Question

1. Describe the relationship between the IRR and the discount rate when NPV=0.

2. Given the following information, should a company invest in a given capital?

	Initial Investment $675,000 Annual Cash Inflow $158,000 Salvage Value $80,000 Years of life of the equipment and project: 6 Minimum required rate of return: 10% Depreciation $99,167 Payback Period in Years 4.3 Accounting Rate of Return 8.72% NPV $27,553.5 IRR 11.32%

Answer 1

Requirement 1

IRR is the rate of return at which the NPV of any project is equal to zero. We can also sat that if the actual rate of return is more that IRR then it’s better to accept the project.

IRR rate is also a discount rate at which a given number of cash flows are discounted to calculate present value of cash inflows and ultimately Net present value (Total present value of cash inflows-initial cash outflow)

Let me give an example to show what is IRR.

Year	Annual Cash Flow	NPV Factor at 10% Discount rate	Discounted Cash Flow
1	$ 1,00,453.00	0.90909	$      91,321
2	$ 1,54,117.00	0.82645	$ 1,27,370
3	$ 2,15,412.00	0.75131	$ 1,61,841
4	$      45,458.00	0.68301	$      31,048
5	$ 1,48,774.00	0.62092	$      92,377
6	$ 5,51,489.00	0.56447	$ 3,11,299
Present velue of Cash Inflows			$ 8,15,256
Less: Initial Investment			$ 815,256
Net Present value			$          0

Year	Annual Cash Flow	NPV Factor at 8% Discount rate	Discounted Cash Flow
1	$ 1,00,453.00	0.92593	$             93,012
2	$ 1,54,117.00	0.85734	$         1,32,130
3	$ 2,15,412.00	0.79383	$         1,71,001
4	$      45,458.00	0.73503	$             33,413
5	$ 1,48,774.00	0.68058	$         1,01,253
6	$ 5,51,489.00	0.63017	$         3,47,532
Present value of Cash Inflows			$         8,78,341
Less: Initial Investment			$         8,15,256
Net Present value			$             63,085

In the above example we can see that NPV at 10% discount rate is zero but taking 8% rate there is a positive NPV of $63,085.

Requirement 2

Advice--- Company should accept the given capital project.

We can clearly see that the NPV in the given solution is positive. At IRR NPV is zero and a positive NPV is an indication that project can be accepted. NPV at minimum rate of return is $58,289 as calculated below.

Year	Annual Cash Flow	NPV Factor at 10% Discount rate	Discounted Cash Flow
1	$ 1,58,000.00	0.90909	$         1,43,636
2	$ 1,58,000.00	0.82645	$         1,30,579
3	$ 1,58,000.00	0.75131	$         1,18,708
4	$ 1,58,000.00	0.68301	$         1,07,916
5	$ 1,58,000.00	0.62092	$             98,106
6	$ 1,58,000.00	0.56447	$             89,187
6	$      80,000.00	0.56447	$             45,158
Present value of Cash Inflows			$         7,33,289
Less: Initial Investment			$         6,75,000
Net Present value			$             58,289