21%) + 21% x 100000 = 21725 + 21000 = 42725

After tax cash flow for year 2 to 5 = 27500(1-21%) + 21% x 0 = 21725

NPV of Company B = - Initial Investment + Sum present values of after tax cash flows for year 1 to 5 discounted at opportunity cost of 10%

NPV of Company B = -100000 + 42725 / (1 + 10%) + 21725 / (1 + 10%)² + 21725 / (1 + 10%)³ +21725 / (1+10%)⁴ + 21725 / (1 + 10%)⁵   = -100000 + 38840.9090 + 17954.5454 + 16322.3140 + 14838.4673 + 13489.5157 = 1445.7514 = 1445.75 (rounded to two decimal places)

Hence NPV for company B = 1445.75

b. Calculating IRR for company A

IRR is rate of return earned by the project such that present value of after tax cash inflows is equal to initial investment of project. We need to find IRR such that

0 = -100000 + 27500 / (1 + IRR) + 27500 / (1 + IRR)² + 27500 / (1 + IRR)³ +27500 / (1+IRR)⁴ + 27500 / (1 + IRR)⁵

We can find IRR for company A using IRR function in excel

Formula to be used in excel: = IRR(Values)

where values represent cash flows of the project

F G H K Calculating IRR for company A 16 17 Year 0 1 2 3 4 18 Cash flow -100000 27500 27500 27500 27500 27500 IRR ( F18: K18) IRR(values, [guess]) 19 IRR of Project 20 21

Using IRR function in excel, we get IRR for company A = 11.6487% = 11.65% (rounded to two decimal places)

Hence IRR for company A = 11.65%

Calculating IRR for company B

IRR is rate of return earned by the project such that present value of after tax cash inflows is equal to initial investment of project. We need to find IRR such that

0 = -100000 + 42725 / (1 + IRR) + 21725 / (1 + IRR)² + 21725 / (1 + IRR)³ +21725 / (1+IRR)⁴ + 21725 / (1 + IRR)⁵

We can find IRR for company B using IRR function in excel

Formula to be used in excel: = IRR(Values)

where values represent cash flows of the project

G H K Cash Flow for Company B 23 24 Year 4 1 2 3 5 25 Cash flow 21725 -100000 42725 21725 21725 21725 26 IRR of Project B IRR (F25: K25 IRR(values, [guess) 27 28

Using IRR function in excel, we get IRR for company B = 10.6428% = 10.64%

Hence IRR for company B = 10.64%