Proposals A, B, C, D, E, F and G are being considered with money flows over...

Proposals A, B, C, D, E, F and G are being considered with money flows over 10 years. A B C D E F G Investment $30,000 $10,000 $55,000 $54,000 $20,000 $65,000 $27,000 Net Annual Benefit $7,000 $2,400 $10,000 $12,000 $4,000 $11,500 $7,500 Salvage Value $3,000 $0 $5,000 $2,000 $500 0 $1,000 Proposal (A and G) are mutually exclusive, (C and D) are also mutually exclusive, and proposal B depends on C or D. The MARR is set at 11%. a) Formulate the problem with Integer Programming. b) Which proposal(s) should be selected if the amount of money available for investment is $100,000?

Expert Solution

First of all let us calculate the IRR for each project which is given below:

IRR	19.84%	20.18%	13.32%	18.16%	15.26%	11.99%	24.86%
Year	A	B	C	D	E	F	G
0	30,000.00	10,000.00	55,000.00	54,000.00	20,000.00	65,000.00	27,000.00
1	-7000	-2400	-10000	-12000	-4000	-11500	-7500
2	-7000	-2400	-10000	-12000	-4000	-11500	-7500
3	-7000	-2400	-10000	-12000	-4000	-11500	-7500
4	-7000	-2400	-10000	-12000	-4000	-11500	-7500
5	-7000	-2400	-10000	-12000	-4000	-11500	-7500
6	-7000	-2400	-10000	-12000	-4000	-11500	-7500
7	-7000	-2400	-10000	-12000	-4000	-11500	-7500
8	-7000	-2400	-10000	-12000	-4000	-11500	-7500
9	-7000	-2400	-10000	-12000	-4000	-11500	-7500
10	-10000	-2400	-15000	-14000	-4500	-11500	-8500

After that we shall first allocate our capital to the option having the highest IRR:

Now based on various permutation we can think of the below mentioned combination and can compare the same on the basis of the combined IRR and NPV of proposed investments. This gives us the following result:

Option 1		NPV	₹ 7,417.42	Option 2			NPV	₹ 7,671.21
24.86%	20.18%	18.16%	20.42%	IRR	19.84%	20.18%	18.16%	18.92%
G	B	D	Total	Year	A	B	D	Total
27,000.00	10,000.00	54,000.00	91,000.00	0	30,000.00	10,000.00	54,000.00	94,000.00
-7500	-2400	-12000	-21,900.00	1	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	2	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	3	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	4	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	5	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	6	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	7	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	8	-7000	-2400	-12000	-21,400.00
-7500	-2400	-12000	-21,900.00	9	-7000	-2400	-12000	-21,400.00
-8500	-2400	-14000	-24,900.00	10	-10000	-2400	-14000	-26,400.00

As can be seen above the option 2 gives us much better proposition as although the IRR is higher under option 1 the overall net present value is higher in option two as we have been able to invest more though at a lower IRR but the increase in amount of investment more than compensates for the lower return.

jeff jeffy answered 1 year ago

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