We are evaluating a project that costs $644,000, has an eight-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 70,000 units per year. Price per unit is $37, variable cost per unit is $21, and fixed costs are $725,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project. Required:
a. Calculate the accounting break-even point.
b. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales.
c. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a $1 decrease in estimated variable costs.

Solution :

a).

Particulars                                                Details

Selling price per unit                                 37

Less : variable cost per unit                     -21

Margin per unit                                           16

No. of units sold per unit                       70,000

Gross margin                                        11,20,000

Less : fixed cost                                     - 7,25,000

Profit before depreciation and tax       3,95,000

Less : depreciation                                -80,500

Profit before tax                                     3,14,500

Less : Tax                                               -1,10,075

Net profit per year                                 2,04,425

Project Cost                                           6,44,000

Accounting breakeven point in years     3.15

b).

Calculating the base Cash - Cash flow and NPV

Particulars                                                       Amount

Net profit per year                                        2,04,425

Add : depreciation                                         80,500

Base Cash cashflow                                     2,84,925

Required rate of return                                    15%

Present value of base cash cash flow        12,78,550

received in 8 years.

Project cost                                                  -6,44,000

NPV                                                               6,34,550

The present value of base cash cash flow received in 8 years is calculated as Present value of annuity received at the end of each year $ 2,84,925 at the rate of interest 15% for a period of 8 years.

The sensitivity of the NPV to 500 units decrease in projected sales :

Particulars                                                          Details

Selling price per unit                                            37

Less : variable cost per unit                                -21

Margin per unit                                                     16

Number of units sold per year                          69,500

Gross margin                                                      11,12,000

Less : fixed cost                                                -7,25,000

Profit before depreciation and tax                   3,87,000

Less : depreciation                                            -80,500

Profit before tax                                                 3,06,500

Less : tax                                                            -1,07,275

Net profit per year                                             1,99,225

Add : depreciation                                              80,500

Base Cash cashflow                                          2,79,725

Required rate of return                                         15%

Present value of base cash cash flow              12,55,216

received in 8 years.

Project cost                                                    -6,44,000

NPV                                                                6,11,216

Original NPV                                                  6,34,550

Sensitive NPV                                                  -23,334

c).

Particulars                                                              Details

Selling price per unit                                               37

Less : variable cost per unit                                   -20

Margin per unit                                                        17

No. of units sold per year                                     70,000

Gross Margin                                                         11,90,000

Less : fixed cost                                                     -7,25,000

Profit before depreciation and tax                       4,65,000

Less : Depreciation                                                -80,500

Profit before tax                                                     3,84,500

Less : tax                                                                -1,34,575

Net profit per year                                                  2,49925

Add : depreciation                                                   80,500

Operating cash flow                                               3,30,425

Original operating cashflow                                   2,84,925

Sensitivity of OCF                                                      45,500

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this