Chapter 14, Problem 41E

a.

To determine

Compute ROI by using historical cost, net book value.

Explanation of Solution

Net book value:

Net book value refers to the value of the asset after the adjustment of the depreciation. The value of the asset is calculated by deducting the cumulative depreciation from the book value of the asset.

Calculate the ROI using historical cost, net book value:

Year	Investment(3) (a)	Operating profit (1) (b)	ROI $\text{c =}\left(\frac{\text{b}}{\text{a}}\right)$
1	$81,000,000	$13,000,000	16.05%
2	$72,000,000	$15,200,000	21.11%
3	$63,000,000	$17,620,000	27.97%
4	$54,000,000	$20,282,000	37.56%

Table (1)

Working note 1:

Calculate the operating profit over the life of the asset:

Year	Gross cash flow (a)	Net cash flow $\text{b = }\left(\text{a + 10\%}\right)$	Depreciation (2) (c)	Operating profit $\text{d = }\left(\text{b - c}\right)$
1	$20,000,000	$22,000,000	$9,000,000	$13,000,000
2	$22,000,000	$24,200,000	$9,000,000	$15,200,000
3	$24,200,000	$26,620,000	$9,000,000	$17,620,000
4	$26,620,000	$29,282,000	$9,000,000	$20,282,000

Table (2)

Working note 2:

Calculate the depreciation:

$\begin{array}{c}\text{Depreciation = Asset value }\times \text{ Depreciation rate}\\ \text{= \$90,000,000 }\times \text{ 10\%}\\ \text{= \$9,000,000}\end{array}$

Working note 3:

Calculate the investment base over the life of the asset:

Year	Gross asset value (a)	Annual depreciation (b)	Depreciation $\text{c = }\left(\text{a ×b}\right)$	Net asset value $\text{d = }\left(\text{a - c}\right)$
1	$90,000,000	10%	$9,000,000	$81,000,000
2	$90,000,000	20%	$18,000,000	$72,000,000
3	$90,000,000	30%	$27,000,000	$63,000,000
4	$90,000,000	40%	$36,000,000	$54,000,000

Table (3)

The depreciation has been calculated on the historical cost in this method.

b.

To determine

Compute ROI using historical cost, gross book value.

Explanation of Solution

Gross book value:

Gross book value is the value of the asset without the adjustment of the depreciation. The asset is recorded on the book value or the cost value.

Calculate the ROI using historical cost, net book value:

Year	Investment (a)	Operating profit (1) (b)	ROI $\text{c =}\left(\frac{\text{b}}{\text{a}}\right)$
1	$90,000,000	$13,000,000	14.44%
2	$90,000,000	$15,200,000	16.89%
3	$90,000,000	$17,620,000	19.58%
4	$90,000,000	$20,282,000	22.54%

Table (4)

c.

To determine

Compute ROI by using current cost, net book value.

Explanation of Solution

Current cost:

Current cost is the current market value of the asset. The depreciation is calculated on the current value of the asset rather than the historical cost of the asset.

Calculate the ROI using historical cost, net book value:

Year	Investment (7) (a)	Operating profit (4) (b)	ROI $\text{c =}\left(\frac{\text{b}}{\text{a}}\right)$
1	$89,100,000	$12,100,000	13.58%
2	$87,120,000	$13,310,000	15.28%
3	$83,853,000	$14,641,000	17.46%
4	$79,061,400	$16,105,100	20.37%

Table (5)

Working note 4:

Calculate the operating profit over the life of the asset:

Year	Gross cash flow (a)	Net cash flow $\text{b = }\left(\text{a + 10\%}\right)$	Depreciation (5) (c)	Operating profit $\text{d = }\left(\text{b - c}\right)$
1	$20,000,000	$22,000,000	$9,900,000	$12,100,000
2	$22,000,000	$24,200,000	$10,890,000	$13,310,000
3	$24,200,000	$26,620,000	$11,979,000	$14,641,000
4	$26,620,000	$29,282,000	$13,176,900	$16,105,100

Table (6)

Working note 5:

Calculate the depreciation over the life of the asset:

Year	Asset value (a)	Annual Increment (b)	The gross value of the asset $\text{c = }\left(\text{a×b}\right)$	Yearly depreciation $\text{d = }\left(\text{c ×25\%}\right)$	Total depreciation $e=\left(c\times \frac{\text{Year of life}}{4}\right)$
1	$36,000,000	10%	$39,600,000	$9,900,000	$9,900,000
2	$39,600,000	10%	$43,560,000	$10,890,000	$21,780,000
3	$43,560,000	10%	$47,916,000	$11,979,000	$35,937,000
4	$47,916,000	10%	$52,707,600	$13,176,900	$52,707,600

Table (7)

The closing gross value of each year will be the opening asset value of the next year.

Working note 6:

Calculate the asset value for the first year:

$\begin{array}{c}\text{Asset value = Cost of the machine - depreciation}\\ \text{= }\$90,000,000–\$54,000,000\\ =\$36,000,000\end{array}$

Working note 7:

Calculate the investment base over the life of the asset:

Year	Gross asset value (a)	Depreciation (5) (b)	Net asset value $\text{d = }\left(\text{a - b}\right)$
1	$9,900,000	$9,900,000	$89,100,000
2	$10,890,000	$21,780,000	$87,120,000
3	$11,979,000	$35,937,000	$83,853,000
4	$13,176,900	$52,707,600	$79,061,400

Table (8)

d.

To determine

Compute ROI using current cost, gross book value.

Explanation of Solution

Calculate the ROI using historical cost, net book value:

Year	Investment (a)	Operating profit (4) (b)	ROI $\text{c =}\left(\frac{\text{b}}{\text{a}}\right)$
1	$99,000,000	$12,100,000	12.22%
2	$108,900,000	$13,310,000	12.22%
3	$119,790,000	$14,641,000	12.22%
4	$131,769,000	$16,105,100	12.22%

Table (9)