Concept explainers
Project Analysis [LO1, 2, 3, 4] You are considering a new product launch. The project will cost $1,750,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 190 units per year; price per unit will be $17,300, variable cost per unit will be $10,400, and fixed costs will be $515,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 35 percent.
a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case
b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.
c. What is the cash break-even level of output for this project (ignoring taxes)?
d. What is the accounting break-even level of output for this project? What is the degree of operating leverage at the accounting break-even point? How do you interpret this number?
a)
To determine: The upper and lower bounds of unit sales, variable costs, and fixed costs projections under the scenario analysis.
Introduction:
Fixed costs remain the same as the total costs despite of the changes in the level of activity. However, the fixed cost per unit has a negative relationship with activity, that is, if the activity volume increases then total cost will decrease and vice-versa.
Variable costs are the type of costs that would vary according to the production output. It depends on the production volume.
Answer to Problem 19QP
Under the scenario analysis, the lower (worst scenario) and upper (best scenario) bounds of unit sales, variable costs, and fixed costs projections are as follows:
Scenarios |
Unit sales (in units) |
Variable cost (in $) |
Fixed cost (in $) |
Base | 190 | 10,400 | 515,000 |
Best | 209 | 9,360 | 463,500 |
Worst | 171 | 11,440 | 566,500 |
Explanation of Solution
Given information:
The unit sales is 190 units, variable costs is $10,400, and fixed costs is $515,000. The accurate estimate is ±10%.
Formula:
The formula to calculate upper bounds of unit sales projection under the scenario analysis:
The formula to calculate upper bounds of variable costs projection under the scenario analysis:
The formula to calculate upper bounds of fixed costs projection under the scenario analysis:
The formula to calculate lower bounds of unit sales projection under the scenario analysis:
The formula to calculate lower bounds of variable costs projection under the scenario analysis:
The formula to calculate lower bounds of fixed costs projection under the scenario analysis:
Compute the upper bounds of unit sales projection under the scenario analysis:
Hence, the upper bounds of unit sales projection under the scenario analysis are 209 units.
Compute the upper bounds of variable costs projection under the scenario analysis:
Hence, the upper bounds of variable costs projection under the scenario analysis are $9,360.
Compute the upper bounds of fixed costs projection under the scenario analysis:
Hence, the upper bounds of fixed costs projection under the scenario analysis are $463,500.
Compute the lower bounds of unit sales projection under the scenario analysis:
Hence, the lower bounds of unit sales projection under the scenario analysis are 171 units.
Compute the lower bounds of variable costs projection under the scenario analysis:
Hence, the lower bounds of variable costs projection under the scenario analysis are $11,440.
Compute the lower bounds of fixed costs projection under the scenario analysis:
Hence, the lower bounds of fixed costs projection under the scenario analysis are $566,500.
To determine: The base-case Net present value (NPV)
Introduction:
Net present value (NPV) refers to the discounted value of the future cash flows at present. The company should accept the project, if the net present value is positive or greater than zero and vice-versa. If there are two mutually exclusive projects, then the company has to select the project that has higher net present value.
Answer to Problem 19QP
The NPV for the base-case scenario is $286,619.11.
Explanation of Solution
Given information:
The fixed costs of the project are $515,000 per year and the initial cost of the project is $1,750,000 for the lifetime of 4 years. The variable cost per unit is $10,400 and the price per unit of the project is $17,300. The unit sold is 190 units per year, the required rate of return is 12%, and the tax rate is 35%.
The formula to calculate the operating cash flow under the base-case scenario:
Where,
P refers to the price per unit of the project
v refers to the variable cost per unit
Q refers to the number of unit sold
FC refers to the fixed costs
The formula to calculate the NPV of base-case operating cash flow:
Compute the operating cash flow in the base-case scenario:
Hence, the operating cash flow under the base-case scenario is $670,525.
Compute the NPV for the base-case scenario:
Note: To determine the present value of annuity of $1 period for 4 period at a discount rate of 12% refer the PV of an annuity of $1 table. Then find out 12% discount rate and period of 8 years value from the table. Here, the value for the rate 12% and 4 years period is 3.03735.
Hence, the NPV for the base-case scenario is $286,619.11.
To determine: The worst-case scenario
Introduction:
Worst-case scenario is a particular case under the scenario analysis to determine the worst scenarios of the project. The financial managers of the company use this worst-case technique to anticipate potential losses and operational issues of the project.
Answer to Problem 19QP
The NPV for the worst-case scenario is -$1,309,315.
Explanation of Solution
Given information:
The fixed costs of the project are $515,000 per year and initial cost of the project is $1,750,000 for the life time of 4 years. The variable cost per unit is $10,400 and price per unit of the project is $17,300. The unit sold is 190 units per year, required rate of return is 12%, and tax rate is 35%.
The formula to calculate the operating cash flow for worst-case scenario:
Where,
P refers to the price per unit of the project
v refers to the variable cost per unit
Q refers to the number of unit sold
FC refers to the fixed costs
The formula to calculate the NPV for worst- case operating cash flow:
Compute the operating cash flow under the worst-case scenario:
Hence, the operating cash flow under the worst-case scenario is $440,685.
Compute the NPV for worst case scenario:
Hence, the NPV for the worst-case scenario is -$1,309,315.
b)
To determine: The sensitivity of base-case NPV to change in fixed costs
Introduction:
Sensitivity analysis is analyzing the impact of changing only one variable of the net present value. It helps to identify the areas in which the forecasting errors would be severe. The basic concept of sensitivity analysis is to freeze all the variables except one variable.
Answer to Problem 19QP
The sensitivity of NPV to change in the sales value is -$1.97.
Explanation of Solution
Given information:
The fixed costs of the project are $515,000 per year and initial cost of the project is $1,750,000 for the life time of 4 years. The variable cost per unit is $10,400 and price per unit of the project is $17,300. The unit sold is 190 units per year, required rate of return is 12%, and tax rate is 35%. Assume the fixed cost has $516,000.
Formula:
The formula to calculate the sensitivity of NPV to make changes in the sales value:
The formula to calculate the NPV of the new case operating cash flow:
The formula to calculate the new case operating cash flow:
Where,
P refers to the price per unit of the project
v refers to the variable cost per unit
Q refers to the number of unit sold
FC refers to the fixed costs
Compute the new case operating cash flow:
Hence, the new case operating cash flow is $669,875.
Compute the NPV of new case operating cash flow:
Note: To determine the present value of annuity of $1 period for 4 period at a discount rate of 12% refer the PV of an annuity of $1 table. Then find out 12% discount rate and period of 8 years value from the table. Here, the value for the rate 12% and 4 years period is 3.03735.
Hence, the NPV of the new case operating cash flow is $284,644.83.
Compute the sensitivity of NPV to change in the sales value:
Hence, the sensitivity of NPV to change in the sales value is -$1.97. As a result, for every dollar of fixed cost, the NPV decrease by $1.97.
c)
To determine: The cash break-even level of output of the project
Introduction:
Cash break-even point specifies a sales level which can result in zero operating cash flow.
Answer to Problem 19QP
The cash break-even level of output is 74.64 units.
Explanation of Solution
Given information:
The unit price is $17,300, unit variable costs are $10,400, and fixed costs are $515,000.
The formula to calculate the cash break-even quantity:
Compute the cash break-even quantity:
Hence, the cash breakeven quantity is 74.64 units.
d)
To determine: The accounting break-even level of output
Introduction:
Accounting break-even is a sales point at which there is no profit or loss. It is the most widely used measure of break-even point.
Answer to Problem 19QP
The accounting break-even level of output is 138.04 units.
Explanation of Solution
Given information:
The fixed costs of the project are $515,000 per year. The initial cost of the project is $1,750,000 for the life time of 4 years. The variable cost per unit is $10,400 and price per unit of the project is $17,300.
The formula to calculate the accounting break-even quantity:
Compute the accounting break-even quantity:
Hence, the accounting breakeven quantity is 138.04 units.
To determine: The degree of operating leverage
Introduction:
Degree of operating leverage is a measure that indicates the sensitivity on the fixed cost of a project. It interprets that a company with more high operating leverage indicates higher fixed costs and vice versa.
Answer to Problem 19QP
The degree of operating leverage is 2.18 times.
Explanation of Solution
Given information:
The fixed costs of the project are $515,000 per year. The operating cash is $$670,525.
The formula to calculate the degree of operating leverage:
Compute the degree of operating leverage:
Hence, the degree of operating leverage is 1.76 times. The operating cash flows will increase by 1.76% for each 1% increase in unit sales.
Want to see more full solutions like this?
Chapter 11 Solutions
Fundamentals of Corporate Finance (Special Edition for Rutgers Business School)
- 13. Project Analysis You are considering a new product launch. The project will cost $1.675 million, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 195 units per year; price per unit will be $16,300; variable cost per unit will be $9,400; and fixed costs will be $550,000 per year. The required return on the proiect is 12 percent and the relevant tax rate is 21 percent. a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within #10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs. c. What is the accounting break-even level of output for this project? use excel to solve thisarrow_forwardYou are considering a new product launch. The project will cost $1,675,000, have a four- year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 195 units per year; price per unit will be $16,300, variable cost per unit will be $9,400, and fixed costs will be $550,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 21 percent. a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What is the NPV for the best-case and worst-case scenarios? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.) Scenario Unit Sales Variable Cost Fixed Costs NPV Base 195 $ 9,400 $…arrow_forwardYou are considering a new product launch. The project will cost $1,675,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 195 units per year; price per unit will be $16,300, variable cost per unit will be $9,400, and fixed costs will be $550,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 21 percent. a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What is the NPV for the best-case and worst-case scenarios? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.) b. Evaluate the sensitivity of your base-case…arrow_forward
- The most likely outcomes for a particular project are estimated as follows: Unit price: Variable cost: Fixed cost: Expected sales: 50 24 30 $370,000 36,000 units per year However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1.4 million, which will be depreclated straight-line over the project life to a final value of zero. The firm's tax rate is 21% and the required rate of return is 14%. (For all the requirements, a negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) a. What is project NPV in the best-case scenario, that is, assuming all variables take on the best possible value? b. What is project NPV in the worst-case scenario?arrow_forwardASAP!! The most likely outcomes for a particular project are estimated as follows: Unit price: $50 Variable cost: $30 Fixed cost: $300,000 Expected sales: 30,000 units per year However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 12 percent higher or 12 percent lower than the initial estimate. The project will last for 5 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 35 percent and the required rate of return is 12 percent. What is project NPV in the “best-case scenario,” that is, assuming all variables take on the best possible value? What about the worst-case scenario?arrow_forwardThe most likely outcomes for a particular project are estimated as follows: Unit price: Variable cost: Fixed cost: Expected sales: $ 50 $ 30 $ 490,000 48,000 units per year However, you recognize that some of these estimates are subject to error. Suppose each variable turns out to be either 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $2.3 million, which will be depreciated straight-line over the project life to a final value of zero. The firm's tax rate is 21%, and the required rate of return is 10%. a. NPV b. NPV a. What is project's NPV in the best-case scenario, that is, assuming all variables take on the best possible value? b. What is project's NPV in the worst-case scenario? Note: For all the requirements, a negative amount should be indicated by a minus sign. Enter your answers in dollars, not in millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount. 4arrow_forward
- You are considering a new product launch. The project will cost $820,000, have a 4-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 210 units per year; price per unit will be $16,400, variable cost per unit will be $11,300, and fixed costs will be $555,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 24 percent. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within +10 percent. a. What are the best-case and worst-case NPVs with these projections? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. b. What is the base-case NPV? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. c. What is the sensitivity of your base-case NPV to changes in fixed costs? Note: A…arrow_forwardI Canvas Desai Industries is analyzing an average-risk project, and the following data have been developed. Unit sales will be constant, but the sales price should increase with inflation. Fixed costs will also be constant, but variable costs should rise with inflation. The project should last for 3 years. Under the new tax law, the equipment used in the project is eligible for 100% bonus depreciation, so it will be fully depreciated at t = 0. At the end of the project's life, the equipment would have no salvage value. No change in net operating working capital (NOWC) would be required for the project. This is just one of many projects for the firm, so any losses on this project can be used to offset gains on other firm projects. What is the project's expected NPV? Do not round the intermediate calculations and round the final answer to the nearest whole number. WACC %0'0I Equipment cost $200,000 Units sold 56,000 Average price per unit, Year 1 $25.00 Fixed op. cost excl. depr.…arrow_forwardYou are considering a new automotive product line in the firm’s business portfolio. The project will cost $ 2.170 billion and have a five-year life with no salvage value; depreciation is straight-line to zero. Sales are projected at 220 units per year; price per unit will be $ 19.70 million, variable cost per unit will be $ 12.80 million, and fixed costs will be $ 590.00 million per year. The required return on the project is 8%, and the relevant tax rate is 21%. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10%. What is the base-case NPV? What is the best-case NPV?What is the worst-case NPV?arrow_forward
- 15 UPS is considering the purchase of a electric truck that would cost $150,000 and would last for 5 years. At the end of 5 years, the truck would have a salvage value of $20,000. By reducing labor and other operating costs, the machine would provide annual cost savings of $45,000. The company requires a minimum return of 19% on all investment projects. The net present value of the proposed project is closest to (Ignore income taxes.): PV factor of $1 annuity for 5 years at 19% is 3.058 and PV of $1 over 5 years is 0.419 A. $85,000 B. -$12,390 C. -$4,010 D. $145,990arrow_forwardPlease show work without excel You are considering a new product launch. The project will cost $1,022,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 400 units per year; price per unit will be $20,200, variable cost per unit will be $16,700, and fixed costs will be $338,000 per year. The required return on the project is 14 percent, and the relevant tax rate is 35 percent. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the best- and worst-case OCFs and NPVs with these projections?arrow_forwardYou are considering a new product launch. The project will cost $750,000, have a 4-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 440 units per year; price per unit will be $17,700, variable cost per unit will be $14,400, and fixed costs will be $725,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 23 percent. a. The unit sales, variable cost, and fixed cost projections given above are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections?arrow_forward
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
- Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage LearningCorporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan ProfessorPublisher:McGraw-Hill Education