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4/16/2010 Chapter 11. Ch 11-18 Build a Model has developed a powerful new s

4/16/2010 Chapter 11. Ch 11-18 Build a Model has developed a powerful new s has developed a powerful new server that would be used for corporations’ Internet activities. It would cost $10 million at Year 0 to buy the equipment necessary to manufacture the server. The project would require net working capital at the beginning of each year in an amount equal to 10% of the year's projected sales; for example, NWC0 = 10%(Sales1). The servers would sell for $24,000 per unit, and Webmasters believes that variable costs would amount to $17,500 per unit. After Year 1, the sales price and variable costs will increase at the inflation rate of 3%. The company’s nonvariable costs would be $1 million at Year 1 and would increase with inflation. 

The server project would have a life of 4 years. If the project is undertaken, it must be continued for the entire 4 years. Also, the project's returns are expected to be highly correlated with returns on the firm's other assets. The firm believes it could sell 1,000 units per year.

The equipment would be depreciated over a 5-year period, using MACRS rates. The estimated market value of the equipment at the end of the project’s 4-year life is $500,000. Webmasters’ federal-plus-state tax rate is 40%. Its cost of capital is 10% for average-risk projects, defined as projects with a coefficient of variation of NPV between 0.8 and 1.2. Low-risk projects are evaluated with a WACC of 8%, and high-risk projects at 13%.

a. Develop a spreadsheet model, and use it to find the project’s NPV, IRR, and payback. 

Key Output: NPV =
Part 1. Input Data (in thousands of dollars) IRR =
Equipment cost $10,000 
Net WC/Sales 10% Market value of equipment at Year 4 $500 
First year sales (in units) 1,000 Tax rate 40%
Sales price per unit $24.00 WACC 10%
Variable cost per unit $17.50 Inflation 3.0%
Nonvariable costs $1,000

Part 2. Depreciation and Amortization Schedule Years Accum'd
Year Initial Cost 1 2 3 4 Depr'n

Equipment Depr'n Rate 20.0% 32.0% 19.0% 12.0%
Equipment Depr'n, Dollars
Ending Bk Val: Cost – Accum Dep'rn

Part 3. Net Salvage Values, in Year 4 Equipment
Estimated Market Value in Year 4
Book Value in Year 4
Expected Gain or Loss
Taxes paid or tax credit
Net cash flow from salvage

Part 4. Projected Net Cash Flows (Time line of Annual Cash Flows)
Years 0 1 2 3 4 
Investment Outlays at Time Zero:

Operating Cash Flows over the Project's Life:
Units sold
Sales price
Variable costs

Sales revenue
Variable costs
Nonvariable operating costs
Depreciation (equipment)
Oper. income before taxes (EBIT)
Taxes on operating income (40%)
After-tax operating income 
Add back depreciation
Operating cash flow

Terminal Year Cash Flows:
Required level of net working capital
Required investment in NWC

Terminal Year Cash Flows:
Net salvage value

Net Cash Flow (Time line of cash flows)

Part 5. Key Output: Appraisal of the Proposed Project

Net Present Value (at 10%)

Payback (See calculation below) 3 

Data for Payback Years 0 1 2 3 4
Net cash flow
Cumulative CF 0 
Part of year required for payback

"b. Now conduct a sensitivity analysis to determine the sensitivity of NPV to changes in the sales price, variable costs 
per unit, and number of units sold. Set these variables’ values at 10% and 20% above and below their base-case 
values. Include a graph in your analysis."

Part 6. Evaluating Risk: Sensitivity Analysis

"I. Sensitivity of NPV to Changes in Inputs. Here we use Excel ""Data Tables"" to find NPVs at different unit sales, 
WACC, variable costs, sales price and nonvariable costs--changing one variable at a time, holding other things 

% Deviation 1st YEAR UNIT SALES % Deviation WACC
from Units NPV from NPV
Base Case Sold $0 Base Case WACC $0 
-20% 0 -20% 0 
-10% 0 -10% 0 
0% 0 0% 0 
10% 0 10% 0 
20% 0 20% 0 

% Deviation VARIABLE COST % Deviation SALES PRICE
from Variable NPV from Sales NPV
Base Case Costs $0 Base Case Price $0
-20% 0 -20% 0 
-10% 0 -10% 0 
0% 0 0% 0 
10% 0 10% 0 
20% 0 20% 0 
Note about data tables. The data in the column input should NOT be input using a cell reference to the column input cell. For example, the base case number of units sold in Cell B105 should be the number 1000; you should NOT have the formula =D29 in that cell. This is because you'll use D29 as the column input cell in the data table and if Excel tries to iteratively replace Cell D29 with the formula =D29 rather than a series of numbers, Excel will calculate the wrong answer. Unfortunately, Excel won't tell you that there is a problem, so you'll just get the wrong values for the data table!
from Fixed NPV
Base Case Costs $0
-20% 0 
-10% 0 
0% 0 
10% 0 
20% 0 

Deviation NPV at Different Deviations from Base
from Sales Variable Nonvariable
Base Case Price Cost/Unit Units Sold Cost WACC
-20% $0 $0 $0 $0 $0 
-10% 0 0 0 0 0 
0% 0 0 0 0 0 
10% 0 0 0 0 0 
20% 0 0 0 0 0 


"c. Now conduct a scenario analysis. Assume that there is a 25% probability that best-case conditions, with each of the 
variables discussed in Part b being 20% better than its base-case value, will occur. There is a 25% probability of 
worst-case conditions, with the variables 20% worse than base, and a 50% probability of base-case conditions."

Part 7. Evaluating Risk: Scenario Analysis Squared
Sales Unit Variable Times
Scenario Probability Price Sales Costs NPV Probability

Best Case 25% $28.80 1,200 $14.00
Base Case 50% $24.00 1,000 $17.50
Worst Case 25% $19.20 800 $21.00

Expected NPV = sum, prob times NPV
Standard Deviation = Sq Root of column H sum
Coefficient of Variation = Std Dev / Expected NPV

d. If the project appears to be more or less risky than an average project, find its risk-adjusted NPV, IRR, and payback.

CV range of firm's average-risk project: 0.8 to 1.2 
Low-risk WACC = 8%
WACC = 10%
High-risk WACC = 13%

Risk-adjusted WACC =
Risk adjusted NPV =
Payback =

Rosa Parks 06-Nov-2017

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