# Finance

Created 7/1/1996
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### Where Do Cash Flows Come From?

Basics:

• Present value of a perpetuity: C/r
• Present value of a growing (or shrinking) perpetuity: C/(r-g)
• Present value of C dollars t years from now: C/[(1+r)t]
• Present value of a C-dollar t-year annuity: C[(1/r)-(1/[r(1+r)t])
• "Rule of 72": (1+r)t = 2 (approximately) whenever rt=.72
• beta = [E((r1-r*1)(rm-r*m)]/[(rm-r*m)2]
• r*i = r*f + betai(r*m-rf)
• Expected return of a portfolio with N securities, a share 1/N invested in each security:
• Standard deviation of a portfolio with N securities, a share 1/N invested in each security:

Exam:

Not good at knowing when your calculator has betrayed you; little sense of what answer should be. Little sense of the relationship between variance of securities, variance of portfolios, and betas...

No Black Boxes:

A black box is something that we accept and use but do not understand. We have been treating capital porjects as black boxes--but a good financial manager should never accept black boxes.

• Primarily because looking inside the black box may suggest some way--some cheap, easy, and valuable way--to resolve uncertainty.

Techniques for project analysis:

• Sensitivity analysis
• Break-even analysis
• Monte-Carlo simulation
• Decision trees

Sensitivity Analysis:

An electric car project:

 Year 0 Years 1-10 Investment - \$150 Revenue \$375 Variable Cost -\$300 Fixed Cost -\$30 Depreciation -\$15 Pretax Profit \$30 Tax - \$15 Net Profit \$15 Operating Cash Flow \$30 Net Cash Flow -\$150 \$30

Assuming that the investment is depreciated straight-line over ten years, and that corporate income is taxed at a rate of 50%.

With a 10% opportunity cost of capital, NPV = -150 +sum(i=1 to 10, \$30/((1.10)t)) = +\$34.3. Should you invest? The right answer is that you should make your forecasting staff do more work:

 Variable Pessimistic Expected Optimistic Market size +\$11 +\$34 +\$57 Market share -\$104 +\$34 +\$173 Unit price -\$42 \$34 +\$50 Unit variable cost -\$150 +\$34 +\$111 Fixed cost +\$4 +\$34 +\$65

The project is by no means a sure thing--if you can find information to improve your forecasts of unit variable costs and of market share, you should do so.

Limits to sensitivity analysis: what does "optimistic" mean?

What if variables are interrelated? Scenarios. Different consistent combinations.

Break-Even Analysis

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