Sound Limited has a financial resource constraint of a maximum sum of Rs 65 lakh in the current year. It has evaluated a large number of investment projects but has discarded all except those listed below. All the listed investment proposals are independent. The selected list of investments provide investment outlays, gross present value, NPV and present value index.
Which investments should be acquired by Sound Limited?
Present\>value\>index  Gross\>present\>value  NPV  Investment\>outlay  Project 
1.69  Rs 36,92,500 \,  Rs 15,07,500 \,  Rs 21,85,000 \,  A 
1.56  29,80,000  10,70,000  19,10,000  B 
1.14  17,65,000  2,15,000  15,50,000  C 
1.21  15,75,000  2,75,000  13,00,000  D 
2.38  27,25,000  15,80,000  11,45,000  E 
1.45  13,65,000  4,25,000  9,40,000  F 
1.92  12,95,000  6,20,000  6,75,000  G 
1.73  9,25,000  3,90,000  5,35,000  H 
2.31  10,75,000  6,10,000  4,65,000  I 
2.11  9,07,500  4,77,500  4,30,000  J 
1.72  7,05,000  2,95,000  4,10,000  K 
1.87  6,55,000  3,05,000  3,50,000  L 
1.39  3,82,500  1,07,500  2,75,000  M 
1.84  4,50,000  2,05,000  2,45,000  N 
2.58  4,90,000

3,00,000

1,90,000

O 
2,09,87,500  83,82,500  1,26,05,000 
First, we should arrange the investment projects in descending order of present value (PI) index. The optimal investment portfolio/set will be one which yields the maximum NPV. The table below lists investment projects accordingly.
\, In case the company is simply guided by the PI index, then it selects the first nine projects (numbered from O through K) plus project B. This investment package yields an NPV of Rs 58,52,500.
\, However, this is not the optimal investment package as it does not provide the highest plausible NPV. By dropping Project K (Rs 4,10,000) and B (Rs 19,10,000) from the proposed investment package and substituting projects A (Rs 21,85,000) and M (Rs 2,75,000) the firm generates a higher NPV of Rs 61,02,500, as shown below.
\, Evidently, such a substitution exercise requires trial and error. Thus, the optimal investment package consists of 10 projects (O, E, I, J, G, L, N, H, A and M) requiring a total investment outlay of Rs 64.95 lakh, yielding a total NPV of Rs 61,02,500.
NPV\>of  Investment\>outlays\>of  PI \, 
Project \, 

Cumulative  Project  Cumulative  Project  
Rs 3,00,000 \,  Rs 3,00,000 \,  Rs 1,90,000 \,  Rs 1,90,000 \,  2.58  O 
18,80,000  15,80,000  13,35,000  11,45,000  2.38  E 
24,90,000  6,10,000  18,00,000  4,65,000  2.31  I 
29,67,500  4,77,500  22,30,000  4,30,000  2.11  J 
35,87,500  6,20,000  29,05,000  6,75,000  1.92  G 
38,92,500  3,05,000  32,55,000  3,50,000  1.87  L 
40,97,500  2,05,000  35,00,000  2,45,000  1.84  N 
44,87,500  3,90,000  40,35,000  5,35,000  1.73  H 
47,82,500  2,95,000  44,45,000  4,10,000  1.72  K 
—  15,07,500  66,30,000¹  21,85,000  1.69  A 
58,52,500²  10,70,000  63,55,000  19,10,000  156  B 
4,25,000  9,40,000  1.45  F  
1,07,500  2,75,000  1.39  M  
2,75,000  13,00,000  1.21  D  
2,15,000  15,50,000  1.14  C 
¹Not feasible at this stage; cumulative investment outlays exceed Rs. 65 lakh.
²Investment outlay as well as NPV consist of projects (from O to H) plus project B.
NPV\>of  Investment\>outlays\>of  Project \, 

Cumulative  Project\>(s)  Cumulative  Project\>(s)  
Rs 44,87,500  —  Rs 40,35,000  —  O to H 
59,95,000  15,07,500  62,20,000  21,85,000  A 
61,02,500  1,07,500  64,95,000  2,75,000  M 