Question

We are evaluating a project that costs $1,770,000, has a 6-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 87,000 units per year. Price per unit is $38.13, variable cost per unit is $23.35, and fixed costs are $824,000 per year. The tax rate is 23 percent, and we require a return of 9 percent on this project. a. Calculate the base-case operating cash flow and NPV. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b. What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) c. If there is a 300-unit decrease in projected sales, how much would the NPV change? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) e. If there is a $1 decrease in estimated variable costs, how much would the OCF change? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) Base-case operating cash flow Base-case NPV NPV sensitivity c. NPV change d. OCF sensitivity e. OCF change

Answer 1

a) Below is the calculation for base operating cash flow and NPV:

A B C D Е G Н Operating Profit (unit*(price-variable cost)-fixed cost Free Cash Flow Present Value of Free Cash flow PBT |(Free Cash flow/1.09^year) 1 Year Tax (PBT 23%) (Operating Profit-Tax) Variable Cost/unit Fixed Cost Initial Cost Depreciation (Initial Cost/6) Units of sales Price of unit sale (Operating for -Depreciation) O (1,770,000.00) 2 (1,770,000.00) (1,770,000.00) 0 23.35 1 295,000.00 87,000.00 38.13 824,000.00 461,860.00 166,860.00 38,377.80 423,482.20 388,515.78 4 295,000.00 166,860.00 2 87,000.00 38.13 23.35 824,000.00 461,860.00 38,377.80 423,482.20 356,436.50 5 3 295,000.00 87,000.00 38.13 23.35 824,000.00 461,860.00 166,860.00 38,377.80 423,482.20 327,005.96 166,860.00 6 461,860.00 4 295,000.00 87,000.00 38.13 23.35 824,00o.00 38,377.80 423,482.20 300,005.47 7 38.13 5 295,000.00 87,000.00 23.35 824,000.00 461,860.00 166,860.00 38,377.80 423,482.20 275,234.37 87,000.00 23.35 824,000.00 461,860.00 6 295,000.00 38.13 166,860.00 38,377.80 423,482.20 252,508.60 129,706.67 Total (NPV) 9 10

b. If we increase 1% in sales unit i.e. 1%*87000=870, then NPV would increase by (174122.30-129706.67)/129706.67=34.24%. Calculation is given below:

A В C D E F G Н К Operating Profit (unit*(price-variable cost)-fixed cost Free Cash Flow Present Value of Free Cash flow РВT Tax (PBT 23%) (Operating Profit-Tax) |(Free Cash flow/1.09^year) 1 Year Variable Cost/unit Fixed Cost Initial Cost Depreciation (Initial Cost/6) Units of sales Price of unit sale (Operating for - Depreciation) O(1,770,000.00) 2 (1,770,000.00) (1,770,000.00) 0 0 3 87,870.00 23.35 824,000.00 474,718.60 179,718.60 41,335.28 397,599.38 1 295,000.00 38.13 433,383.32 4 295,000.00 2 87,870.00 38.13 23.35 824,000.00 474,718.60 179,718.60 41,335.28 433,383.32 364,770.07 5 474,718.60 3 295,000.00 87,870.00 38.13 23.35 824,000.00 179,718.60 41,335.28 433,383.32 334,651.44 6 295,000.00 307,019.67 87,870.00 38.13 23.35 824,000.00 474,718.60 179,718.60 41,335.28 433,383.32 7 295,000.00 38.13 23.35 824,000.00 5 87,870.00 474,718.60 179,718.60 41,335.28 433,383.32 281,669.42 23.35 824,000.00 433,383.32 6 295,000.00 87,870.00 38.13 474,718.60 179,718.60 41,335.28 258,412.31 Total (NPV) 9 174,122.30 10 11

c. Below is the calculation of NPV if sales decrease by 300 units:

A B C Е G Н К Operating Profit (unit*(price-variable cost)-fixed cost Free Cash Flow Present Value of Free Cash flow РВT Tax (PBT 23%)(Operating Profit-Tax) 1 Year Initial Cost Depreciation (Initial Cost/6) Variable Cost/unit Fixed Cost (Free Cash flow/1.09^year) (1,770,000.00) Units of sales Price of unit sale (Operating for -Depreciation) 0 (1,770,000.00) (1,770,000.00) 0 23.35 3 295,000.00 457,426.00 162,426.00 1 86,700.00 38.13 824,000.00 37,357.98 420,068.02 385,383.50 4 86,700.00 23.35 824,000.00 37,357.98 420,068.02 353,562.85 2 295,000.00 38.13 457,426.00 162,426.00 5 295,000.00 86,700.00 457,426.00 324,369.59 38.13 23.35 824,000.00 162,426.00 37,357.98 420,068.02 6 295,000.00 297,586.78 4 86,700.00 38.13 23.35 824,00o.00 457,426.00 162,426.00 37,357.98 420,068.02 7 457,426.00 5 295,000.00 86,700.00 38.13 23.35 824,000.00 162,426.00 37,357.98 420,068.02 273,015.39 8 86,700.00 457,426.00 250,472.84 6 295,000.00 38.13 23.35 824,000.00 162,426.00 37,357.98 420,068.02 Total (NPV) 9 114,390.94 10

Hence, NPV would decrease by (129706.67-114390.94)=$15315.73

d. If variable cost increase by 1% i.e. 23.35*1.01=23.5835 , then OCF for a year= 87000*(38.13-23.5835)-824000=441545.5 i.e OCF decreases by (457426-441545.5)/457426= 3.472%

e. Similarly, if variable cost increase 1% i.e. 23.35*.99=23.1165 , then OCF for a year= 87000*(38.13-23.1165)-824000=482174.5 i.e OCF increases by (482174.5-457426)/457426= 5.41%