Chapter 20, Problem 9QP

(a)

Summary Introduction

To evaluate: Whether the company should fill the order.

Introduction:

Credit policy refers to a set of procedures that include the terms and conditions for providing goods on credit and principles for making collections.

Answer to Problem 9QP

The net present value (NPV) is $69,474.45.

Explanation of Solution

Given information:

AS is a wholesaler of stock engine components and test equipment. AS got an order. The variable cost and credit price is $1.9 million per unit and $2.015 million per unit respectively, 1 out of 200 such orders of payment are never collected. The require return is 1.8% per period.

If the order is one time, then the cash inflow is the net present value.

The formula to calculate the net present value:

$\text{NPV}=-\text{Variable cost}+\left[\frac{\left(1-\text{Default probablity}\right)\left(\text{Credit price}\right)}{1+\text{Required return}}\right]$

Compute the net present value:

$\begin{array}{c}\text{NPV}=\left(\begin{array}{l}-\text{Variable cost}\\ +\left[\frac{\left(1-\text{Default probablity}\right)\left(\text{Credit price}\right)}{1+\text{Required return}}\right]\end{array}\right)\\ =-\text{\$1,900,000}+\left[\frac{\left(1-\text{0}\text{.005}\right)\left(\text{\$2,015,000}\right)}{1+\text{0}\text{.018}}\right]\\ =-\text{\$1,900,000}+\left[\frac{\$2,004,925}{1.\text{018}}\right]\\ =\text{\$69,474}\text{.45}\end{array}$

Hence, the net present value is $69,474.45.

Since the amount of NPV is positive, the company should fill the order.

(b)

Summary Introduction

To determine: The break-even default probability.

Introduction:

Credit policy refers to a set of procedures that include the terms and conditions for providing goods on credit and principles for making collections.

Answer to Problem 9QP

The break-even default probability is 4.009%. It is recommended that the firm was not able to accept the order when the default probability is higher than 4.009%.

Explanation of Solution

Given information:

AS is a wholesaler of stock engine components and test equipment. AS got an order. The variable cost and credit price is $1.9 million per unit and $2.015 million per unit respectively, 1 out of 200 such orders of payment are never collected. The require return is 1.8% per period.

Consider $\pi$ as the break-even default probability.

The formula to calculate the break-even default probability by using the NPV formula:

$\text{NPV}=\left(\begin{array}{l}-\text{Variable cost}\\ +\left[\frac{\left(1-\text{Default probablity}\right)\times \left(\text{Credit price}\right)}{1+\text{Required return}}\right]\end{array}\right)$

Compute the net present value:

$\begin{array}{c}\text{NPV}=\left(\begin{array}{c}-\text{Variable cost}\\ +\left[\frac{\left(1-\text{Default probablity}\right)\times \left(\text{Credit price}\right)}{1+\text{Required return}}\right]\end{array}\right)\\ \text{\$0}=-\text{\$1,900,000}+\left[\frac{\left(1-\pi \right)\times \left(\text{\$2,015,000}\right)}{1+\text{0}\text{.018}}\right]\\ \text{\$1,900,000}\times \text{1}\text{.018}=\text{\$2,015,000}-\text{\$2,015,000}\pi \\ \text{\$1,934,200}-\text{\$2,015,000}=-\text{\$2,015,000}\pi \\ -\$80,800=-\$2,015,000\pi \\ \pi =\frac{-\$80,800}{-\$2,015,000}\\ \pi =0.04009\text{or 4}\text{.009\%}\end{array}$

Hence, the break-even default probability is 4.009%.

(c)

Summary Introduction

To determine: The net present value.

Introduction:

Credit policy refers to a set of procedures that include the terms and conditions for providing goods on credit and principles for making collections.

Answer to Problem 9QP

The net present value (NPV) is $4,456,944.444 and the default probability is 70.26%. Since the amount of NPV is positive, the company can take up the order.

Here, all the customers become repeat customers. So, cash inflow will be credit price minus variable cost. Hence, AS needs to make arrangements for on more engines for one period, cash inflow becomes perpetuity.

Explanation of Solution

Given information:

AS is a wholesaler of stock engine components and test equipment. AS got an order. The variable cost and credit price is $1.9 million per unit and $2.015 million per unit respectively, 1 out of 200 such orders of payment are never collected. The require return is 1.8% per period.

The formula to calculate the net present value:

$\text{NPV}=\left(\begin{array}{l}-\text{Variable cost}\\ +\left[\frac{\left(1-\text{Default probablity}\right)\times \left(\text{Credit price}-\text{Variable cost}\right)}{\text{Required return}}\right]\end{array}\right)$

Compute the net present value:

$\begin{array}{c}\text{NPV}=\left(\begin{array}{l}-\text{Variable cost}\\ +\left[\frac{\left(1-\text{Default probablity}\right)\times \left(\text{Credit price}-\text{Variable cost}\right)}{\text{Required return}}\right]\end{array}\right)\\ =-\text{\$1,900,000}+\left[\frac{\left(1-\text{0}\text{.005}\right)\times \left(\text{\$2,015,000}-\$1,900,000\right)}{\text{0}\text{.018}}\right]\\ =-\text{\$1,900,000}+\left[\frac{\$114,452}{0.\text{018}}\right]\\ =\$4,456,944.444\end{array}$

Hence, the net present value (NPV) is $4,456,944.444 per unit.

(d)

Summary Introduction

To discuss: Credit terms are more liberal when repeated orders are a possibility.

Explanation of Solution

When repeat orders are feasible then the credit terms become more moderate. This is because the likely losses from granting credit for the first time can be compensated from the future period’s possible gain.