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Worksheet Grade 12 Social Studies & Civics

Cost Shares at Quillsmere Reservoir: Who Repays What

A grade 12 worksheet that splits a fictional multipurpose reservoir's cost among flood control, water supply, hydropower, and recreation, then asks who repays each share.

Objectives

  1. Students will allocate a multipurpose project's capital cost among its purposes using a stated benefit-share method.
  2. Students will distinguish reimbursable from non-reimbursable cost shares and compute the annual repayment each beneficiary owes.
  3. Students will evaluate who gains and who loses when the allocation method changes.

Vocabulary

Key words: multipurpose project, cost allocation, reimbursable cost, separable cost, beneficiary

Teacher overview

A large dam is rarely built for one reason. The same structure holds back floods, stores drinking water, spins turbines, and creates a lake that people fish and boat on, and each of those purposes has a different beneficiary who may or may not be asked to pay. This worksheet uses the fictional Quillsmere Reservoir and a fictional state repayment statute to work through a benefit-share allocation, the repayment each beneficiary owes, and the political question underneath the arithmetic. The misconception to correct before students start is the assumption that a share labeled non-reimbursable costs nobody anything; taxpayers pay it, so the label records a decision about who bears the cost rather than the absence of one. Items 1 through 11 are computational, and items 12 through 14 ask students to judge who gains from the method that was chosen.

Cost Shares at Quillsmere Reservoir: Who Repays What — Grade 12 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

Quillsmere Reservoir is a fictional project built for four purposes: flood control, municipal water supply, hydropower, and recreation. The project cost $480 million to build. A study estimated the annual benefit of each purpose at $20 million for flood control, $15 million for water supply, $10 million for hydropower, and $5 million for recreation.

Under the fictional state statute that governs repayment, capital cost is divided among the purposes in proportion to their annual benefits. The flood control share is non-reimbursable, meaning state taxpayers pay it. The water supply, hydropower, and recreation shares are reimbursable, meaning the beneficiary of each purpose repays it. Use the figures stated in each item, and round money answers to the nearest dollar.

  1. Add the four annual benefit estimates. What is the total annual benefit of the project?
  2. Flood control's annual benefit is $20 million. Using your total from item 1, what percent of the total benefit does flood control account for?
  3. Water supply accounts for 30 percent of the total benefit. Using the $480 million project cost, what capital cost is allocated to water supply?
  4. Hydropower accounts for 20 percent of the total benefit. What capital cost is allocated to hydropower?
  5. Recreation is allocated $48 million and flood control is allocated $192 million. Using your answers from items 3 and 4, what is the total reimbursable capital cost?
  6. State taxpayers pay only the $192 million flood control share. What percent of the $480 million project cost do state taxpayers carry?
  7. The fictional city of Wraycombe holds the water supply contract and repays its $144 million share in equal payments over 40 years with no interest. What does Wraycombe owe each year?
  8. Wraycombe serves 24,000 households. Using your answer from item 7, what does the annual repayment come to per household?
  9. The water supply contract delivers 8,000 acre-feet per year. Using your answer from item 7, what is the repayment cost per acre-foot?
  10. Engineers reported that if recreation had been left out of the design, the project would have cost $455 million instead of $480 million. That difference is recreation's separable cost. What is it?
  11. Recreation was allocated $48 million under the benefit-share method. Using your answer from item 10, how much larger is the benefit-share allocation than the separable cost?
  12. The fictional state park agency repays the recreation share. Which allocation method would the agency argue for, and what does the difference you found in item 11 tell you about why?
  13. The hydropower share is repaid by electricity customers, and the water supply share is repaid by Wraycombe's water customers. Explain why the state legislature might have chosen to make flood control non-reimbursable while requiring repayment for these two purposes.
  14. Name two groups affected by the reservoir who pay nothing under this allocation, and explain in one or two sentences how each is affected.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: $50 million per year.
    The four annual benefits are $20 million, $15 million, $10 million, and $5 million. 20 + 15 + 10 + 5 = 50.
  2. Answer: 40 percent.
    $20 million divided by $50 million equals 0.40, which is 40 percent.
  3. Answer: $144 million.
    30 percent of $480 million is 0.30 x 480 = $144 million.
  4. Answer: $96 million.
    20 percent of $480 million is 0.20 x 480 = $96 million.
  5. Answer: $288 million.
    Water supply $144 million plus hydropower $96 million plus recreation $48 million equals $288 million.
  6. Answer: 40 percent.
    $192 million divided by $480 million equals 0.40, which is 40 percent. Notice that this matches flood control's benefit share, because the allocation and the repayment rule use the same division.
  7. Answer: $3,600,000 per year.
    $144,000,000 divided by 40 years equals $3,600,000 each year.
  8. Answer: $150 per household per year.
    $3,600,000 divided by 24,000 households equals $150.
  9. Answer: $450 per acre-foot.
    $3,600,000 divided by 8,000 acre-feet equals $450 per acre-foot.
  10. Answer: $25 million.
    $480 million minus $455 million equals $25 million, which is the added cost of including recreation in the design.
  11. Answer: $23 million.
    $48 million minus $25 million equals $23 million. The benefit-share method charges recreation $23 million more than the cost recreation actually added to the project.
  12. Answer: The separable-cost method.
    The park agency repays $25 million under separable cost instead of $48 million under benefit share, so it saves $23 million by arguing that a purpose should repay only the cost it added. Accept any answer that names the separable-cost method and connects it to the $23 million gap.
  13. Answer: Water and power are metered and billed, while flood protection is not.
    A utility can identify who receives water or power and charge them for it, so repayment is workable. Nobody can be excluded from flood protection, and no bill can be tied to it, so the legislature assigned that share to taxpayers. Accept answers that distinguish a service sold to identifiable customers from a benefit that reaches everyone in the floodplain.
  14. Answer: Accept any two with sound reasoning.
    Examples: landowners whose property was flooded by the reservoir lost land and are not listed as beneficiaries; downstream farms whose seasonal flooding once deposited sediment now receive steadier flows and no sediment; anglers downstream of the dam see a changed fishery; a community that was moved for the reservoir bears a cost that appears nowhere in the allocation.

Differentiation

Support

Give students a partially completed allocation table for the fictional reservoir, with the benefit column filled in and the percent column blank, so items 2 through 4 become one repeated operation rather than four separate setups. Confirm item 1 with the whole class before students continue, because items 2 through 6 all depend on that total.

Extension

Ask students to redo items 3 through 6 under a rule that allocates capital cost equally among the four purposes instead of by benefit share, then write a short paragraph naming which beneficiary gains most from the change and which loses most.

ELL supports

Pre-teach "allocate," "reimbursable," and "beneficiary" with a simple diagram showing one dam, four labeled purposes, and an arrow from each purpose to the group that pays for it. Provide sentence frames for items 12 through 14, such as "The agency would argue for ___ because ___" and "This group is affected because ___."

Extensions

Have students look up how a reservoir near them is operated and who holds the water supply contract, then write one paragraph comparing that ownership arrangement with the fictional Quillsmere structure. Students who prefer a policy task can draft a two-sentence amendment to the repayment statute that would treat recreation differently, and explain which group would lobby for it.