Question

Your firm's average daily transaction consists of a sales order for $75,000. COGS is generally equal to 60% of the sale. Assume that your firm's DPO is 15 days and that the operating cycle is 80 days. Further, the discount rate used for valuing working capital decisions is 9%.

a. Calculate the NPV of the typical sales transaction.

b. Recalculate the NPV, assuming an increase in DPO to 30 days.

c. Estimate the all-in effect of the increase in DPO using a daily perpetuity approach.

Answer 1

a) Sales order = $75,000 | COGS = 60% of sales = 60% * 75,000 = $45,000

DPO = 15 days | Operating cycle = 80 days | Discount rate = 9%

At Day 0 - Order of $75,000 received

At Day 15 - $45,000 payment made to Suppliers

At Day 80 - $75,000 received from customers

Daily Discount rate = 9% / 365

Present Value of Cash outflow to Suppliers = 45,000 / (1+9%/365)¹⁵ = $44,833.89

Present Value of Cash inflow from customers = 75,000 / (1+9%/365)⁸⁰ = $73,535.22

NPV = PV of cash inflow - PV of cash outflow

NPV = 73,535.22 - 44,833.89

NPV of the typical sales transaction = $28,701.33

b) With everything same as part (a), except New DPO = 30 days

At Day 0 - Order of $75,000 received

At Day 30 - $45,000 payment made to Suppliers

At Day 80 - $75,000 received from customers

Daily Discount rate = 9% / 365

Present Value of Cash outflow to Suppliers = 45,000 / (1+9%/365)³⁰= $44,668.39

Present Value of Cash inflow from customers = 75,000 / (1+9%/365)⁸⁰ = $73,535.22

NPV = PV of cash inflow - PV of cash outflow

NPV = 73,535.22 - 44,668.39

NPV with DPO increased to 30 days = $28,866.83

c) Increase in NPV with Increase in DPO to 30 days = NPV with DPO as 30 days - NPV with DPO as 15 days

Increase in NPV with Increase in DPO to 30 days = 28,866.83 - 28,701.33

Increase in NPV with Increase in DPO to 30 days = $165.50

Daily Discount rate = 9% / 365

Using the Daily discount rate and Increase in NPV with increase in DPO to 30 days as perpetuity, we can find the Value of increase in DPO.

PV of Perpetuity = Increase in NPV / Daily Discount rate

Value of Increase in DPO = 165.50 / (9% / 365)

Value of Increase in DPO = $671,185.62

Hence, The all-in effect of the increase in DPO is $671,185.62