Chapter 3: The Valuation Principle: The Foundation of Financial Decision Making¶

Cost-Benefit Analysis¶

Makes decisions on behalf of the firm’s investors.
A decision is good if the value of benefits exceeds the cost.
Real-world decisions require interdisciplinary input (e.g., marketing, economics, operations).

Convert all benefits and costs into a common unit (usually dollars).
Example:
- Trade 600 oz silver at $20/oz = $12,000 cost
- Receive 10 oz gold at $1500/oz = $15,000 benefit
- Net Value = $15,000 − $12,000 = **$3,000** → Accept

Identical goods in competitive markets must have the same price.
Arbitrage: Buy low, sell high without risk.
No Arbitrage Principle: Markets adjust prices to eliminate arbitrage opportunities.

Future Value: FV = C × (1 + r)^n
Present Value: PV = C / (1 + r)^n
Discount Factor: 1 / (1 + r)^n

PV of $1.6B = $1.6B / 1.08 = $1.481B
Cost of Delay = $2B - $1.481B = $519M

→ Launch now to avoid losing $519M

Future Value of a Cash Flow

FV = C × (1 + r)^n

To calculate the value of a future cash flow at an earlier point in time, we must discount it.

PV = C / (1 + r)^n

PV = 15,000 / (1.06)^10 = $8,375.92

→ Bond is worth much less today due to TVM (Time Value of Money)

Valuation Principle: Use market prices to evaluate decisions.
Cost-Benefit Analysis: Accept projects where benefits > costs.
Competitive Market: Identical goods sell at the same price.
Law of One Price: No identical goods can have different prices in the same market.
Arbitrage: Risk-free profit opportunity from price differences.
No Arbitrage Principle: Arbitrage opportunities are eliminated by market forces.
Interest Rate (r): Cost of borrowing or reward for saving.
Interest Rate Factor (1 + r): Converts dollars across time.
Present Value (PV): Today's value of future cash.
Future Value (FV): Future worth of money today.
Discount Factor: Value today of $1 received later: 1 / (1 + r)^n
Timeline: Tool to visualize when cash flows occur.