Question

Y our firm just received an order from a customer for $50,000 of widgets. You have been tasked with evaluating the effect of time value of money on your firm’s cash flows (on a transaction-bytransaction basis). To fulfill this order your firm will need to produce and transport the widgets. T his will take 50 days. Assume that the widgets will cost $30,000 in COGS; your firm is given 20 days to pay for the raw materials. Once the widgets are delivered to your customer, 40 days of trade credit will be provided to the customer. Assume a discount rate of 7%.

a. W ith the aforementioned assumptions, what is the NPV of this transaction?

b. R ecalculate the NPV, assuming that your firm reduced the time needed to produce and transport the widgets to 35 days.

c. N ext, treat the difference in NPV (NPV from part b minus NPV from part a) as a daily perpetuity and determine the total increase in firm value attributable to the improvement in inventory management.

Answer 1

Answer a

First Payment is made at 20th day, hence there will be a cashflow of -$30000

Payment is received at 50+40=90th day, hence there will be a cashflow of $50000

PV of first cashflow = -30000/(1+7%)^(20/365) = -30000/1.07^0.0548 = -30000/1.0037 = -$29888.99

PV of second cashflow = 50000/(1+7%)^(90/365) = 50000/1.07^0.2466 = 50000/1.0168 = $49172.77

NPV = 49172.77-29888.99=$19283.78

Answer b

First Payment is made at 20th day, hence there will be a cashflow of -$30000

Payment is received at 35+40=75th day, hence there will be a cashflow of $50000

PV of first cashflow = -30000/(1+7%)^(20/365) = -30000/1.07^0.0548 = -30000/1.0037 = -$29888.99

PV of second cashflow = 50000/(1+7%)^(75/365) = 50000/1.07^0.2055 = 50000/1.0140 = $49309.69

NPV = 49309.69-29888.99=$19420.70

Answer c

NPV difference = 19420.70-19283.78=$136.92

If this is a daily perpetuity, total value will be given by a present value of perpetuity as follows:

Total Value = 136.92*365/7% = $713940