# Chapter 13. solution to ch 13-11 build a model

Chapter 13.  Solution to Ch 13-11 Build a Model

Webmasters.com has developed a powerful new server that would be used for corporations’ Internet activities.  It would cost \$10 million to buy the equipment necessary to manufacture the server, and it would require net working capital equal to 10% of sales.  The servers would sell for \$24,000 per unit, and Webmasters believes that variable costs would amount to \$17,500 per unit.  After the first year, the sales price and variable costs would increase at the inflation rate of 3%.  The company’s fixed costs would be \$1 million per year, and would increase with inflation. It would take one year to buy the required equipment and set up operations, and 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 for 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    =
MIRR =
Equipment  cost        \$10.000
Net Operating WC/sales    10%        Market value of equipment in 2006    \$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%
Fixed 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:
Equipment

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

Sales revenue
Variable costs
Fixed operating costs
Depreciation (equipment)
Oper. income before taxes (EBIT)
Taxes on operating income (40%)
Net Operating Profit After Taxes (NOPAT)
Operating cash flow

Terminal Year Cash Flows:
Required level of net operating working capital    \$0     \$0     \$0     \$0     \$0
Required investment in NOWC        \$0     \$0     \$0     \$0     \$0

Terminal Year Cash Flows:
Net salvage value                            0

Net Cash Flow (Time line of cash flows)    \$0     \$0     \$0     \$0     \$0

Part 5.  Key Output:  Appraisal of the Proposed Project

Net Present Value (at 10%)    \$0
IRR            #NUM!
MIRR            #DIV/0!

Payback (See calculation below)    0.00

Data for Payback    Years        0    1    2    3    4
Cumulative CF from Row 53    0     0     0     0     0
IF Function to find payback        FALSE    FALSE    FALSE    FALSE

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 an Excel “Data Table” to find NPV    different unit sales, holding other thing constant.

% Deviation    1st YEAR UNIT SALES        % Deviation    WACC
from    Units    NPV        from         NPV
Base Case    Sold    \$0        Base Case    WACC    0
-20%                 800     \$0        -20%    8.0%    \$0
-10%                 900     \$0        -10%    9.0%    \$0
0%
1.000
\$0        0%    10.0%    \$0
10%              1.100     \$0        10%    11.0%    \$0
20%              1.200     \$0        20%    12.0%    \$0

% Deviation    VARIABLE COSTS        % Deviation    SALES PRICE
from    Variable    NPV        from    Sales    NPV
Base Case    Costs    \$0        Base Case    Price    \$0
-20%    \$14.00    \$0        -20%    \$19.20    \$0
-10%    \$15.75    \$0        -10%    \$21.60    \$0
0%    \$17.50    \$0        0%    \$24.00    \$0
10%    \$19.25    \$0        10%    \$26.40    \$0
20%    \$21.00    \$0        20%    \$28.80    \$0

% Deviation    FIXED COSTS        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 B104 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%    \$800    \$0
-10%    \$900    \$0
0%    \$1.000    \$0
10%    \$1.100    \$0
20%    \$1.200    \$0

Deviation    NPV at Different Deviations from Base
from    Sales    Variable         Fixed
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

Range    0     0     0     0     0

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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
Deviation
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        \$0
Standard Deviation  = Sq Root of column H sum    \$0
Coefficient of Variation = Std Dev / Expected NPV    #DIV/0!

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

With the high CV, we must re-evaluate the project using a higher WACC, 13%.  That results in: