Question

5- The Nile Basin countries are considering three flood control projects in Ethiopia. Project A is a dam. The dam will have recreation and irrigation benefits as well as the flood control benefits. Projects B and C consist of permanent dikes along the river. Facts about the three projects are shown in the following table. Each project has a life of 25 years. The MARR is 10%. Use (a) BCR & (b) IRR method to choose the best project. Project A Project B Project C First Cost (millions of 5) Annual Benefits (millions of $) 4.2 3.3 Annual Operating and Maintenance Costs (millions $) 52 32 25 7.1 0.5 0.3 0.3

Written solution please

Answer 1

It shall be noted that Project A, Project B, and Project C have a life span of 25 years.

MARR = 10%

Under IRR, Internal rate of return (IRR) is estimated such that the present value of the net cash inflow is zero over the life span of the project.

Under BCR, the benefit to the cost ratio would be estimated such that B/C ratio = Sum of PV of Cash Inflow/Sum of PV of Cash Outflow

Here, Cash Inflow constitutes the benefit and Cash Outflow constitutes the costs.

The PV of Cash Inflow = Cash Inflow/(1+MARR)^n

The PV of Cash Outflow = Cash Outflow/(1+MARR)^n

Where n = nth Year

The estimate of IRR and B/C ratio for Project A is given as follows:

Project A
Year	Cash Inflow	Cash Outflow	Net Cash Inflow	PV of Cash Inflow	PV of Cash Outflow
0		52	-52	0	52
1	7.1	0.5	6.6	6.454545	0.454545
2	7.1	0.5	6.6	5.867769	0.413223
3	7.1	0.5	6.6	5.334335	0.375657
4	7.1	0.5	6.6	4.849396	0.341507
5	7.1	0.5	6.6	4.408541	0.310461
6	7.1	0.5	6.6	4.007765	0.282237
7	7.1	0.5	6.6	3.643423	0.256579
8	7.1	0.5	6.6	3.312202	0.233254
9	7.1	0.5	6.6	3.011093	0.212049
10	7.1	0.5	6.6	2.737357	0.192772
11	7.1	0.5	6.6	2.488507	0.175247
12	7.1	0.5	6.6	2.262279	0.159315
13	7.1	0.5	6.6	2.056617	0.144832
14	7.1	0.5	6.6	1.869652	0.131666
15	7.1	0.5	6.6	1.699684	0.119696
16	7.1	0.5	6.6	1.545167	0.108815
17	7.1	0.5	6.6	1.404697	0.098922
18	7.1	0.5	6.6	1.276997	0.089929
19	7.1	0.5	6.6	1.160907	0.081754
20	7.1	0.5	6.6	1.05537	0.074322
21	7.1	0.5	6.6	0.959427	0.067565
22	7.1	0.5	6.6	0.872206	0.061423
23	7.1	0.5	6.6	0.792915	0.055839
24	7.1	0.5	6.6	0.720832	0.050763
25	7.1	0.5	6.6	0.655302	0.046148
		IRR	11.935%	B/C	1.139877

The estimate of IRR and B/C ratio for Project B is given as follows:

Project B
Year	Cash Inflow	Cash Outflow	Net Cash Inflow	PV of Cash Inflow	PV of Cash Outflow
0		32	-32	0	32
1	4.2	0.3	3.9	3.818182	0.272727
2	4.2	0.3	3.9	3.471074	0.247934
3	4.2	0.3	3.9	3.155522	0.225394
4	4.2	0.3	3.9	2.868657	0.204904
5	4.2	0.3	3.9	2.60787	0.186276
6	4.2	0.3	3.9	2.370791	0.169342
7	4.2	0.3	3.9	2.155264	0.153947
8	4.2	0.3	3.9	1.959331	0.139952
9	4.2	0.3	3.9	1.78121	0.127229
10	4.2	0.3	3.9	1.619282	0.115663
11	4.2	0.3	3.9	1.472074	0.105148
12	4.2	0.3	3.9	1.338249	0.095589
13	4.2	0.3	3.9	1.21659	0.086899
14	4.2	0.3	3.9	1.105991	0.078999
15	4.2	0.3	3.9	1.005447	0.071818
16	4.2	0.3	3.9	0.914042	0.065289
17	4.2	0.3	3.9	0.830948	0.059353
18	4.2	0.3	3.9	0.755407	0.053958
19	4.2	0.3	3.9	0.686734	0.049052
20	4.2	0.3	3.9	0.624303	0.044593
21	4.2	0.3	3.9	0.567548	0.040539
22	4.2	0.3	3.9	0.515953	0.036854
23	4.2	0.3	3.9	0.469048	0.033503
24	4.2	0.3	3.9	0.426408	0.030458
25	4.2	0.3	3.9	0.387643	0.027689
		IRR	11.360%	B/C	1.097931

The estimate of IRR and B/C ratio for Project C is given as follows:

Project C
Year	Cash Inflow	Cash Outflow	Net Cash Inflow	PV of Cash Inflow	PV of Cash Outflow
0		25	-25	0	25
1	3.3	0.3	3	3	0.272727
2	3.3	0.3	3	2.727273	0.247934
3	3.3	0.3	3	2.479339	0.225394
4	3.3	0.3	3	2.253944	0.204904
5	3.3	0.3	3	2.04904	0.186276
6	3.3	0.3	3	1.862764	0.169342
7	3.3	0.3	3	1.693422	0.153947
8	3.3	0.3	3	1.539474	0.139952
9	3.3	0.3	3	1.399522	0.127229
10	3.3	0.3	3	1.272293	0.115663
11	3.3	0.3	3	1.15663	0.105148
12	3.3	0.3	3	1.051482	0.095589
13	3.3	0.3	3	0.955892	0.086899
14	3.3	0.3	3	0.868993	0.078999
15	3.3	0.3	3	0.789994	0.071818
16	3.3	0.3	3	0.718176	0.065289
17	3.3	0.3	3	0.652887	0.059353
18	3.3	0.3	3	0.593534	0.053958
19	3.3	0.3	3	0.539576	0.049052
20	3.3	0.3	3	0.490524	0.044593
21	3.3	0.3	3	0.445931	0.040539
22	3.3	0.3	3	0.405392	0.036854
23	3.3	0.3	3	0.368538	0.033503
24	3.3	0.3	3	0.335034	0.030458
25	3.3	0.3	3	0.304577	0.027689
		IRR	11.145%	B/C	1.080479

Thus, on the basis of IRR, Project A is chosen as the best project as the IRR of 11.935% is the highest.

On the basis of B/C ratio, Project A is chosen as the best project as the B/C ratio of 1.139877 is the highest.