Finance

Created 7/1/1996
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Business Administration 130:

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)(r_m-r*_m)]/[(r_m-r*_m)²]
• r*_i = r*_f + beta_i(r*_m-r_f)
• 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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