1. **Problem Statement:** Tricia Velasquez wants to decide whether to approve a $30,000 order with credit terms net 45 days, opportunity cost 12%, variable costs 65% of sales, and incremental credit/collection expenses 1% of sales. 2. **Formula and Rules:** We use Net Present Value (NPV) analysis to decide if the order is profitable. NPV formula for cash flows received at time $t$ is: $$NPV = \sum \frac{CF_t}{(1 + r)^{t/365}}$$ where $CF_t$ is cash flow at day $t$, $r=0.12$ annual discount rate. Variable costs reduce revenue, and credit/collection expenses reduce net cash flow. 3. **Part (a) - Customer pays exactly at 45 days:** - Sales = 30000 - Variable costs = $0.65 \times 30000 = 19500$ - Credit/collection expenses = $0.01 \times 30000 = 300$ - Net cash inflow = $30000 - 19500 - 300 = 10200$ - Discount factor for 45 days = $\frac{1}{(1 + 0.12)^{45/365}}$ Calculate discount factor: $$ (1 + 0.12)^{45/365} = (1.12)^{0.1233} \approx 1.0145 $$ Discount factor = $\frac{1}{1.0145} = 0.9857$ NPV: $$ NPV = 10200 \times 0.9857 = 10056.14 $$ Since NPV > 0, Tricia should approve the order if payment is certain at 45 days. 4. **Part (b) - Payment probabilities and timing:** Payment probabilities and days: - 30 days: 40% - 60 days: 30% - 90 days: 15% - 120 days: 10% - 150 days: 5% Variable costs and credit expenses remain the same. 5. **Calculate expected cash flows:** - For payments within 90 days (30, 60, 90 days), no agency collection cost. - For payments after 90 days (120, 150 days), collection agency charges 30% of invoice and collects 65% of invoice one month after referral (i.e., at 120 + 30 = 150 days and 150 + 30 = 180 days). - Additional $125 collection cost every 15 days after 45 days until referral at 90 days. 6. **Calculate net cash flows for each payment period:** - Sales = 30000 - Variable costs = 19500 - Credit expenses = 300 **Payments within 90 days:** - 30 days (40%): Net = $30000 - 19500 - 300 = 10200$ - 60 days (30%): Additional collection cost applies for 15 days (from day 45 to 60), so add $125 cost. Net = $10200 - 125 = 10075$ - 90 days (15%): Additional collection cost applies for 30 days (two 15-day periods: 45-60 and 60-75), so $125 \times 2 = 250$ Net = $10200 - 250 = 9950$ **Payments after 90 days:** - 120 days (10%): Referral at day 90, agency collects 65% of invoice = $0.65 \times 30000 = 19500$ Agency fee = 30% of invoice = $0.30 \times 30000 = 9000$ Net from agency = $19500 - 9000 = 10500$ Collection cost before referral (45 to 90 days) = $125 \times 3 = 375$ Net cash flow = $10500 - 375 = 10125$ Received at day 120 + 30 = 150 days - 150 days (5%): Agency collects 65% of invoice = 19500 Agency fee = 9000 Net from agency = 10500 Collection cost before referral (45 to 90 days) = 375 Net cash flow = 10125 Received at day 150 + 30 = 180 days 7. **Calculate expected NPV:** Discount factors: - 30 days: $\frac{1}{(1.12)^{30/365}} = \frac{1}{1.0097} = 0.9904$ - 60 days: $\frac{1}{(1.12)^{60/365}} = \frac{1}{1.0195} = 0.9809$ - 90 days: $\frac{1}{(1.12)^{90/365}} = \frac{1}{1.0295} = 0.9713$ - 150 days: $\frac{1}{(1.12)^{150/365}} = \frac{1}{1.0509} = 0.9516$ - 180 days: $\frac{1}{(1.12)^{180/365}} = \frac{1}{1.0619} = 0.9417$ Expected NPV: $$ NPV = 0.40 \times 10200 \times 0.9904 + 0.30 \times 10075 \times 0.9809 + 0.15 \times 9950 \times 0.9713 + 0.10 \times 10125 \times 0.9516 + 0.05 \times 10125 \times 0.9417 $$ Calculate each term: - $0.40 \times 10200 \times 0.9904 = 4040.83$ - $0.30 \times 10075 \times 0.9809 = 2961.44$ - $0.15 \times 9950 \times 0.9713 = 1450.43$ - $0.10 \times 10125 \times 0.9516 = 963.44$ - $0.05 \times 10125 \times 0.9417 = 476.55$ Sum: $$ 4040.83 + 2961.44 + 1450.43 + 963.44 + 476.55 = 9892.69 $$ 8. **Conclusion:** Expected NPV is approximately 9892.69, which is positive. Therefore, based on expected NPV, Tricia should recommend credit extension.