Question

You are analyzing a project which has a $20,000 sunk cost. The project’s cost is $150,000 and the expected cash flows are: (Use this info for questions #1-4)

            Year 1: $60,000

            Year 2: $0

            Year 3: $100,000

            Year 4: $0

            Year 5: $60,000

The discount rate is 18% (the required return is also 18%). The required payback is 2.3 years.

1. Calculate the internal rate of return (must have correct set-up and your answer should be between two consecutive whole percentages). Accept or reject?

2. Calculate the discounted payback period. Accept or reject?

3. Calculate the payback period. Accept or reject?

4. Calculate the NPV.  Accept or reject?

Answer 1

1) IRR is the rate at which NPV is 0,Let us assume rate to be 14%

Statement showing NPV at 14%

Year	Cash flow	PVIF @ 14%	Present value
1	60000	0.8772	52632
2	0	0.7695	0
3	100000	0.6750	67497
4	0	0.5921	0
5	60000	0.5194	31162
Total			151291
Less: Initial Investment			150000
NPV			1291

Now let us assume rate to be 15%,

Statement showing Npv at 15%

Year	Cash flow	PVIF @ 15%	Present value
1	60000	0.8696	52174
2	0	0.7561	0
3	100000	0.6575	65752
4	0	0.5718	0
5	60000	0.4972	29831
Total			147756
Less: Initial Investment			150000
NPV			-2244

Using interpolation one can find IRR

Rate	NPV
14%	1291
15%	-2244
1% up	-3535
?	-1291

=1291/3535 = 0.36

Thus IRR = 14+0.36

=14.36%

Since IRR is less than NPV, project should be rejected

2) Statement showing discounted cash payback period

Year	Cash flow	PVIF @ 18%	Present value	Cummulative Present value
1	60000	0.8475	50847.46	50,847.46
2	0	0.7182	0.00	50,847.46
3	100000	0.6086	60863.09	111,710.54
4	0	0.5158	0.00	111,710.54
5	60000	0.4371	26226.55	137,937.10

Total cummulative present value at end of year 5 is 137,937.1$ which is less that projects initial cost i.e 150,000$

hence project won't pay back even at end of year 5

one should reject the project

3) Statement showing payback period

Year	Cash flow	CummulatiCash flow
1	60000	60000
2	0	60000
3	100000	160000
4	0	160000
5	60000	220000

Using interpolation one can find payback period

Year	Cummulative cash flow
2	60000
3	160000
1 up	100000
?	90000

=1*90000/1000000

=0.9

Thus payback period = 2 + 0.9 =2.9 years

Reject the project

4) Statement showing NPV

Year	Cash flow	PVIF @ 18%	Present value
1	60000	0.8475	50847
2	0	0.7182	0
3	100000	0.6086	60863
4	0	0.5158	0
5	60000	0.4371	26227
Total			137937
Less: Initial Investment			150000
NPV			-12063

Since NPV is negative , project should be rejected