Question

Problem 14-45 (Algo) Comparing Business Units Using EVA: Solving for the Economic Life of the Investment (LO 14-4)

Colonial Pharmaceuticals is a small firm specializing in new products. It is organized into two divisions, which are based on the products they produce. AC Division is smaller and the life of the products it produces tend to be shorter than those produced by the larger SO Division. Selected financial data for the past year is shown as follows. Divisional investment is as of the beginning of the year. Colonial Pharmaceuticals uses a 9 percent cost of capital and uses beginning-of-the-year investment when computing ROI and residual income. Ignore income taxes.

 

	AC Division			SO Division
Allocated corp. overhead	$	615		$	1,650
Cost of goods sold		3,230			7,300
Divisional investment		9,300			78,500
R&D		1,565			3,600
Sales		8,600			20,300
SG&A		745			1,380

 

R&D is assumed to have a two-year life in the AC Division and a nine-year life in the SO division. All R&D expenditures are spent at the beginning of the year. Assume there are no current liabilities and (unrealistically) that no R&D investments had taken place before this year.

 

Al, the manager of the AC Division, complains that the calculation of EVA is unfair, because a much longer life is assumed for the SO Division in calculating EVA. Sean, the manager of SO, responds that EVA is supposed to reflect economic reality and that the reality is that R&D investments in SO Division do have a longer life.

 

Required:

a. Assume that the economic life of R&D investments is two years in the AC Division. What economic life would the R&D investments in the SO Division have to make EVA in the two divisions equal? (Round EVA to 2 decimal places and final answer to 1 decimal places. Do not round intermediate calculations.)

Answer 1

step 1) AC income: 8,600- 3,230- 745- 1,565- 615= 2,445

step 2) 0.5(half of) *1,565= 782.5

step 3) 2,445+ 782.5= 3,227.5

step 4) 9,300+ 782.5= 10,082.5

step 5) 10,082.5* 9%= 907.425

step 6) 907.425- 3,227.5= -2,320.075 EVA

step 7) SO income: 20,300 -7,300 -1,380 -3,600 -1,650= 6,370

step 8) 3,600* 0.91(1-9%) = 3,276

step 9) 78,500* 0.09= 7,065

step 10) 2,320.075= 6,370+ 3,276Y -7065

              2,320.075 +7,065- 6,370= 3,276Y

                       3,015.075= 3,276Y

           3015X= 3,276X -3,276

           3,276X -3,015X= 3,276

                261X= 3,276

                3,276/ 261= 12.5517241379

              Answer: 12.6 years

other solution method 

We need to recognize that the same proportion of the R&D investment is added to net (or in this case operating) income and divisional investment. Let p = this proportion. For example, p = 0.50 [= (2 year life − 1 year) ÷ 2 year life] for AC Division and p = 8/9 [= (9 year life − 1 year) ÷ 9 year life] for SO Division. Once we solve for p, we can find the implied life in years of the R&D (Life), by solving:

P = (Life − 1)/Life.

Thus, we need to solve:
$2,320.07 = [($6,370 + $3,600 × p) − (0.09 × ($78,500 + $3,600 × p))].

Solving,
$2,320.07 = $6,370 − $7,065 + (0.91 × $3,600)p

or

p = 0.9204 and Life = 12.6 years.