Question

We are evaluating a project that costs $937,000, has a nine-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 115,000 units per year. Price per unit is $42, variable cost per unit is $23, and fixed costs are $947,307 per year. The tax rate is 38 percent, and we require a 12 percent return on this project.

Requirement 1:

Calculate the accounting break-even point.(Round your answer to the nearest whole number. (e.g., 32))

Break-even point

units

Requirement 2:

(a)	Calculate the base-case cash flow and NPV.(Do not include the dollar signs ($). Round your answers to 2 decimal places. (e.g., 32.16))

Base-case cash flow	$
NPV	$

(b)	What is the sensitivity of NPV to changes in the sales figure? (Do not include the dollar sign ($). Round your answer to 3 decimal places. (e.g., 32.161))

Sensitivity of NPV

$

(c)	Calculate the change in NPV If there is a 500-unit decrease in projected sales. (Do not include the dollar sign ($). Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16))

Change in NPV

$

Requirement 3:

(a)	What is the sensitivity of OCF to changes in the variable cost figure? (Do not include the dollar sign ($). Negative amount should be indicated by a minus sign. Round your answer to the nearest whole number. (e.g., 32))

Sensitivity of OCF

$

(b)	Calculate the change in OCF if there is a $1 decrease in estimated variable costs. (Do not include the dollar sign ($). Round your answer to the nearest whole number. (e.g., 32))

Change in OCF

$

Answer 1

Requirement 1

Calculation of Accounting Break Even Point

In this question, first we need to determine the depreciation amount incurred for each year.

Depreciation = Project Cost / Life of the project

                        = 937000 / 9

                        = 104,111

Accounting Break Even Point = Fixed Cost + Depreciation / [ Sales price per Unit – Variable Cost per unit])

                                                    = 947,307 + 104,111 / [42-23]

                                                     = 1,051,418 / 19

                                                     = 55338 units

Requirement 2

a) Calculation of Base Cash Flow

Base Cash Flow = [(Price per unit – Variable Cost per unit) (Quantity Sold) – Fixed Cost] (1-Tax) + Depreciation after tax

= [(42-23)(115000)-947,307 (0.62) + 0.38(104,111)

= 767,370 + 39,562

= $806,932

Calculation of NPV using Base-Case Cash Flow

NPV_Base = -937,000 + 806,932 x PVIFA 12% for 9 years

               = -937,000 + 806,932 x 5.3282

               = $3,362,495

b) Calculation of sensitivity of NPV to changes in Sales Figure

In the question, to ascertain sensitivity of NPV to changes in sales figure, we assume 120,000 as the sales figure

Base Cash Flow = [(Price per unit – Variable Cost per unit) (Quantity Sold) – Fixed Cost] (1-Tax) + Depreciation after tax

= [(42-23) (120,000)-947,307 (0.62) + 0.38(104,111)

= 826,270 + 39,562

= $865,832

Calculation of NPV using Base-Case Cash Flow

NPV_Base = -937,000 + 865,832 x PVIFA 12% for 9 years

               = -937,000 + 806,932 x 5.3282

               = $3,676,326

Sensitivity of NPV to change in sales figure = Change in NPV / Change in sales

                                                                             = (3,362,495 - 3,676,326) / (115,000 – 120,000)

                                                                             = 313,831 / 5000

                                                                             = $63

c) If sales are to drop by 500 units,

• Drop in NPV = 63 (500) = 31500

        

Note: Whatever number is assumed as the sales figure, in the event of computation of change in NPV per unit sold, the ratio will remain the same.

Requirement 3

a) For computation of sensitivity of OCF to changes in Variable cost figure, we assume variable cost to be $26 per unit.

New OCF = [(Price per unit – Variable Cost per unit) (Quantity Sold) – Fixed Cost] (1-Tax) + Depreciation after tax

= [(42-26) (115,000)-947,307 (0.62) + 0.38(104,111)

= 553,470 + 39,562

= $593,032

b) Change in OCF if there is $1 decrease in variable costs

= Change in OCF / Change in Variable Cost

= (806,932 – 593,032) / (25 – 26)

= -$213,900