PArT 2: VALUATION, rISk AND reTUrN

the block, paying taxes and covering other expenses. If the landlord wants to sell the apartment block,

what price should he expect to receive? According to our fundamental valuation principle here, the

price should equal the present value of all future net cash flows. Investors value financial assets such

as bonds and shares in much the same way. First, they estimate how much cash a particular investment

distributes over time. Second, investors discount the expected cash payments using the time value of

money mathematics covered in Chapter 3. The investment’s value, or its current market price, equals the

present value of its future cash flows.

This implies that pricing an asset requires knowledge of its future benefits, the time horizon over

which those benefits will occur, and the appropriate discount rate that converts future benefits into a

present value. For some assets, investors know with a high degree of certainty what the future benefit

stream will be. For other investments, the future benefit stream is much harder to predict. Generally, the

greater the risk or uncertainty surrounding an asset’s future benefits, the higher the discount rate investors will

apply when discounting those benefits to the present.

Consequently, the valuation process links an asset’s future benefits and the risk surrounding those

benefits to determine its price. Holding future benefits (cash flows) constant, an inverse relationship exists

between risk and value. If two investments promise identical cash flows in the future, investors will pay a

higher price for the one with the more credible (less risky) promise. Or, to state that relationship another

way, if a risky asset and a safe asset trade at the same price, the risky asset must offer investors higher future

returns.

4 -1a THe FUNDAMeNTAL VALUATION MODeL

Chapters 6 and 7 present an in-depth analysis of the relationship between risk and return. For now, take

as given the market’s required rate of return, which is the rate of return that investors expect or require a

specific investment to earn, given its risk. The riskier the asset, the higher will be the return required

by investors in the marketplace. We can also say that the required rate of return on an asset is the

return available in the market on another equally risky investment. When someone purchases a specific

investment, he or she loses the opportunity to invest their money in another asset. The forgone return on

the alternative investment represents an opportunity cost.

How do investors use this required rate of return to determine the prices of different types of

securities? Equation 4.1 expresses the fundamental valuation model mathematically:

Eq. 4.1 P (^01122)
11 1

CF
r
CF
r
CF
r
n
()+ +()+ + ⋅⋅⋅⋅+()+ n
In this equation, P 0 represents the asset’s price today (at time 0), CFt represents the asset’s
expected cash flow at time t, and r is the required return – the discount rate that reflects the asset’s
risk. Equation 4.1 establishes a price that accounts for the asset’s cash flows and the risk associated
with those cash flows. The letter n stands for the asset’s life, the period over which it distributes cash
flows to investors, usually measured in years. As you will see, n may be a finite number, as in the case
of a bond that matures in a certain number of years; or it may be infinite, as in the case of an ordinary
share with an indefinite life span. In either case, this equation provides us with a vehicle for valuing
almost any type of asset.
LO4.1
required rate of return
The rate of return that investors
expect or require an investment
to earn given its risk
Todd Richter, Managing
Director, Head of equity
Healthcare Research, Bank
of America Securities
‘The concepts of value,
the things that drive
value, don’t change.’
See the entire interview on
the CourseMate website.
COUrSeMATe
SMArT VIDeO