# 2.16 Solution for “Question #2”

Here, once again, is question #2, its solution, and some comments.

2. Yur Company has two mutually exclusive investment choices for replacing old machinery.  Assume that both projects can be repeated and that the relevant WACC, cost of capital discount rate, is 14%.

 Machine A Machine B Investment Cost \$190,000 \$360,000 Expected Life 3 Years 6 Years Free Cash Flow (Per Year) \$87,000 \$98,300

Using both the Replacement Chain and Annual Annuity approaches, should the firm replace the old machine and, if so, which machine should it select?

Under AAA it may appear that “B” should be selected; its annual cash flow is higher and its overall cost is about the same.  In calculating RCA, using the same assumptions for “Machine A” iteratively, we should favor B.  Let’s see how that works out. First, let’s draw a timeline.

(190,000) + \$87,000

 RCA 0 1 2 3 4 5 6 A (\$190,000) 0 0 (190,000) + \$87,000 0 0 0 \$87,000 \$87,000 \$87,000 \$87,000 \$87,000 B (\$360,000) \$98,300 \$98,300 \$98,300 \$98,300 \$98,300 \$98,300

NPVA = [(\$87,000) (2.3216) – 190,000] + [(87,000) (2.3216) – 190,000] ÷ [1.143]

= \$20,064.81

(Where PVAF 14%, 3 periods = 2.3216)

Another solution: NPV A = [(\$87,000) (3.8887) – 190,000] – [190,000 ÷ 1.143]

(Where PVAF 14%, 6 periods = 3.8887)

NPVB = [(\$98,300) (3.8887) – (360,000]

= \$22,259.21

(Where PVAF 14%, 6 periods = 3.8887)

We see that, using “RCA / NPV” analysis Machine B is favored.  Of course, there is no assurance that the original assumptions for “A” will repeat themselves upon project renewal. Changing assumptions could change the choice.