Question

Here are the cash flows for two mutually exclusive projects:

Project

C0

C1

C2

C3

A

−$

23,000

+$

10,120

+$

10,120

+$

10,120

B

−

23,000

0

0

+

31,050

What is the IRR of each project? (Round your answers to 2 decimal places.)

Answer 1

IRR is the rate of return at which NPV = 0.

IRR will be calculated using trial & error method. Steps to be followed are as follows:

Step 1: Calculate NPV of the project different discount rates.Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflows
Step 2: Choose 2 discount rates. Preferabably one discount rate at which NPV is positive and another discount rate at which NPV is negative. (The difference between 2 discount rates shall not be more than 5%)
Step 3 : Apply interpolation

A) Calculation of IRR of Project A

Let Discount rate = 15%
Calculation of NPV at discount rate = 15%

Year	Cash flows	PVF@15%	Present value
0	$(23,000.00)	1	$(23,000.00)
1	$10,120.00	0.869565217	$8,800.00
2	$10,120.00	0.756143667	$7,652.17
3	$10,120.00	0.657516232	$6,654.06
		NPV	$106.24

At discount rate = 15%, NPV is positive. Therefore, we need to discount at a higher rate.

Let Discount rate = 16%
Calculation of NPV at discount rate = 16%

Year	Cash flows	PVF@16%	Present value
0	$(23,000.00)	1	$(23,000.00)
1	$10,120.00	0.862068966	$8,724.14
2	$10,120.00	0.743162901	$7,520.81
3	$10,120.00	0.640657674	$6,483.46
		NPV	$(271.60)

At discount rate = 16%, NPV is negative. Therefore, IRR lies between 15% & 16%

Using interpolation
IRR = 15% + (16%-15%) $106.24 / $106.24-(-$271.60)
IRR = 15% + 1%* $106.24 / $377.84
IRR = 15% + 0.2811754%
IRR = 15.28 % approx.

B) Calculation of IRR of Project B

Let Discount rate = 10%
Calculation of NPV at discount rate = 10%

Year	Cash flows	PVF@10%	Present value
0	-23,000	1	$(23,000.00)
1	0	0.909090909	$-
2	0	0.826446281	$-
3	31,050	0.751314801	$23,328.32
		NPV	$328.32

At discount rate = 10%, NPV is positive. Therefore, we need to discount at a higher rate.

Let Discount rate = 11%
Calculation of NPV at discount rate = 11%

Year	Cash flows	PVF@11%	Present value
0	-23,000	1	$(23,000.00)
1	0	0.900900901	$-
2	0	0.811622433	$-
3	31,050	0.731191381	$22,703.49
		NPV	$(296.51)

At discount rate = 11%, NPV is negative. Therefore, IRR lies between 10% & 11%

Using interpolation
IRR = 10% + (11%-10%) $328.32 / $328.32 -(-$296.51)
IRR = 10% + 1%* $328.32 / $624.83
IRR = 10% + 0.5254604%
IRR = 10.53 % approx.

Note :
PVF(r,t) = (1/(1+r))^n