Chapter 15, Problem 39P

a.

To determine

Compute the residual income for company T.

Explanation of Solution

Residual income:

Residual income is the amount of profit that is left after adjusting the cost of capital of the business.  It is calculated by subtracting the profit after tax from the total cost of capital invested in the business unit.

Compute the residual income:

$\begin{array}{c}\text{RI =}\left(\begin{array}{l}\left(\text{Number of units produced}\times \left(\text{Transfer price }-\text{Variable cost}\right)\right)\\ -\left(\text{Fixed cost}\right)-\left(\text{Residual income percentage }\times \text{ Total capital}\right)\end{array}\right)\\ \text{=}\left(900,000\times \left(\$140-\$40\right)\right)-\left(\$70\times 1,000,000\right)-\left(0.13\times \$80,000,000\right)\\ =\$9,600,000\end{array}$

Thus, the value of residual income is $9,600,000.

b.

To determine

Compute the Residual income of Company T.

Explanation of Solution

Residual income:

Residual income is the amount of profit that is left after adjusting the cost of capital of the business.  It is calculated by subtracting the profit after tax from the total cost of capital invested in the business unit.

Compute the Residual income:

$\begin{array}{c}\text{RI=}\left(\begin{array}{l}\left(\text{Number of units produced}\times \left(\text{Transfer price }-\text{Variable cost}\right)\right)\\ +\left(\text{Minimum units transferred}\times \left(\text{Transfer price }-\text{Variable cost}\right)\right)\\ -\left(\text{Fixed cost}\right)-\left(\text{Residual income percentage }\times \text{ Total capital}\right)\end{array}\right)\\ \text{=}\left[\begin{array}{l}\left(800,000\times \left(\$140-\$40\right)\right)+\left(200,000\times \left(\$80-\$40\right)\right)\\ -\left(\$70\times 1,000,000\right)-\left(0.13\times \$80,000,000\right)\end{array}\right]\\ =\$7,600,000\end{array}$

Thus, the Residual income is $7,600,000.

c.

To determine

Compute the minimum transfer price according to the information given in the question.

Explanation of Solution

Transfer price:

Transfer price is tool for tax savings. It refers to the price of those goods or services that are transferred in between subsidiaries, inter-department or commonly controlled companies.

Compute the transfer price:

$\begin{array}{c}\left(\begin{array}{l}\left[\begin{array}{l}\left(\begin{array}{l}\text{Units purchased }\\ \text{by L division}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Transfer price}\\ -\text{variable price}\end{array}\right)\end{array}\right]+\\ \left[\begin{array}{l}\left(\begin{array}{l}\text{Capacity of T division}-\\ \text{Units purchased by L division}\end{array}\right)\\ \times \left(\begin{array}{l}\text{Market price }\\ -\text{Variable cost}\end{array}\right)\end{array}\right]-\text{Revenue}\end{array}\right)\text{= Operating profit}\\ \left(200,000\times \left(\text{TP}-\$40\right)\right)+\left(800,000\times \$100\right)-\$70,000,000=\$20,000,000\\ \$80,000,000+200,000\text{TP}-\$8,000,000-\$70,000,000=\$20,000,000\\ 200,000\text{TP}\text{=}\text{\$18,000,000}\end{array}$

Thus,

$\begin{array}{c}\text{TP =}\frac{\$18,000,000}{200,000}\\ =\$90.00\end{array}$

Thus, the value of transfer price is $90.00.