The vice president of operations of Free Ride Bike Company is evaluating the performance of two divisions organized as investment centers. Invested assets and condensed income statement data for the past year for each division are as follows: Road bike division Mountain bike divisionSales $1,728,000 $1,760,000Cost of goods sold $1,380,000 $1,400,000Operating expenses $175,200 $236,800Invested assets $1,440,000 $800,0001) Prepare condensed divisional income statements for the year ended December 31, 2014, assuming that there were no service department charges.2) Using the DuPont formula for rate of return on investment, determine the profit margin, investment turnover, and rate of return on investment for each division.3) If management's minimum acceptable rate of return is 10%, determine the residual income for each division.4) Discuss the evaluation of the two divisions, using the performance measures determined in parts (1), (2), and (3).

Free Ride Bike Company

1. Condensed Divisional Income Statements for the year ended December 31, 2014:

1.                                Road bike division      Mountain bike division     Total

Sales                          $1,728,000                $1,760,000               $3,488,000

Cost of goods sold   $1,380,000                $1,400,000               $2,780,000

Operating expenses   $175,200                  $236,800                   $412,000

Net Income                  $172,800                   $123,200                  $296,000

2. Du Pont ROI = Return on sales * Asset Turnover

                            Road bike division      Mountain bike division

=                            1.2 * 10% = 12%                     2.2 * 7% = 15.4%

3. Residual income

                            Road bike division      Mountain bike division          Residual income        $28,800                     $43,200

4. Evaluation of the two divisions, using the performance measures determined in parts (1), (2), and (3):

The Road bike division outperformed the Mountain bike division when we evaluate their performances based on the Return on Sales or Net Income margin.  However, using the DuPont  formula on the return on investment and residual income parameters, one understands that the Mountain bike division outperformed the Road bike division.  These show that performance evaluation should not be based on one measure.  Using the different performance evaluation measures yield clearer pictures of divisional performance.

Explanation:

a) Data and Calculations:

                              Road bike division      Mountain bike division     Total

Sales                          $1,728,000                $1,760,000               $3,488,000

Cost of goods sold   $1,380,000                $1,400,000               $2,780,000

Operating expenses   $175,200                  $236,800                   $412,000

Net Income                  $172,800                   $123,200                  $296,000

Return on sales              10%                         7%                              8.5%

Invested assets       $1,440,000                  $800,000               $2,240,000

Asset Turnover     1.2($1,728,000/$1,440,00)  2.2($1,760,000/$800,000)

Du Pont ROI = Return on sales * Asset Turnover

=                            1.2 * 10% = 12%                     2.2 * 7% = 15.4%

b) Residual income

                              Road bike division      Mountain bike division     Total

Net Income                  $172,800                   $123,200                  $296,000

Minimum rate of return    10%                          10%                             10%

Dollar minimum return 144,000                     $80,000                    224,000

Residual income          $28,800                     $43,200                    $72,000

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

i would say their habit of breaking down.