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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 your

Explanation / 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.