Lesson 2

Opportunity Cost of Capital

Opportunity Cost is the expected rate of return offered by alternative, equivalent (in time and risk) investments in financial markets.

Opportunity Cost Image

Interests

Simple Interest

Simple Interest Image

Student borrows €100 for five years at 5% per year simple interest.

Initial debt = €100

Year 0 = €100
Year 1 = Year 0 + (5% x €100) = €100 + €5 = €105
Year 2 = Year 1 + (5% x €100) = 105 + €5 = €110
Year 3 = Year 2 + (5% x €100) = 110 + €5 = €115
Year 4 = Year 3 + (5% x €100) = 115 + €5 = €120
Year 5 = Year 4 + (5% x €100) = 120 + €5 = €125

Final debt = €100 + (5 x 5) = €125

For simple interest, only the two following formulas are useful:

Debt at a specific year = Debt(Year - 1) + (Interest x Initial Debt)
Total debt = Initial debt + (N. of years x Interest)

Compound Interest

Compound Interest Image

Student borrows €100 for five years at 5% per year simple interest.

Initial debt = €100

Year 0 = €100
Year 1 = Year 0 + (5% x €100) = €100 + €5 = €105
Year 2 = Year 1 + (5% x Year 1) = 105 + €5.25 = €110.25
Year 3 = Year 2 + (5% x €Year 2) = 110.25 + €5.26 = €115.51
Year 4 = Year 3 + (5% x Year 3) = 115.51 + €5.263 = €120.773
Year 5 = Year 4 + (5% x Year 4) = 120.773 + €5.2632 = €126.04

Final debt = €126.04

The time value of money

€1 now is worth more than €1 in a years time.

Asset Value

An Asset is the sum of its Cash-Flows.

Each asset is defined by its cash flow (CF) stream

Asset Cash flow Image

Value of an asset = present value of its cash flows
Value of a firm = total value of its assets

Important characteristics of a cash flow

1. Time

€100 today vs. €100 next year

In general, the further in the future a payoff, the smaller its present value.

2. Risk

€100 with certainty vs. €200 or €0 with equal odds.

In general, people are risk-averse attribute lower value to uncertain outcomes.

Valuation of an investment

When making profit, manager can:

Re-invest: opportunity cost for shareholders
Paying out shareholders (dividend)

Project Present Value (PV) = discounting its future cash flows by its appropriate cost of capital

Summary

(1) An asset = cash flow stream, whose value is driven by timing and risk.
(2) Evaluating a business = valuation of its assets.
(3) Perfect and complete capital markets create consensus among shareholders as consumption and investment decisions can be separated. This is because it allows shareholders to allocate wealth over time as they like.
(4) Shareholder value maximisation (increasing number of shareholders) = objective of the financial manager.
(5) Present value (PV): Value of a cash flow is its expected value discounted at the opportunity cost of capital, which adjusts for both time and risk.

Classic