1. **Problem Statement:** Tricia Velasquez wants to analyze the Net Present Value (NPV) of a $30,000 order with net 45-day credit terms, 12% opportunity cost, 65% variable costs, and 1% credit administration costs. 2. **Formula and Concepts:** - NPV = Present Value of Cash Inflows - Present Value of Cash Outflows - Present Value (PV) = Future Value / (1 + r)^{t} - Variable costs = 65% of sales - Credit administration costs = 1% of sales - Opportunity cost rate = 12% annually, convert to daily rate for discounting 3. **Step a: Assuming payment at 45 days with certainty** - Sales = 30000 - Variable costs = 0.65 * 30000 = 19500 - Credit admin costs = 0.01 * 30000 = 300 - Net cash inflow at 45 days = 30000 - 19500 - 300 = 10200 - Daily discount rate = 0.12 / 365 = 0.00032877 - PV = 10200 / (1 + 0.00032877)^{45} = 10200 / 1.015 = 10044.33 - Since PV > 0, approve order 4. **Step b: Considering payment probabilities and timing** - Payment brackets and probabilities: - Within 45 days: 0.50 - 45-60 days: 0.30 - 60-90 days: 0.15 - Over 90 days: 0.05 - Payments are evenly distributed within brackets - Collection agency charges 30% of invoice and collects 65% of invoice one month after referral (day 120) - Additional collection cost $125 every 15 days after day 45 until referral 5. **Calculate expected cash flows:** - Sales = 30000 - Variable costs = 19500 - Credit admin costs = 300 - Net sales = 10200 6. **Payments within 45 days (0.50 probability):** - Amount = 0.50 * 10200 = 5100 - PV = 5100 / (1 + 0.00032877)^{22.5} = 5100 / 1.0074 = 5062.5 7. **Payments 45-60 days (0.30 probability):** - Amount = 0.30 * 10200 = 3060 - Average payment day = 52.5 - PV = 3060 / (1 + 0.00032877)^{52.5} = 3060 / 1.0173 = 3009.3 - Collection cost for 1 period (day 60 - day 45 = 15 days): $125 - PV of collection cost = 125 / (1 + 0.00032877)^{52.5} = 125 / 1.0173 = 122.9 8. **Payments 60-90 days (0.15 probability):** - Amount = 0.15 * 10200 = 1530 - Average payment day = 75 - PV = 1530 / (1 + 0.00032877)^{75} = 1530 / 1.025 = 1493.2 - Collection costs for 2 periods (days 60 and 75): 2 * 125 = 250 - PV of collection costs = 125 / 1.0173 + 125 / 1.0213 = 122.9 + 122.3 = 245.2 9. **Payments over 90 days (0.05 probability):** - Invoice amount = 0.05 * 30000 = 1500 - Collection agency collects 65% of 1500 = 975 - Agency fee = 30% of 1500 = 450 - Net collection = 975 - 450 = 525 - Collection costs before referral: from day 60 to 90 every 15 days = 2 periods * 125 = 250 - Collection costs PV: - Day 60: 125 / 1.0213 = 122.3 - Day 75: 125 / 1.025 = 121.9 - Day 90: 125 / 1.029 = 121.4 - Total = 365.6 - Payment received at day 120 (one month after referral): - PV = 525 / (1 + 0.00032877)^{120} = 525 / 1.041 = 504.3 10. **Total expected PV:** - Sum PV payments = 5062.5 + 3009.3 + 1493.2 + 504.3 = 10069.3 - Sum PV collection costs = 0 + 122.9 + 245.2 + 365.6 = 733.7 - Net PV = 10069.3 - 733.7 - 300 (credit admin) - 19500 (variable costs) + 19500 (already subtracted in net sales) = 10069.3 - 733.7 - 300 = 9035.6 11. **Conclusion:** Since the expected NPV is positive, Tricia should recommend credit extension.