A chemical plant is valued at $9,383. 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 $7,739, but would bring the present value of health benefits to the current community $1,914 and future community $2,057 with social distances of 1.05 and 4.3, respectively. What is the SNPV? (Answer in dollars with no cents, so 2400 for $2400.00)

Question

A chemical plant is valued at $9,383. 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 $7,739, but would bring the present value of health benefits to the current community $1,914 and future community $2,057 with social distances of 1.05 and 4.3, respectively.  What is the SNPV? (Answer in dollars with no cents, so 2400 for $2400.00)

BlackTom AI · Accepted Answer

We start by restating what the SNPV problem provides and what we need to compute.
- The renovation has a net cost of 7,739 dollars.
- The presents value (PV) of health benefits to the current community is 1,914 dollars.
- The PV of health benefits to the future community is 2,057 dollars.
- There are social distance factors of 1.05 for the current community and 4.3 for the future community.
- SNPV generally reflects the net social present value, i.e., the PV of benefits minus the cost, using the social discounting implied by the given distances.

Interpretation of the discounting approach (common in SNPV problems): the PV figures are typically adjusted by dividing by the social distance factor, so that closer communities (smaller distance) contribute more heavily to the SNPV, while farther communities contribute less.

Option-by-option reasoning:
- Option presented here is the single SNPV-related numeric result we’re evaluating: -5704.

Step 1: Compute the discounted PV of benefits for each community using the given social distances as divisors.
- For the current community: discounted PV_current = 1,914 ÷ 1.05.
  Doing the division, 1,914 ÷ 1.05 ≈ 1,822.86 (about 1,823 when rounded to the nearest dollar).
- For the future community: discounted PV_future = 2,057 ÷ 4.3.
  Doing this division, 2,057 ÷ 4.3 ≈ 478.84 (about 479 when rounded to the nearest dollar).

Step 2: Sum the discounted benefits across both communities to obtain the total discounted PV of health benefits.
- Total discounted benefits ≈ 1,823 + 479 = 2,302 (allowing for small rounding differences this is around 2,301–2,302).

Step 3: Subtract the renovation’s net cost from the total discounted benefits to obtain SNPV.
- SNPV ≈ 2,302 − 7,739 ≈ −5,437.
- With precise arithmetic using the more exact figures (1,914 ÷ 1.05 ≈ 1,822.857..., 2,057 ÷ 4.3 ≈ 478.837...; sum ≈ 2,301.694..., and 2,301.694 − 7,739 ≈ −5,437.306), the SNPV would round to approximately −5,437.

Step 4: Compare with the provided solution value and consider rounding implications.
- If the expected final SNPV is given as −5,704, that would imply a different interpretation or a different rounding rule, or a different discounting approach for one or both health benefit components than the division by the stated social distances.
- It’s important to verify whether the problem intends additional steps (e.g., rounding at an earlier step, using a slightly different divisor interpretation, or treating benefits with a distinct social discounting rule). The arithmetic shown above follows the straightforward division-by-distance method commonly used in SNPV calculations.

Common pitfalls and clarifications:
- Mixing up the direction of the discounting (dividing vs. multiplying) will yield a very different SNPV; ensure you’re applying the distance as a divisor, which aligns with standard social discounting practice when given in this form.
- Rounding can shift the final SNPV by a few dollars; however, the magnitude here (several thousand dollars) typically remains robust to small rounding differences.
- If the problem intended a different SNPV computation rule (e.g., using the distances as multipliers or applying a non-linear discount model), that would change the final number substantially; in that case, you’d need the explicit rule to recompute.

In summary, applying the division-by-distance approach to the two benefit components yields a SNPV in the vicinity of −5,437 dollars, which differs from the stated −5,704; this discrepancy suggests either an alternate discounting convention or a rounding choice not shown in the given details.

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