Chapter 7, Problem 26QP

Scenario Analysis Consider a project to supply Detroit with 25,000 tons of machine screws annually for automobile production. You will need an initial $2,700,000 investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be $275,000 and that variable costs should be $265 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over !he five-year project life. It also estimates a salvage value of $250,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $345 per ton. The engineering department estimates you will need an initial net working capital investment of $400,000. You require a 13 percent return and face a marginal tax rate of 38 percent on this project.

1. a. What is the estimated OCF for this project? The NPV? Should you pursue this project?
2. b. Suppose you believe that the accounting department’s initial cost and salvage value projections are accurate only to within ±15 percent; the marketing department’s price estimate is accurate only to within ±10 percent; and the engineering department’s net working capital estimate is accurate only to within ±5 percent. What is your worst-case scenario for this project? Your best-case scenario? Do you still want to pursue the project?

Summary Introduction

To determine: The operating cash flow and net present value.

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 26QP

Solution: The operating cash flow is $1,274,700 and the net present value is $1,684,650.59.

Explanation of Solution

Given information:

The annual fixed costs are $275,000, variable cost per unit is $265 per ton, number of quantity supplied is 25,000, marginal tax rate is 38%, initial investment on the equipment is $2,700,000, and life of the project is five years. The net initial working capital investment is $400,000 and required rate of return is 13%. The salvage value is $250,000. The selling price is $345 per ton. The marginal tax rate at 38%

The formula to calculate the operating cash flow:

$\text{Operating cash flow}=\left(\begin{array}{c}\left[\left(\text{Unit sold}\times \left[\text{Selling price}-\text{Variable price}\right]\right)-\text{Fixed cost}\right]\times \\ \left(1-\text{Tax rate}\right)\\ +\left(\text{Depreciation}\times \text{Tax rate}\right)\end{array}\right)$

The formula to calculate the net present value:

$\text{NPV }=\left(\begin{array}{l}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\text{Estimated Operating cash flow}\left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)$

Where,

n refers to the number of years.

Compute the operating cash flows:

$\begin{array}{c}\text{Operating cash flow}=\left(\begin{array}{c}\left[\left(\text{Unit sold}\times \left[\text{Selling price}-\text{Variable price}\right]\right)-\text{Fixed cost}\right]\times \\ \left(1-\text{Tax rate}\right)\\ +\left(\text{Depreciation}\times \text{Tax rate}\right)\end{array}\right)\\ =\left(\begin{array}{c}\left[\left(25,000\times \left[\$345-\$265\right]\right)-\$275,000\right]\times \\ \left(1-0.38\right)\\ +\left(\frac{\$2,700,000}{5}\times 0.38\right)\end{array}\right)\\ =\left(\$1,069,500+\$205,200\right)\\ =\$1,274,700\end{array}$

Hence, the operating cash flow is $1,274,700.

Compute the net present value:

Note: The increase in operating cash flow at present value of interest factor annuity at 13% for 5 years is 3.51723.

Calculate the net present value:

$\begin{array}{c}\text{NPV }=\left(\begin{array}{l}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\text{Estimated operating cash flow}\left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)\\ =\left(\begin{array}{l}\left[\begin{array}{l}\left(-\$2,700,000-\$400,000\right)\\ +\left(\$1,274,700\left(3.51723\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\$400,000\\ +\$250,000\left(1-0.38\right)\end{array}}{{\left(1+0.13\right)}^5}\right]\end{array}\right)\\ =\$1,383,413.081+\left[\frac{\begin{array}{l}\$400,000\\ +\$155,000\end{array}}{1.8424}\right]\end{array}$

$\begin{array}{c}=\$1,383,413.081+\$301,237.51\\ =\$1,684,650.59\end{array}$

Hence, the net present value is $1,684,650.59.

Summary Introduction

To determine: The worst-case scenario and best-case scenario of the project.

Introduction:

Scenario analysis is a process of analyzing the possible future events. This analysis helps to determine the effect of what-if questions towards the net present value estimates. At the time when the firm begins to look for an alternative, then they can be able to find the possible project, which would result in positive net present value (NPV).

Answer to Problem 26QP

Solution:

Worst-case scenario:

The operating cash flow of the worst-case scenario is $770,730 and the NPV of worst-case scenario is −$514,691.82.

Best-case scenario:

The operating cash flow of the best-case scenario is $1,778,670 and the NPV of best-case scenario is $3,883,992.99.

Explanation of Solution

Given information:

The annual fixed costs are $275,000, variable cost per unit is $265 per ton, number of quantity supplied is 25,000, marginal tax rate is 38%, initial investment on the equipment is $2,700,000, and life of the project is five years. The net initial working capital investment is $400,000 and required rate of return is 13%. The salvage value is $250,000. The selling price is $345 per ton. The marginal tax rate at 38%

Formulae:

The formula to calculate the operating cash flow for best or worst-cases scenarios:

$\begin{array}{l}\text{Operating cash flow }\\ \text{of best or worst case scenario}\end{array}\}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}$

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 best or worst-cases:

$\begin{array}{l}\text{Net present value }\\ \text{of best or worst-cases}\end{array}\}=-\text{Initial investment}+\text{Best or worst-cases operating cash flow}$

Note: In the best-case scenario, both the price and sales indicates an increase in the value whereas the costs will indicate a decrease in the value. In the worst-case scenario, both the price and sales indicates a decrease in the value but the costs will specify an increase in the value.

Compute the operating cash flow for worst-case scenario:

Note: The tax shield approach is used to determine the operating cash flow of the worst-case scenario. In this given problem, the price and quantity is decreased by 10%. As a result, both price and quantity is multiplied by 10 percent decrease. However, the variable and fixed costs will indicate an increase by 15 percent.

$\begin{array}{c}\begin{array}{l}\text{Operating cash flow }\\ \text{of worst-case scenario}\end{array}\}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}\\ \text{=}\left[\left(\$345\left(1-0.1\right)-\$265\right)25,000-\$275,000\right]\times \left(1-0.38\right)+0.38\\ \times \left(\frac{\$2,700,000\left(1+0.15\right)}{5}\right)\\ =\left(\$1,137,500-\$275,000\right)\times 0.62+0.38\times \$621,000\end{array}$

$\begin{array}{c}=\$534,750+\$235,980\\ =\$770,730\end{array}$

Hence, the operating cash flow of the worst-case scenario is $770,730.

Compute the NPV of worst-case scenario:

$\begin{array}{c}\text{Net present value }=\left(\begin{array}{c}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\begin{array}{l}\text{Estimated Operating cash flow}\\ \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\end{array}\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)\\ =\left(\begin{array}{c}\left[\begin{array}{l}\left(-\left(\frac{\$2,700,000\left(1+0.15\right)}{5}\right)-\$400,000(1+0.05\right)\\ +\left(\$770,730\left(3.51723\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\$400,000\left(1+0.05\right)\\ +\$250,000\left(1-0.15\right)\left(1-0.38\right)\end{array}}{{\left(1+0.13\right)}^5}\right]\end{array}\right)\\ =-\$3,105,000-\$420,000+\$2,710,834.67+\left[\frac{\$420,000+\$131,750}{1.8424}\right]\end{array}$

$\begin{array}{l}=-\$814,165.33+\$299,473.51\\ =-\$514,691.82\end{array}$

Hence, the NPV of the worst-case scenario is −$514,691.82.

Compute the operating cash flow for best-case scenario:

$\begin{array}{c}\begin{array}{l}\text{Operating cash flow }\\ \text{of best-case scenario}\end{array}\}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}\\ \text{=}\left[\left(\$345\left(1+0.10\right)-265\right)25,000-\$275,000\right]\times \left(1-0.38\right)+0.38\\ \times \left(\frac{\$2,700,000\left(1-0.15\right)}{5}\right)\\ =\left(\$2,862,500-\$275,000\right)\times 0.62+0.38\times \$459,000\end{array}$

$\begin{array}{c}=\$1,604,250+\$174,420\\ =\$1,778,670\end{array}$

Hence, the operating cash flow of the best-case scenario is $1,778,670.

Compute the net present value of best-case scenario:

$\begin{array}{c}\text{Net present value }=\left(\begin{array}{c}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\begin{array}{l}\text{Estimated operating cash flow}\\ \left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\end{array}\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)\\ =-\left(\frac{\$2,700,000\left(1-0.15\right)}{5}\right)-\$400,000\left(1-0.05\right)+\$1,778,670\times 3.51723\\ +\frac{\$400,000\left(1-0.05\right)+\$250,000\left(1+0.15\right)\left(1-0.38\right)}{{\left(1+0.13\right)}^5}\\ =-\$2,295,000-\$380,000+\$6,255,991.48+\left(\frac{\$380,000+\$178,250}{{\left(1+0.13\right)}^5}\right)\\ =\$3,580,991.48+\frac{\$558,250}{1.8424}\end{array}$

$\begin{array}{c}=\$3,580,991.48+\$303,001.51\\ =\$3,883,992.99\end{array}$

Hence, the net present value of the best-case scenario is $3,883,992.99.

Summary Introduction

To discuss: Whether the project is pursued or not based on the computation of NPV.

Explanation of Solution

The worst-case scenario indicates a negative NPV whereas the best-case indicates the positive NPV. Therefore, to proceed with the project would not be difficult.