Question

Suppose that a company currently manufactures widgets and requires immediate cash payment upfront for all sales. They also pay immediately for all goods produced.

Suppose the following:

Current Price per unit (P) = $9

Current average monthly sales quantity (Q) = 10,000

Variable cost per unit (v) = $4

Fixed costs = $0 per month

In order to solve this problem, you will need to model the cash flows in each month. For simplicity, assume that ALL cash flows (both positive and negative) occur on the same day each month. Also, assume that today is time 0, next month is time 1, the following month is time 2, etc.). Assume that cash flows will happen each period forever.

ANNUAL required rate of return = 15%

i) What is the present value of all cash flows, including those occurring today?

Present Value = $ (Round to the nearest dollar, with NO decimal! Do NOT use commas!)

The company is considering a change to its credit policy whereby it will require payment within 30 days of the sale (Net 30) instead of cash upfront. Assume that all customers will pay on the due date. It is believed that, under the new policy, price will increase by $1/unit and average monthly sales will increase to 10,500. There is no anticipated change to variable unit costs.

ii) What is the net present value (NPV) of this proposed policy change if the company were to make the change immediately (ie. today, in period 0)? (HINT: Be careful! I am not asking for the present value of the new cash flows, I am asking for the NPV of the CHANGE in cash flows!)

NPV = $ (Round to the nearest dollar, with NO decimal! Do NOT use commas!)

Answer 1

(i)

Cash Flow each month = (Selling Price per unit - Variable Cost per unit)×Number of units sold

= (9-4)×10000 = $50000

Assumption: Interest rate is compounded monthly

Therefore, monthly interest rate will be 15/12 = 1.25%

It is given that cashflows will be occured at the same time(lets assume at the end), forever i.e. for perpetuity.

PV of all cash flows from period 1= Cash Flow every month/Monthly Interest Rate =50000/1.25% = $4000000

Cash flow for 0 period = $50000

Therefore, PV of all cash flows including today's = $4000000+$50000 = $4050000

(ii)

Additional selling price = $1

Additional units sold = 10500-10000 = 500

New contribution = New selling price - variable cost = 10-4 = 6 per unit

Additional cash flows due to change in policy

= Additional Selling price for existing units + Additional Contribution from additional units

= (10000×1) + (500×6) = $13000

NPV due to change = PV of ADDITIONAL cash flows due to change - Cost for change i.e.0

(PV will be same as above)

= Today's cash flows + PV of all cash flows from period 1 till perpetuity

= 13000 + (13000/1.25%) = $105300