Aswath Damodaran

Aswath Damodaran!

1!

Approaches to Valuation!

Intrinsic valuation, relates the value of an asset to the present value of expected future cashﬂows on that asset. In its most common form, this takes the form of a discounted cash ﬂow valuation.

Relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable like earnings, cashﬂows, book value or sales.

Contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics.

Aswath Damodaran!

2!

I. Discounted Cash Flow Valuation!

What is it: In discounted cash ﬂow valuation, the value of an asset is the present value of the expected cash ﬂows on the asset.

Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash ﬂows, growth and risk.

Information Needed: To use discounted cash ﬂow valuation, you need

• to estimate the life of the asset

• to estimate the cash ﬂows during the life of the asset

• to estimate the discount rate to apply to these cash ﬂows to get present value

Market Inefﬁciency: Markets are assumed to make mistakes in pricing assets across time, and are assumed to correct themselves over time, as new information comes out about assets.

3!

Aswath Damodaran!

Risk Adjusted Value: Three Basic Propositions

The value of an asset is the present value of the expected cash ﬂows on that asset, over its expected life:

Proposition 1: If “it” does not affect the cash ﬂows or alter risk (thus changing discount rates), “it” cannot affect value.

Proposition 2: For an asset to have value, the expected cash ﬂows have to be positive some time over the life of the asset.

Proposition 3: Assets that generate cash ﬂows early in their life will be worth more than assets that generate cash ﬂows later; the latter may however have greater growth and higher cash ﬂows to compensate.

Aswath Damodaran! 4!

Let’s start simple: Valuing a default-free bond !

The value of a default free bond can be computed as the present value of the coupons and the face value, discounted back to today at the risk free rate.

Thus, the value of ﬁve-year US treasury bond (assuming that the US treasury is default free) with a coupon rate of 5.50%, annual coupons and a market interest rate of 5.00% can be computed as follows:

Value of bond = PV of coupons of $55 each year for 5 years @ 5% + PV of $1000 at the end of year 5 @5% = $1021.64

The value of this bond will increase (decrease) as interest rates decrease (increase) and the sensitivity of the bond value to interest rate changes is measured with the duration of the bond.

Aswath Damodaran!

5!

A little messier: Valuing a bond with default risk !

When valuing a bond with default risk, there are two ways in which you can approach the problem.

In the more conventional approach, you discount the promised coupons back at a “default-risk” adjusted discount rate. Thus, if you have a ten-year corporate bond, with an annual coupon of 4% and the interest rate (with default risk embedded in it) of 5%, the value of the bond can be written as follows:

t=10

Price of bond =

∑

t=1

40 1,000 + = $922.78 (1.05)t (1.05)10

You can also value this bond, by adjusting the coupons for the likelihood of default (making them expected cash ﬂows) and discounting back at a risk free rate.

Aswath Damodaran! 6!

Valuing Equity !

Equity represents a residual cashﬂow rather than a promised cashﬂow.

You can value equity in one of two ways:

• By discounting cashﬂows to equity at the cost of equity to arrive at the value of equity directly.

• By discounting cashﬂows to the ﬁrm at the cost of...