Question

NPV profiles: scale differences

A company is considering two mutually exclusive expansion plans. Plan A requires a $41 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.55 million per year for 20 years. Plan B requires a $11 million expenditure to build a somewhat less efficient, more labor-intensive plant with an expected cash flow of $2.47 million per year for 20 years. The firm's WACC is 10%.

1. NPV profiles for Plan A and Plan B, approximate the crossover rate to the nearest percent.

Answer 1

Answer: The cross-over rate is 12.25%. It means that to the nearest % it is 12% (rounded to 0 decimal place)

Calculations and explanations:

The NPV at WACC of 10% for A and B is shown below:

Year	A's cash flow (in $ millions)	1+r	PVIF	PV of A = cash flow*PVIF		B's cash flow (in $ millions)	PV of B = cash flow*PVIF
0	-41	1.1	1.00000	-                   41.00		-                                                  11	-                        11.00
1	6.55		0.90909	5.95		2.47	2.25
2	6.55		0.82645	5.41		2.47	2.04
3	6.55		0.75131	4.92		2.47	1.86
4	6.55		0.68301	4.47		2.47	1.69
5	6.55		0.62092	4.07		2.47	1.53
6	6.55		0.56447	3.70		2.47	1.39
7	6.55		0.51316	3.36		2.47	1.27
8	6.55		0.46651	3.06		2.47	1.15
9	6.55		0.42410	2.78		2.47	1.05
10	6.55		0.38554	2.53		2.47	0.95
11	6.55		0.35049	2.30		2.47	0.87
12	6.55		0.31863	2.09		2.47	0.79
13	6.55		0.28966	1.90		2.47	0.72
14	6.55		0.26333	1.72		2.47	0.65
15	6.55		0.23939	1.57		2.47	0.59
16	6.55		0.21763	1.43		2.47	0.54
17	6.55		0.19784	1.30		2.47	0.49
18	6.55		0.17986	1.18		2.47	0.44
19	6.55		0.16351	1.07		2.47	0.40
20	6.55		0.14864	0.97		2.47	0.37
			NPV of A	14.76		NPV of B	10.03

(1) Using the above model I have determined the NPV profiles for A and B starting from 0% and at incremental rates of 1 %

Rate	NPV of A	NPV of B
0.00%	90.00	38.40
1.00%	77.20	33.57
2.00%	66.10	29.39
3.00%	56.45	25.75
4.00%	48.02	22.57
5.00%	40.63	19.78
6.00%	34.13	17.33
7.00%	28.39	15.17
8.00%	23.31	13.25
9.00%	18.79	11.55
10.00%	14.76	10.03
11.00%	11.16	8.67
12.00%	7.92	7.45
12.25%	7.16	7.16
13.00%	5.01	6.35

Thus cross over rate is 12.25% and this can be rounded off to 12% (nearest %)

The same can be seen from the graph below: