The Net Present Value Objective has Several Advantages - Engineering Assignment Help

Assignment Task:

Task:

The net-present-value objective has several advantages. It represents the financing component of the holding cost in real, tangible terms. Financing charges arise from the time gaps between purchasing ex- penditures and sales revenues. To bridge such gaps, firms must borrow money and pay interest. A unit in inventory has been purchased but not sold, so we can think of it as “generating” interest costs at some rate α.

The average-cost formulation tries to incorporate this by charging a cost I · C of holding inventory per year, but that is only a rough approximation. A box sitting in a warehouse does not really generate interest costs. The new approach includes financing costs as they actually occur. This approach is especially helpful, indeed essential, in analyzing complex models with intricate costs and revenues

Before you start: This assignment uses the concept of continuously compounding interest. If you are not familiar with this idea, please read this introduction from Dr. Silber at NYU: http://people. stern.nyu.edu/wsilber/Continuous%20Compounding.pdf.

Suppose we can invest money at a constant, continuously compounding interest rate α. An investment of $1 now (time 0) will be worth $e αt at time t. For the investment to be worth $1 at time t, the initial investment must be in the amount of $e −αt. In general, a cash flow y at time t can be exchanged for a cash flow y × e −αt now. This latter quantity is the present value of the original cash flow.
Suppose that we can also borrow money at rate α. If we must pay a cost of $1 now, we can borrow the money, wait until time t, and then pay the larger amount $e αt. Similarly, an obligation to pay $y at time t is equivalent to a cost of $y × e −αt today. This quantity is called the discounted cost. Thus, a cost works just like a negative cash flow.
Now, suppose we face a sequence of cash flows {yj} at times {tj}. Some of these may be positive and some negative, representing costs. As above, we can replace each cash flow by its present value. The sum of these present values P j yj e −αtj is the net present value of the entire sequence.

The assumptions above are rather special. In reality, for example, one cannot borrow and invest at the same interest rate; the borrowing rate is higher. Still, the present-value criterion does reflect the fact that a cost today is more burdensome than a cost tomorrow. Some authors consider this is a real advantage over the average-cost measure.

In this assignment you will construct and EOQ model using the net present value criterion. Use the following assumptions throughout:
 Demand comes in at a constant rate of λ units per year.
 The ordering cost is K per order, and doesn’t change over time.
 The purchasing cost is C per unit, and doesn’t change over time.
 There is no direct cost of holding inventory, h = 0. (Unless otherwise stated).
 The initial inventory is zero, I0 = 0. (Unless otherwise stated)
 The lead time is zero τ = 0.
Solve the following problems. Use Q to denote the order quantity and T for the order period. Remember that T = Q/λ.

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