A chemical plant is valued at $11,981. Wanting to be more sustainable the company would have to renovate the waste treatment facility to stop leakage into a nearby stream. The net cost of the renovation would be $1,136, but would bring the present value of health benefits to the current community $1,104 and future community $3,052 with social distances of 1.41 and 4.6, respectively. What is the SNPV? (Answer in dollars with no cents, so 2400 for $2400.00)

Question

A chemical plant is valued at $11,981. Wanting to be more sustainable the company would have to renovate the waste treatment facility to stop leakage into a nearby stream. The net cost of the renovation would be $1,136, but would bring the present value of health benefits to the current community $1,104 and future community $3,052 with social distances of 1.41 and 4.6, respectively.  What is the SNPV? (Answer in dollars with no cents, so 2400 for $2400.00)

BlackTom AI · Accepted Answer

Let me restate the scenario and lay out the data clearly so we can analyze SNPV step by step.

Question data:
- Plant value: 11,981 dollars
- Renovation cost (net cost): 1,136 dollars
- Present value of health benefits to the current community: 1,104 dollars
- Present value of health benefits to the future community: 3,052 dollars
- Social distances (weights) for current and future communities: 1.41 and 4.6, respectively
- Asked quantity: SNPV, in dollars (no cents)

Approach 1: Discount the health benefits by the social distances and then subtract the renovation cost
- Step 1: Discount current community benefits by its social distance: 1,104 / 1.41
  - Calculation: 1,104 ÷ 1.41 ≈ 783.0
- Step 2: Discount future community benefits by its social distance: 3,052 / 4.6
  - Calculation: 3,052 ÷ 4.6 ≈ 663.0
- Step 3: Sum the discounted benefits: 783.0 + 663.0 ≈ 1,446.0
- Step 4: Subtract the renovation cost to obtain SNPV: 1,446.0 − 1,136 = 310.0
- Result under this method: SNPV ≈ 310 dollars

Approach 2: Use the raw health benefits and apply the social distances as multipliers to obtain a weighted benefits total, then subtract cost
- Step 1: Weight the health benefits by multiplying by the social distances:
  - Current: 1,104 × 1.41 ≈ 1,556.64
  - Future: 3,052 × 4.6 ≈ 14,039.2
- Step 2: Sum the weighted benefits: 1,556.64 + 14,039.2 ≈ 15,595.84
- Step 3: Subtract the renovation cost: 15,595.84 − 1,136 ≈ 14,459.84
- Result under this method: SNPV ≈ 14,460 dollars

Approach 3: Combine PVs of benefits (unweighted) and then incorporate the plant’s current value or other reference values (if the SNPV calculation explicitly includes opportunity costs or baseline asset value)
- Step 1: Sum unweighted PV health benefits: 1,104 + 3,052 = 4,156
- Step 2: Decide how to incorporate the social distances (e.g., as division factors, multipliers, or ignored)
  - If we divide by (1.41 + 4.6) ≈ 6.01 as a rough composite discount, we get 4,156 / 6.01 ≈ 691.2
  - If we use a more complex weighting rule, results will differ accordingly
- Step 3: Subtract the renovation cost (1,136) from the weighted total to get SNPV
- Step 4: Depending on the exact weighting rule chosen, this SNPV could come out around 691 minus 1,136 (≈ −445) or other values, but with this simple composite approach you don’t land neatly on a tidy 613.

Observations on consistency and potential sources of confusion:
- The problem provides social distances for current and future communities. In economic evaluation, the way these distances are applied (as divisors, as multipliers, or in some other transformation) critically changes the SNPV result. The two straightforward, common interpretations (discounting benefits by the given distances, or weighting benefits by multiplying with the distances) produce markedly different SNPV values: around 310 under discounting, or around 14,460 under pure multiplication.
- If the SNPV in the question is defined with a nonstandard or institution-specific rule (e.g., subtracting some baseline asset value, or applying a separate discounting framework for social rather than economic benefits), that could yield a result like 613, but such a rule would need to be explicitly stated or derivable from the course material or problem context.
- The mention of the plant value (11,981) could represent an opportunity cost or baseline asset value that should be incorporated in the SNPV per a specific formula. However, without an explicit instruction to subtract or otherwise integrate the plant’s baseline value into SNPV, the natural SNPV computation centers on the net present value of health benefits minus renovation costs, adjusted by the chosen social discounting approach.

Given the data as provided, multiple plausible implementations of SNPV lead to substantially different numbers. The most conventional interpretation (discounting benefits by the social distances and then subtracting the renovation cost) yields SNPV around 310 dollars, not 613. If the intended method uses a different weighting rule (e.g., multiplying by the social distances or combining PVs with a composite divisor), the result could diverge significantly.

Tip: To determine the exact SNPV the question expects, confirm the precise SNPV formula being used in this context (how to apply social distances: division, multiplication, or another transformation) and whether the plant’s baseline value enters the calculation in a specific way. Without that specification, the computed SNPV can reasonably differ depending on the chosen method.

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