The Retired Entrepreneurs Association for People (REAP) is funding projects for

Question

The Retired Entrepreneurs Association for People (REAP) is funding projects for improving the grain supply in countries with food shortages.  Their staff has obtained proposals as follows.  Each proposal has a upfront investment, estimated costs per year, and an estimated tons of food that would be produced.   Using a 10 year time span and a discount rate (MARR) of 7%, create a priority order in which the proposals should be funded.  REAP will then attempt to raise funds for as many as possible.

Proposal Upfront Investment Annual Costs Annual Tons of food produced P1 $14,000,000 $2,400,000 150,000 P2 $20,000,000 $2,700,000 140,000 P3 $17,000,000 $2,300,000 164,000 P4 $25,000,000 $2,240,000 155,000 P5 $10,000,000 $1,900,000 130,000 P6 $12,000,000 $2,000,000 144,000

Explanation / Answer

You should take into account the cost of financing over the ten year span by discounting to present value the annual costs for each project, using a discount rate of 7%. This is necessary because projects with a higher "up-front" cost might nonetheless be more economical in the long run, and thus may deserve to be ranked higher than they otherwise would be if the time value of money were not taken into account.

At any rate, dollars should be measured at the same time frame to be accurate. Use this formula to discount the annual cost for each project.:

=-PV($L$1,$L$2,C1)

Where:
C1 = P1 annual cost
L1 = 7%
L2 = 10

Once the present values are calculated, add the lump sum costs at time zero to each present value to arrive at a total cost figure for each project. Then calculate the cost per ton of food. Since the dollars are all present value dollars, it doesn't matter that the food is in per year/per ton amounts, the resulting statistic is the same for each project.

Then, you could rank the projects using the following.:

=RANK(H1,$H$1:$H$6,1)
Where:
H1 = the first per ton dollar amount
H1:H6 = are all the per/ton per/year amounts in one column

Given limited funding, management could choose the most economical (highest ranked) projects first, and deliver more food per dollar than without ranking.

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