Question

A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $27,800 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 11%. Ignore inflation.

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

Company A's NPV?

Company B's NPV?

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.)

Company A's IRR?

Company B's IRR?

Answer 1

Net Present Value (NPV) is a sum of present values of all present and future cash flows, due to the difference in the timming of cash flows they are discounted to the present.

Internal rate of Return (IRR) is the discounted rate where the NPV of a project or asset is equal to zero.

A.  Calculation of NPV:

Company A -

Initial Investment = $100,000

Before tax cash inflow = $27,800

Total years of cash inflow = 5 years

Since Comapny A not paying any taxes, then After tax cash flow = Before tax cash flow for 5 years

Years	Cash Inflow (CF)	PVIF @ 11%	Present Value of CF
1	$ 27,800	0.9009	$25,045.05
2	$ 27,800	0.8116	$22,563.10
3	$ 27,800	0.7312	$20,327.12
4	$ 27,800	0.6587	$18,312.72
5	$ 27,800	0.5935	$16,497.95
Total			$1,02,745.94

NPV = Present Value of Inflows - Present Value of Outflow

= $102,745.94 - $100,000 * PVIF (11%,0)

= $102,745.94 - $100,000 *1

= $2745.94

NPV of Project A = $2,746 (round off nearest dollor amount)

Company B -

Initial Investment = $100,000

Before tax cash inflow = $27,800

Total years of cash inflow = 5 years

Since Comapny B qualifies for 100% bonus depreciation, so depreciation in 1_st year= 100% of Initial Investment = $100,000 * 100% = $100,000

Depreciation for 2_nd to 5_th year = 0 , because claim full in first year.

After Tax Cash Inflow ( 1 - 5 ) = $27,800 * ( 1 - 0.21) = $27,800 * 0.79 = $21,962

Tax Saving on Depreciation in year 1 = $100,000 * 0.21 = $21,000

total inflow in year 1 = $21,962 + $21,000 = $42,962

Years	Cash Inflow (CF)	PVIF	Present Value of CF
1	$ 42,962	0.9009	$ 38,704.50
2	$ 21,962	0.8116	$ 17,824.85
3	$ 21,962	0.7312	$ 16,058.43
4	$ 21,962	0.6587	$ 14,467.05
5	$ 21,962	0.5935	$ 13,033.38
Total			$ 1,00,088.21

NPV = Present Value of Inflows - Present Value of Outflow

= $100,088.21 - $100,000 * PVIF (11%,0)

= $100,088.21 - $100,000 * 1

= $88.21

NPV of Project B = $88 (round off nearest dollor amount)

B.  Calculation of IRR:

We calculate IRR from Excel Function -

IRR of Project A= 12.09%

IRR of Project B= 11.04%