Q7 : Sensitivity analysis (Decision reversal) (15 pts) You have to evaluate two
ID: 1170581 • Letter: Q
Question
Q7 : Sensitivity analysis (Decision reversal) (15 pts) You have to evaluate two projects with the data given below. Your MARR is 6 years. 10% and the study period |Capital Investment Annual overhead cost (Fixed cost) Unit sales price (p) Unit production cost (Cu) (Variable cost) Annual sales volume 10.000$ 15.000s 2.000$/yr 2.250$/yr 5,00$/u 5,00$/u 2,50$/u2,00$/u 2.000 u/yr 2.000/yr Show which project is prefered using PW method. Find decision) a. b. the sales volume for decision reversal point. (The sales volume required to switch yourExplanation / Answer
(a)
Project A
Selling price per unit = $ 5
Variable cost per unit = $ 2.5
Contribution per unit = $ 5 - 2.5
= $ 2.5
Units sold = 2,000
Total contribution = 2,000 x 2.5
= $ 5,000
Annual fixed cost = $ 2,000
Annual profit = 5,000 - 2,000
= $ 3,000
This annual profit (or cash flow) will accrue for the 6 years. Hence , there is an annuity for 6 years.
Present value of future cash flows = Annuity amount x Present value annuity factor (10% , 6 )
= 3,000 x 4.3553
= $ 13,066
Cost of project = $10,000
Present worth of project = Present value of future cash flows - Cost of project
= 13,066 - 10,000
= $ 3,066
Project B
Selling price per unit = $ 5
Variable cost per unit = $ 2
Contribution per unit = $ 5 - 2
= $ 3
Units sold = 2,000
Total contribution = 2,000 x 3
= $ 6,000
Annual fixed cost = $ 2,250
Annual profit = 6,000 - 2,250
= $ 3,750
This annual profit (or cash flow) will accrue for the 6 years. Hence , there is an annuity for 6 years.
Present value of future cash flows = Annuity amount x Present value annuity factor (10% , 6 )
= 3,750 x 4.3553
= $ 16,332
Cost of project = $15,000
Present worth of project = Present value of future cash flows - Cost of project
= 16,332 - 15,000
= $ 1,332
According to Present worth method, Project A should be chosen since its present worth ( $3,066) is more than the present worth of the Project B ( $1,332 )
(b)
Let the sales volume be y units at which the present worth of both the projects will be same.
Present worth of project A = Present worth of project B
(2.5 y - 2,000 ) x 4.3553 - 10,000 = (3 y - 2,250 ) x 4.3553 - 15,000
10.888 y - 8,710.6 - 10,000 = 13.065 y - 9,799.42 - 15,000
2.177 y = 6,088.82
y = 2,797
Hence when output is more than 2,797 units, present worth of project B will be more than present worth of project A. Hence sales volume for decision reversal is output level of beyond 2,797 units.
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