Chapter 11, Problem 27QP

Scenario Analysis [LO2] Consider a project to supply Detroit with 35,000 tons of machine screws annually for automobile production. You will need an initial $5,200,000 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 $985,000 and that variable costs should be $185 per ton; accounting will depreciate the initial fixed asset investment straight-fine to zero over the five-year project life. It also estimates a salvage value of $500,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $280 per ton. The engineering department estimates you will need an initial net working capital investment of $410,000. You require a return of 13 percent and face a marginal tax rate of 38 percent on this project.

a. What is the estimated OCF for this project? The NPV? Should you pursue this project?

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 estimated operating cash flow (OCF) and Net present value of the project.

Introduction:

Net present value (NPV) refers to the discounted value of the future cash flows at present. In case, the NPV is positive or greater than zero, then the company will accept the project or 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 27QP

The estimated Operating cash flow is $1,846,000.

The NPV of the project is $1,273,596.06.

Explanation of Solution

Given information:

The annual fixed costs are $985,000, variable cost per unit is $185 per ton, number of quantity supplied is 35,000, marginal tax rate is 38%, initial investment on the equipment is $5,200,000, and life of the project is five years. The net initial working capital investment is $410,000 and the required rate of return is 13%.

Formulae:

The formula to calculate the operating cash flow:

$\text{Operating cash flow}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}$

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:

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

Where,

n refers to the number of years.

Compute the Operating cash flow (OCF):

$\begin{array}{c}\text{Operating cash flow}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}\\ =\left[\left(\$280-185\right)\times 35,000-\$985,000\right]\times \left(1-\frac{38}{100}\right)+\frac{38}{100}\times \left(\frac{\$5,200,000}{5}\right)\\ =\left[\$95\times 35,000-\$985,000\right]\left(1-0.38\right)+\left(0.38\times \$1,040,000\right)\\ =\left[\$3,325,000-\$985,000\right]\times 0.62+\$395,200\\ =\left(\$2,340,000\times 0.62\right)+\$395,200\\ =\$1,450,800+\$395,200\\ =\$1,846,000\end{array}$

Hence, the estimated Operating cash flow (OCF) is $1,846,000.

Compute the NPV:

Note: To determine the present value of annuity of $1 period for 8 period at a discount rate of 10%, refer the PV of an annuity of $1 table. Then, find out the 10% discount rate and period of 8 years’ value from the table. Here, the value for the rate 10% and 8 years’ period value is 5.3349.

$\begin{array}{c}\text{Net present value }=\left(\begin{array}{c}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\text{Estimated Operating cash flow}\left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)\\ =\left(\begin{array}{c}-\$5,200,000-\$410,000+\$1,846,000\left(\begin{array}{l}\text{Present value of an annuity }\\ \text{of }\$1\text{ period for }13\%\text{ of }5\text{ period}\end{array}\right)\\ +\frac{\left[\$410,000+\$500,000\times \left(1-\frac{38}{100}\right)\right]}{{\left(1+\frac{13}{100}\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}\$5,200,000-\$410,000+\$1,846,000\left(3.51723\right)\\ +\frac{\$410,000+\left(\$500,000\times 0.62\right)}{1.842435}\end{array}\right)\\ =\left(\begin{array}{c}-\$5,200,000-\$410,000+\$6,492,806.58\\ +\left(\frac{\$410,000+\$3,100,000}{1.842435}\right)\end{array}\right)\\ =\$882,806.58+\left(\frac{\$720,000}{1.842435}\right)\\ =\$882,806.588+\$390787.19\\ =\$1,273,593.77\end{array}$

Hence, the NPV is $1,273,593.77.

Summary Introduction

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

Explanation of Solution

A project is accepted, when the net present value is positive or greater than zero. This project indicates a positive NPV of $1,273,593.77. Therefore, the project is pursed.

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 might be able to find the possible project, which would result in a positive net present value (NPV).

Answer to Problem 27QP

Worst-case scenario:

The operating cash flow of the worst-case is $1,297,680.

The Net present value (NPV) of the worst-case is -$1,469,585.54.

Best-case scenario:

The operating cash flow of the best-case is $2,394,320.

The Net present value (NPV) of best-case scenario is -$3,206,975.18195.

Explanation of Solution

Given information:

The fixed costs of the project are $985,000. The variable cost per unit is $185 per ton and selling price per unit of the project is $280 per ton. The unit sold is 35,000 tons, required rate of return is 13%, and marginal tax rate is 38%.

The initial cost and salvage value of the projection is ±15%. The price estimate will be accurate within ±10% as per the marketing department. The estimate of net working capital is ±5%.

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 units 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 indicate 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 indicate a decrease 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 worst-case scenario. In this problem, the price and quantity is decreased by 10%. As a result, both the price and quantity is multiplied by a 10 percent decrease. However, the variable and fixed costs will indicate an increase by 15 percent.

$\begin{array}{c}\begin{array}{l}\text{Operating cash flow }\\ \text{of worst case scenario}\end{array}\}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}\\ =\left[\begin{array}{l}\left[\left(\$280\times \left(1-\frac{10}{100}\right)-\$185\right)35,000-\$985,000\right]\times \left(1-\frac{38}{100}\right)\\ +\frac{38}{100}\times \frac{\$5,200,000\times \left(1+\frac{15}{100}\right)}{5}\end{array}\right]\\ =\left[\begin{array}{c}\left[\left(\left(\$280\times 0.9\right)-\$185\right)35,000-\$985,000\right]\times 0.62\\ +0.38\times \frac{\left(\$5,200,000\times 1.15\right)}{5}\end{array}\right]\\ =\left[\$252-\$185\times 35,000-\$985,000\right]\times 0.62+0.38\times \left(\frac{\$5,980,000}{5}\right)\\ =\left[\left(\$67\times 35,000\right)-\$985,000\right]\times 0.62+\left(0.38\times \$1,196,000\right)\\ =\left[\$2,345,000-\$985,000\right]\times 0.62+\$454,480\\ =\left(\$1,360,000\times 0.62\right)+\$454,480\\ =\$843,200+\$454,480\\ =\$1,297,680\end{array}$

Hence, the operating cash flow of worst-case scenario is $1,297,680.

Compute the NPV of worst-case scenario:

$\begin{array}{c}\text{Net present value }=\left(\begin{array}{c}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\text{Estimated Operating cash flow}\left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)\\ =\left(\begin{array}{c}-\$5,200,000\left(1+\frac{15}{100}\right)-\$410,000\left(1+\frac{5}{100}\right)\\ +\$1,297,680\left(\begin{array}{l}\text{Present value of an annuity }\\ \text{of }\$1\text{ period for }13\%\text{ of }5\text{ period}\end{array}\right)\\ +\frac{\left[\$410,000\left(1+\frac{5}{100}\right)+\$500,000\left(1-\frac{15}{100}\right)\times \left(1-\frac{38}{100}\right)\right]}{{\left(1+\frac{13}{100}\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}-\$5,200,000\left(1.15\right)-\$410,000\left(1.05\right)+\$1,297,680\left(3.51723\right)\\ +\frac{\$410,000\left(1.05\right)+\left(\$500,000\times 0.85\times 0.62\right)}{1.842435}\end{array}\right)\\ =\left(\begin{array}{c}-\$5,980,000-\$430,500+\$4,564,239.02\\ +\left(\frac{\$430,500+\$263,500}{1.842435}\right)\end{array}\right)\\ =-\$1,846,260.98+\left(\frac{\$694,000}{1.842435}\right)\\ =-\$1,846,260.98+\$376,675.43224\\ =-\$1,469,585.54\end{array}$

Hence, the NPV of worst-case scenario is -$1,469,585.54.

Compute the operating cash flow for best-case scenario:

$\begin{array}{c}\begin{array}{l}\text{Operating cash flow }\\ \text{of best case scenario}\end{array}\}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\times \left(1-\text{Tax rate}\right)+\text{Tax rate}\times \text{Depreciation}\\ =\left[\begin{array}{l}\left[\left(\$280\times \left(1+\frac{10}{100}\right)-\$185\right)35,000-\$985,000\right]\times \left(1-\frac{38}{100}\right)\\ +\frac{38}{100}\times \frac{\$5,200,000\times \left(1-\frac{15}{100}\right)}{5}\end{array}\right]\\ =\left[\begin{array}{c}\left[\left(\left(\$280\times 1.1\right)-\$185\right)35,000-\$985,000\right]\times 0.62\\ +0.38\times \frac{\left(\$5,200,000\times 0.85\right)}{5}\end{array}\right]\\ =\left[\$308-\$185\times 35,000-\$985,000\right]\times 0.62+0.38\times \left(\frac{\$4,420,000}{5}\right)\\ =\left[\left(\$123\times 35,000\right)-\$985,000\right]\times 0.62+\left(0.38\times \$884,000\right)\\ =\left[\$4,305,000-\$985,000\right]\times 0.62+\$335,920\\ =\left(\$3,320,000\times 0.62\right)+\$335,920\\ =\$2,058,400+\$335,920\\ =\$2,394,320\end{array}$

Hence, the operating cash flow of best-case scenario is $2,394,320.

Compute the NPV of best-case scenario:

$\begin{array}{c}\text{Net present value }=\left(\begin{array}{c}\left[\begin{array}{l}\left(-\text{Initial investment}-\text{Initial working capital investment}\right)\\ +\left(\text{Estimated Operating cash flow}\left(\begin{array}{l}\text{Present value of an annuity}\\ \text{ of \$1 period for R\% of N period}\end{array}\right)\right)\end{array}\right]\\ +\left[\frac{\begin{array}{l}\text{Net initial working capital investment}\\ +\text{Salvage value}\left(1-\text{Marginal tax rate}\right)\end{array}}{{\left(1+\text{Required rate of return}\right)}^n}\right]\end{array}\right)\\ =\left(\begin{array}{c}-\$5,200,000\left(1-\frac{15}{100}\right)-\$410,000\left(1-\frac{5}{100}\right)\\ +\$2,394,320\left(\begin{array}{l}\text{Present value of an annuity }\\ \text{of }\$1\text{ period for }13\%\text{ of }5\text{ period}\end{array}\right)\\ +\frac{\left[\$410,000\left(1-\frac{5}{100}\right)+\$500,000\left(1+\frac{15}{100}\right)\times \left(1-\frac{38}{100}\right)\right]}{{\left(1+\frac{13}{100}\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}-\$5,200,000\left(0.85\right)-\$410,000\left(0.95\right)+\$2,394,320\left(3.51723\right)\\ +\frac{\$410,000\left(0.95\right)+\left(\$500,000\times 1.15\times 0.62\right)}{1.842435}\end{array}\right)\\ =\left(\begin{array}{c}-\$4,420,000-\$389,500+\$8,421,374.1336\\ +\left(\frac{\$389,500+\$356,500}{1.842435}\right)\end{array}\right)\\ =-\$3,611,874.1336+\left(\frac{\$746,000}{1.842435}\right)\\ =-\$3,611,874.1336+\$404,898.95165\\ =-\$3,206,975.18195\end{array}$

Hence, the NPV of best-case scenario is −$3,206,975.18195. Both the best and worst-case scenarios indicate a negative NPV. Therefore, it will be difficult to proceed with project.