Chapter 14, Problem 56P

a.

To determine

Describe whether Person GD would prefer to lease or purchase the technology if the manager of GD is evaluated using return on investment (ROI).

Explanation of Solution

Return on investment:

Return on investment is the amount of total profit earned by a division with its assets. The return on investment is used to check the efficiency of the unit. It shows the efficiency of the unit to utilize its assets to generate the profit.

Describe whether Person GD would prefer to lease or purchase the technology if the manager of GD is evaluated using return on investment (ROI):

Return on investment when purchased:

$\begin{array}{c}\text{Purchase}=\frac{\text{Annual income}-\text{Annual amortization}}{\left[\begin{array}{l}\text{Investment for GD}+\text{Purchase}\\ \text{value of technology}\end{array}\right]}\\ =\frac{\text{\$5,000,000}-\text{\$400,000 (1)}}{\$30,000,000+\$2,800,000}\\ =14.02\%\end{array}$

Return on investment when leased:

$\begin{array}{c}\text{Purchase}=\frac{\left[\begin{array}{l}\text{Annual income}-\text{Annual}\\ \text{payments required for lease}\end{array}\right]}{\text{Investment for GD}}\\ =\frac{\text{\$5,000,000}-\text{\$775,000}}{\$30,000,000}\\ =14.08\%\end{array}$

Working note 1:

Compute the value of Annual amortization:

$\begin{array}{c}\text{Annual amortization}=\frac{\text{Purchase value of technology}}{\text{Number of years of lease}}\\ =\frac{\$2,800,000}{7}\\ =\$400,000\end{array}$

From the above calculation, it is clear that the manager should prefer lease. 

b.

To determine

Describe whether Person GD would prefer to lease or purchase the technology if the manager of GD is evaluated using residual income.

Explanation of Solution

Investment in the project:

The investment in the project is a very important decision. Before selecting the project, the management should consider the profitability of the project with the help of present value, IRR, ROI, etc.

The residual incomes of the two options are as follows:

Residual incomes when purchased:

$\begin{array}{c}\text{Purchase}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual income}\\ -\text{Annual amortization}\end{array}\right)-12\%\\ \times \left(\begin{array}{l}\text{Investment for GD}+\text{Purchase}\\ \text{value of technology}\end{array}\right)\end{array}\right]\\ =\left[\begin{array}{l}\$5\text{,000,000}-400,000-\\ \text{(0}\text{.12}\times \left(\begin{array}{l}\$30,000,000\\ +\$2,800,000\end{array}\right)\end{array}\right]\\ =\text{\$664,000}\end{array}$

Residual incomes when leased:

$\begin{array}{c}\text{Lease}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual income}-\text{Annual}\\ \text{payments required for lease}\end{array}\right)\\ -\left(12\%\times \text{Investment for GD}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(\$5\text{,000,000}-775,000\right)\\ -\left(\text{0}\text{.12}\times \$30,000,000\right)\end{array}\right]\\ =\text{\$625,000}\end{array}$

From the above calculation, it is clear that the manager should prefer purchase. 

c.

To determine

Describe the lease payment that the manager would make indifferent between leasing and purchasing the technology if the manager of GD is evaluated using return on investment (ROI).

Explanation of Solution

Describe the lease payment that the manager would make indifferent between leasing and purchasing the technology if the manager of GD is evaluated using return on investment (ROI):

$\begin{array}{c}\text{Purchase}=\frac{\left[\text{Annual income}-\text{X}\right]}{\text{Investment for GD}}\\ 14.02\%=\frac{\text{\$5,000,000}-\text{X}}{\$30,000,000}\\ \text{X}=\left[\text{\$5,000,000}-\left(\begin{array}{l}14.02\%\times \\ \$30,000,000\end{array}\right)\right]\\ =\$794,000\end{array}$

Note: Assume that the breakeven lease payment as X.

d.

To determine

Describe the lease payment that the manager would make indifferent between leasing and purchasing the technology the manager of GD is evaluated using residual income.

Explanation of Solution

Describe the lease payment that the manager would make indifferent between leasing and purchasing the technology the manager of GD is evaluated using residual income:

$\begin{array}{c}\text{Purchase}=\left[\begin{array}{l}\left(\text{Annual income}-\text{X}\right)-\\ \left(12\%\times \text{Investment for GD}\right)\end{array}\right]\\ \$664,000=\left[\begin{array}{l}\left(\$5\text{,000,000}-\text{X}\right)-\\ \left(\text{0}\text{.12}\times \$30,000,000\right)\end{array}\right]\\ \text{X}=\left[\begin{array}{l}\text{\$5,000,000}-\$3,600,000\\ -\$664,000\end{array}\right]\\ =\$736,000\end{array}$

Note: Assume that the breakeven lease payment as X.