Let's break down the problem and calculate the **NPV (Net Present Value) of sales** step by step. ### **Given Data** - **Sales (Revenue):** $5,000,000 - **COGS (Cost of Goods Sold):** 35% of Sales - **DIH (Days Inventory Held):** 25 days - **DPO (Days Payable Outstanding):** 35 days (credit from supplier) - **DSO (Days Sales Outstanding):** 30 days (credit to customer) - **Interest Rate (Discount Rate):** 6% per annum --- ## **Step 1: Calculate COGS** \[ \text{COGS} = 35\% \times \$5,000,000 = \$1,750,000 \] --- ## **Step 2: Calculate Cash Cycle** The cash cycle is the time between when cash is paid to suppliers and cash is received from customers: \[ \text{Cash Cycle} = \text{DIH} + \text{DSO} - \text{DPO} \] \[ = 25 + 30 - 35 = 20 \text{ days} \] --- ## **Step 3: Calculate NPV of Sales** Since the cash is tied up for 20 days, we discount the cash flows for this period. The formula for NPV of sales (simplified for one cycle): \[ \text{NPV} = \frac{\text{Net Cash Flow}}{(1 + r)^{\frac{\text{Cash Cycle}}{365}}} \] Where: - \( r \) = interest rate = 6% = .06 - Net Cash Flow = Sales - COGS = $5,000,000 - $1,750,000 = $3,250,000 Plug in the values: \[ \text{Discount Factor} = (1 + .06)^{\frac{20}{365}} \] First, compute the exponent: \[ \frac{20}{365} = .05479 \] \[ \text{Discount Factor} = (1.06)^{.05479} \] Calculate this value: \[ \ln(1.06) = .05827 \\ .05827 \times .05479 = .003195 \\ e^{.003195} \approx 1.0032 \] So, \[ \text{Discount Factor} \approx 1.0032 \] \[ \text{NPV} = \frac{3,250,000}{1.0032} \approx \$3,239,646 \] --- ## **Final Answer** \[ \boxed{ \text{NPV of sales} \approx \$3,239,646 } \] --- ### **Summary Table** | Item | Value | |----------------------|--------------| | Sales | \$5,000,000 | | COGS | \$1,750,000 | | Net Cash Flow | \$3,250,000 | | Cash Cycle | 20 days | | Discount Factor | 1.0032 | | **NPV of Sales** | **\$3,239,646** |