Question

A company is evaluating two equal risky projects, S & L. Project S cost $2,050 and have cash inflows of $750, $760, $770, and $780 in years 1,2,3, and 4, respectively. Project L, costs $4,300 and have cash inflows of $1,500, $1,518, $1,536, and $1,554 in years 1,2,3, and 4 , respectively. The cost of Capital for both projects is 11%.

What is the NPV and IRR of project S? What is the NPV and IRR for Project L?

Is there a conflict between NPV and IRR, if the WACC is 11%

What is the Cross Over point for these mutually Exclusive Projects?

Answer 1

Calculation of NPV for Project S
Year	Cash Flow	Present Value Factor	Net Present Value
0	-2050	1	-2050
1	750	0.90	675.68
2	760	0.81	616.83
3	770	0.73	563.02
4	780	0.66	513.81
Net Present Value			319.34

To Know the IRR, the rate at which the present value of cash outflows equals cash inflows and Net present value is Zero. In Project S the IRR will be higher than 11% as the NPV is positive. By using the interpolation method, we would calculate the IRR of the project.

Calculation of IRR for Project S
Year	Cash Flow	Present Value Factor = Rate 18%	Net Present Value
0	-2050	1	-2050
1	750	0.85	635.59
2	760	0.72	545.82
3	770	0.61	468.65
4	780	0.52	402.32
Net Present Value			2.37

Calculation of NPV for Project L
Year	Cash Flow	Present Value Factor (1/(1+r)^n)	Net Present Value
0	-4300	1	-4300
1	1500	0.90	1351.35
2	1518	0.81	1232.04
3	1536	0.73	1123.11
4	1554	0.66	1023.67
Net Present Value			430.17

Calculation of IRR for Project S
Year	Cash Flow	Present Value Factor = Rate 16%	Net Present Value
0	-4300	1	-4300
1	1500	0.87	1298.70
2	1518	0.75	1137.91
3	1536	0.65	996.89
4	1554	0.56	873.22
Net Present Value			6.72

There is a conflict in IRR and NPV when using 11% as the discount rate. this can be observed as the project S has higher IRR but lower NPV.

To Calculate Crossover point we will discount the differences in the cash flows.

Calculation of Crossover Point
Year	Cash Flow	Present Value Factor (1/(1+r)^n) = Rate 13%	Net Present Value
0	-2250	1	-2250
1	750	0.88	663.72
2	758	0.78	593.63
3	766	0.69	530.88
4	774	0.61	474.71
Net Present Value			12.93