# Question 3.14: Sound Limited has a financial resource constraint of a maxim......

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
Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.

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

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