Chapter 14, Problem 45P

a.

To determine

Calculate the F division’s residual income if Company O does not acquire the new machine.

Answer to Problem 45P

The residual income for division S is $3,000,000 if Company O does not acquire the new machine.

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.

Calculate the residual income if Company O does not acquire the new machine:

$\begin{array}{c}\text{RI = Investment center operating profits - }\left(\text{Capital charge × Investment center assets}\right)\\ =\text{ \$3,750,000 }-\text{ (0}\text{.12 }\times \text{ \$6,250,000 (1))}\\ \text{= \$3,000,000}\end{array}$

Thus, the residual income for division S is $3,000,000.

Working note 1:

Calculate the net asset value:

Particulars	Amount
Opening asset value	$4,000,000
Add: addition in the year	$5,000,000
Total asset value	$9,000,000
Less: depreciation on new equipment	$1,500,000
Less: depreciation on others	$1,250,000
Net asset value	$6,250,000

Table: (1)

b.

To determine

Calculate the division F’s residual income if Company O acquires the new machine

Answer to Problem 45P

The residual income is $860,000 if Company O acquires the new machine.

Explanation of Solution

Adjusted residual income:

Adjusted residual income is calculated by changing the profit and investment of the company as per the new business proposal.

Calculate the residual income if Company O acquires the new machine:

$\begin{array}{c}\text{RI = Investment center operating profits - }\left(\text{Capital charge × Investment center assets}\right)\\ =\text{ \$250,000 (3) }-\text{ (0}\text{.12 }\times \text{ \$9,250,000 (2))}\\ \text{= \$860,000}\end{array}$

Thus, the residual income is $860,000 if Company O acquires the new machine.

Working note 2:

Calculate the net asset value:

Particulars	Amount
Opening asset value	$4,000,000
Add: improvement  in the asset	$6,500,000
Total asset value	$10,500,000
Less: depreciation on others	$1,250,000
Net asset value	$9,250,000

Table: (2)

Working note 3:

Calculate the after-tax divisional profit:

Particulars	Amount
Operating profit	$3,750,000
Less: loss on old equipment	$5,000,000
Add: saving in the depreciation of old equipment	$1,500,000
Net operating profit	$250,000

Table: (3)

c.

To determine

Calculate the residual income if the company acquires new machine and operates it according to specifications.

Answer to Problem 45P

The residual income is $4,305,000 if the machine is operated as per the specifications.

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.

Calculate the residual income if the machine is operated as per the specifications:

$\begin{array}{c}\text{RI = Investment center operating profits - }\left(\text{Capital charge × Investment center assets}\right)\\ =\text{ \$5,025,000 (4) }-\text{ (0}\text{.12 }\times \text{ \$6,000,000 (5))}\\ \text{= \$4,305,000}\end{array}$

Thus, the residual income is $4,305,000 if the machine is operated as per the specifications.

Working note 4:

Calculate the divisional operating income:

Particulars	Amount (a)	% change (b)	Net amount $\text{c = (a }\pm \text{ (\% change)}$
Sales	$16,000,000	+10%	$17,600,000
Operating costs:
Variable	$2,000,000	+10%	$2,200,000
Fixed	$7,500,000	-5%	$7,125,000
Deprecation:
New equipment(6)	$1,500,000		$2,000,000
Others	$1,250,000		$1,250,000
Divisional operating profit			$5,025,000

Table: (4)

Working note 5:

Calculate the net asset value:

Particulars	Amount
Opening asset value	$4,000,000
Add: improvement  in the asset	$6,500,000
Total asset value	$10,500,000
Less: depreciation on others $(2\times \text{ \$1,250,000)}$	$2,500,000
Less: depreciation on improved assets (6)	$2,000,000
Net asset value	$6,000,000

Table: (5)

Working note 6:

Calculate the depreciation on new equipment:

$\begin{array}{c}\text{Depreciation = }\frac{\text{Cost of the asset - Scrap value}}{\text{Life of the asset}}\\ =\frac{\$6,500,000\text{ - \$500,000}}{3}\\ =\text{ \$2,000,000}\end{array}$