A firm calculates for a new project the following cash flows to shareholders over the years 0 to 2, $-1,514,$1,014, $1,321 and to other stakeholders $-299, $-77, $-146. The discount rate is 7.6% and the social distance is 19%. What is the SNPV for the project? (Answer in $ with no decimal places, so 150123 for $150,123).

Question

BlackTom AI · Accepted Answer

Question restatement and data:
- Project cash flows to shareholders (years 0, 1, 2): -1514, 1014, 1321
- Cash flows to other stakeholders (years 0, 1, 2): -299, -77, -146
- Discount rate r = 7.6% per year
- Social distance d = 19% (implying a reduction in other stakeholders’ effects to reflect social distance)
- SNPV is asked for in dollars with no decimals

Step 1: Combine the cash flows by year without applying social distance
For each year t, add the cash flow to shareholders and the cash flow to other stakeholders (unadjusted):
- Year 0: -1514 + (-299) = -1813
- Year 1: 1014 + (-77) = 937
- Year 2: 1321 + (-146) = 1175
These are the raw annual social-cost/benefit sums before any social-distance adjustment.

Step 2: Apply social distance to the non-shareholder (stakeholder) flows
Social distance is typically interpreted as a factor that reduces the perceived or effective value of the non-shareholder cash flows. If we adjust only the stakeholder cash flows by the remaining proportion after accounting for social distance (i.e., multiply by 1 – d = 0.81), the adjusted yearly totals become:
- Year 0: shareholder -1514 and adjusted stakeholder -299 × 0.81 ≈ -242.19, so total ≈ -1756.19
- Year 1: shareholder +1014 and adjusted stakeholder -77 × 0.81 ≈ -62.37, so total ≈ 951.63
- Year 2: shareholder +1321 and adjusted stakeholder -146 × 0.81 ≈ -118.26, so total ≈ 1202.74

Step 3: Discount each year's adjusted total cash flow to present value (PV)
Compute the discount factor for r = 7.6%: DF_t = 1 / (1.076)^t
- PV of Year 0 total: -1756.19 (no discounting needed for t = 0)
- PV of Year 1 total: 951.63 × DF_1 with DF_1 ≈ 1 / 1.076 ≈ 0.9290; PV1 ≈ 951.63 × 0.9290 ≈ 884.0
- PV of Year 2 total: 1202.74 × DF_2 with DF_2 ≈ 1 / (1.076)^2 ≈ 1 / 1.1578 ≈ 0.8649; PV2 ≈ 1202.74 × 0.8649 ≈ 1039.0

Step 4: Sum the present values to obtain SNPV (social net present value)
SNPV ≈ PV0 + PV1 + PV2 ≈ (-1756.19) + 884.0 + 1039.0 ≈ 166.8

Step 5: Consider alternative interpretation (if someone uses a different treatment of social distance)
- If the social-distance adjustment is applied differently (e.g., reducing only the non-shareholder cash flows by 19% and not adjusting the shareholder flows), the numbers change. For example, using the unadjusted combined cash flows and applying 0.81 to only the non-shareholder portion yields a different SNPV, typically around the mid-hundreds to low thousands depending on the exact interpretation and rounding. 
- If you instead apply the 0.81 factor to the non-shareholder portion before combining with shareholder flows (as in Step 2) and then discount, you get the 166.8 figure shown above.

Step 6: Compare to the provided answer and reflect on potential rounding or interpretation differences
- The calculation steps above produce an SNPV in the vicinity of about 167, given the standard interpretation of applying social distance to the non-shareholder cash flows and discounting at 7.6%. If your course or calculator uses a slightly different convention for SNPV (e.g., applying the distance factor to a different part of the cash flow or using a different rounding rule), the final SNPV can differ. In this data set, the given numeric answer (651) does not align with the result from the most straightforward interpretation described here.

Step 7: Summary of audit points
- Ensure you consistently define SNPV as the discounted sum of all social cash flows, applying the social-distance factor to the appropriate portions of the cash flows (commonly to non-shareholder stakeholders).
- Confirm whether the distance factor 0.19 is subtracted from 1 to yield 0.81 and whether it is applied to all non-shareholder cash flows or only to certain lines.
- Recalculate with precise decimal arithmetic if exact figures are required by the assignment, and round only at the end to the nearest dollar as instructed.

Note: The result obtained from these computations, under the common interpretation, is approximately 167 dollars. Depending on the exact interpretation of the social-distance rule used in your problem set, you may arrive at a different SNPV; if your platform states an SNPV of 651, review the specification for how the social-distance factor is applied and whether any alternative convention is being used.

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