Suppose a corporation currently sells Q units per month for a cash-only price of P. Under a new credit policy that allows one

QUESTION:

Suppose a corporation currently sells Q units per month for a cash-only price of P. Under a new credit policy that allows one month’s credit, the quantity sold will be Q 9 and the price per unit will be P 9. Defaults will be p percent of credit sales. The variable cost is n per unit and is not expected to change. The percentage of customers who will take the credit is a, and the required return is R per month. What is the NPV of the decision to switch? Interpret the various parts of your answer.

ANSWER:

We can express the old cash flow as:

Old cash flow = (P – v)Q

And the new cash flow1 will be:

New cash flow = (P – v) (1 – α) Q’ + αQ’ [(1 – π)P’ – v]

So, the incremental cash flow is:

Incremental cash flow = –(P – v)Q + (P – v)(1 – α)Q’ + αQ’ [(1 – π)P’ – v]

Incremental cash flow = (P – v)(Q’ – Q) + αQ’ [(1 – π)P’ – P]

Thus:

NPV = (P – v)(Q’ – Q) – αPQ’ +

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