Concept explainers
Project Analysis. You are considering a new product launch. The project will cost $780,000, have a four-year life, and have no salvage value;
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 best and worst cases for these projections? What is the base-case
b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.
a)
To calculate: The best and the worst case of the net present value.
Introduction:
The process of analyzing the future proceedings compared to the figures of the net present value is scenario analysis. A project often experiences the best and the worst case of scenarios.
Answer to Problem 23QP
The best case of the net present value is $980,214.89 and the worst case of the net present value is -$418,874.44.
Explanation of Solution
Given information:
A project with 4-year life is being evaluated, the cost of the project is $780,000 and it has no salvage value. The depreciation is assumed to be a straight-line to zero over the project’s life. The projected sales is 180 units for one year.
The price for a unit is $16,300, the fixed cost for a year is $535,000, and the variable cost for a unit is $11,100. The rate of tax is 35% and the required return is 11%. The projections for the quantity, price, variable cost, and fixed costs are within 11%. The rate of tax is 35%.
Scenario | Unit sales | Variable cost | Fixed costs |
Base | 180 | $11,100 | $535,000 |
Best | 198 | $9,990 | $481,500 |
Worst | 162 | $12,120 | $588,500 |
Formula to calculate the operating cash flow using the tax shield approach:
Here,
Computation of the base case of the operating cash flow:
Hence, the base case of the operating cash flow is $328,900.
Formula to calculate the net present value:
Note: As there are many years, PVIFA is used. PVIFA is the present value interest factor of annuity.
Computation of the base case of the net present value:
Hence, the base case of the net present value is $240,379.36.
Computation of the worst case of the operating cash flow:
Hence, the worst case of the operating cash flow is $116,402.
Computation of the worst case of the net present value:
Hence, the worst case of the net present value is -$418,874.44.
Formula to calculate the operating cash flow using the tax shield approach:
Here,
Computation of the best case of the operating cash flow:
Hence, the best case of the operating cash flow is $567,372.
Formula to calculate the net present value:
Computation of the best case of the net present value:
Hence, the best case of the net present value is $980,214.89.
b)
To evaluate: The sensitivity of the base-case net present value to the changes in fixed costs.
Introduction:
The process of analyzing the future proceedings compared to the figures of the net present value is scenario analysis. A project often experiences the best and the worst case of scenarios.
Answer to Problem 23QP
For each dollar, the fixed costs will increase and the NPV declines by $2.02.
Explanation of Solution
Given information:
A project with 4-year life is being evaluated, the cost of the project is $780,000 and it has no salvage value. The depreciation is assumed to be a straight-line to zero over the project’s life. The projected sales is 180 units for one year.
The price for a unit is $16,300, the fixed cost for a year is $535,000, and the variable cost for a unit is $11,100. The rate of tax is 35% and the required return is 11%. The projections for the quantity, price, variable cost, and fixed costs are within 11%. The rate of tax is 35%.
Note: To find the sensitivity of the net present value to the changes in fixed costs, other level of fixed costs is chosen. The chosen fixed cost is $545,000.
Formula to calculate the operating cash flow using the tax shield approach:
Here,
Computation of the operating cash flow:
Hence, the operating cash flow is $322,400.
Formula to calculate the net present value:
Computation the net present value:
Hence, the net present value is $220,213.76.
Formula to compute the sensitivity of net present value to the changes in fixed costs:
Compute the sensitivity of net present value to the changes in fixed costs:
Hence, the sensitivity of the NPV to the changes in fixed costs is -$2.02.
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Chapter 9 Solutions
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
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