Chapter 13: Valuation of investments

Question 1

Why will different investors use different valuation methods?

Answer 1

Different investors may used differing valuation methods depending upon:

• General aims and objectives of investment
• Reasons for valuing the asset
• Type of asset being values

Question 2

Why is it necessary to value individual assets?

Answer 2

Ability to value individual assets is crucial for:

• Identifying whether asset or asset class appears to be cheap or dear and hence should be include within portfolio
• Monitoring ongoing performance of asset to assess whether or not we should continue to hold it

Question 3

What is the role of the market value when valuing individual investments?

Answer 3

1. Valuing individual investments – the role of market value
   - Market value is reference point for all valuations – if asset is traded on open market and published prices are freely available
   - No market price then other methods used to determine best proxy for market value
   - After establishing market value or proxy on the valuation date, actuary may decide to employ alternative asset valuation method appropriate to purpose of the valuation – in particular adopting consistent methods for values of assets and liabilities
   - Often interested in relationship between value of fund’s assets and its liabilities -difficult to place market value on liabilities
   - New trend has been to use market value of assets or proxy for all purposes and then ensure equivalence by adopting market-consistent method of valuing liabilities
   - Methods of adjusting the asset valuation methods to fit with predetermined lability valuation basis have fallen out of favour as they mean that neither value of assets nor liabilities are related to observable data
   - Market-consistent method of valuing liabilities will involve determining market-consistent discount rate for discounting the liabilities
   - So, value of assets and liabilities will react in a similar way to changes in investment environment

Question 4

Discuss the market value as a valuation method.

Answer 4

Market value

• Market value of asset varies constantly – only known with certainty at date a transaction in asset takes place
• Even in open market more than one figure may be quoted at any time
• Objective and easily obtained figure (for many securities)
• Starting point for asset valuation
• Quoted securities generally have following prices:

 Bid price at which market makers prepared to buy

 Slightly higher offer price at which prepared to sell

 Mid-market value – an average of bid and offer prices

• Market values are generally:

 Fairly easily available

 Objective

 Well understood

• Possible problems with using market value:

 Volatility

o subject to wide fluctuations in short term which may not reflect changes in expected future proceeds from assets, thus

o may be different results from valuation depending on exact date

 Achieving consistency

o Volatility of market values makes it difficult to value liabilities in consistent manner, unless

o very closely matched in which case their values with vary correspondingly

 No quoted price

o Determining market value for quoted securities is straightforward

o Not true for unquoted investments – direct property investment

Question 5

Discuss the smoothed market value as a valuation method.

Answer 5

Smoothed market value
- Can be smoothed by taking some form of average over a specified period to remove daily fluctuations

• Use moving average so that value of asset on any day is taken as average of market price over, say, previous 3 months – way of obtaining smoothed mv
• This method does not lend itself to consistent liability valuations because appropriate discount rate for liability valuation is indeterminate and requires judgment
• May be judgement in:

 Length of smoothing period

 Whether average should be simple average of weighted average, with more weight on recent values

• Assessment becomes view as to whether asset is cheap or expensive in relation to its smoothed market value

Question 6

Discuss the smoothed market value as a valuation method.

Answer 6

Smoothed market value

• Can be smoothed by taking some form of average over a specified period to remove daily fluctuations
• Use moving average so that value of asset on any day is taken as average of market price over, say, previous 3 months – way of obtaining smoothed mv
• This method does not lend itself to consistent liability valuations because appropriate discount rate for liability valuation is indeterminate and requires judgment
• May be judgement in:

 Length of smoothing period

 Whether average should be simple average or weighted average, with more weight on recent values

• Assessment becomes view as to whether asset is cheap or expensive in relation to its smoothed market value

Question 7

Discuss the discounted cashflow as a valuation method.

Answer 7

Discounted cashflow

• This involves discounting expected future cashflows from an investment using long-term assumptions
• Values an asset as the PV of the expected income stream and capital from the assets
• E.g. discounted dividend model for equities and discounted rental income for property
• Has advantage of being easily made consistent with basis used to value investor’s liabilities
• Method used will be consistent if assets and liabilities are valued on discounted cashflow basis using same approach to determine discount rate
• Where portfolio of assets is held – weighted discount rate calculated reflecting proportions in each asset class
• This weighted discount rate can be used to value liabilities
• Relies on assessment of suitable discount rate which is straightforward where assets are high-quality fixed-interest stocks – less so otherwise
• If an investment has adverse features, it is normal to increase rate of interest used to discount cashflows
• By doing this as lower value is placed on more risky investments

Question 8

Discuss the stochastic model as a valuation method.

Answer 8

Stochastic model

• Extension of discounted cashflow method in which future cashflows, interest rate or both are treated as random variables
• Result is a distribution of values from which expected value and other statistics can be determined
• Appropriate in complicated cases where future cashflows are dependent on exercise of embedded options – liked option to wind up in adverse financial circumstances
• Advantages:

 Good for valuing derivatives

 Gives better picture of valuation – by giving distribution of results

 Consistency with liability valuation is achievable

• Disadvantages:

 May be too complex for many applications

 Results dependent on assumed distributions for the variables – assumptions may be subjective

Question 9

Discuss the arbitrage value as a valuation method.

Answer 9

Arbitrage value

• Means of obtaining proxy market value
• Calculated by replicating investment with combination of other investments and applying condition that in efficient market values must be equal
• Used in valuation of derivatives
• In other markets this is difficult or impossible to apply – difficult to replicate many assets

Question 10

Discuss the historic book value as a valuation method.

Answer 10

Historic book value

• Price originally paid for asset and often used for fixed assets in published accounts
• This method is:

 Objective

 Conservative (but only if value has risen since purchase)

 Well understood

 Used for some accounting purposes
- Book value has little merit – for most valuation purposes

Question 11

Discuss the historic book value as a valuation method.

Answer 11

Historic book value

• Price originally paid for asset and often used for fixed assets in published accounts
• This method is:

 Objective

 Conservative (but only if value has risen since purchase)

 Well understood

 Used for some accounting purposes

• Book value has little merit – for most valuation purposes

Question 12

How do market values compare with calculated values?

Answer 12

Market values compared with calculated values

• Modern finance theory suggests that where efficient market exists resulting market value will reflect all publicly available information and,
• is the underlying economic value of asset at a given point in time
• Advantages:

 Objective

 Realistic as realisable value on sale (assuming bid price used)

 Easy -doesn’t require calculation

 Well understood and accepted

 Can be used as comparison to other valuation methods to see if asset is over- or under-priced

• Disadvantages:

 May not be readily obtainable – unquoted instruments

 Volatile – values may fluctuate greatly even in short term

 May not reflect value of future proceeds

 Decision required about whether bid, mid or offer prices should be used

 Difficult to ensure consistency of basis with that of liability valuation

 Value reflects position of marginal investor rather than the individual

 May not be realisable value on sale

• Can be subject to considerable fluctuation
• Argued that use of market value depends on vagaries of the market and obscures underlying or intrinsic value of the asset
• Counter argument is using another valuation method to try identifying intrinsic worth of asset involves investment call as to the direction the market in that asset will move
• In practice other factors would be taken into account before making buying or selling decisions:

 Nature, term, certainty and currency of investor’s liabilities

 Investor’s tax position

 Investor’s risk appetite
 Regulatory restrictions

 Dealing costs

 Temporary inefficiencies in the market

• If market value not used, then it is important to make implications of this clear to client
• E.g. if discounted cashflow approach used then the client needs to be aware that this is not necessarily value that would be obtained on sale of assets
• Particularly true when short-term solvency is being considered
• E.g. discounted value may make it appear that client is solvent but if assets were realized at their market value, they would be insufficient to cover cost of liabilities

Question 13

How do market values compare with calculated values?

Answer 13

Market values compared with calculated values

• Modern finance theory suggests that where efficient market exists resulting market value will reflect all publicly available information and,
• is the underlying economic value of asset at a given point in time
• Advantages:

 Objective

 Realistic as realisable value on sale (assuming bid price used)

 Easy -doesn’t require calculation

 Well understood and accepted

 Can be used as comparison to other valuation methods to see if asset is over- or under-priced

• Disadvantages:

 May not be readily obtainable – unquoted instruments

 Volatile – values may fluctuate greatly even in short term

 May not reflect value of future proceeds

 Decision required about whether bid, mid or offer prices should be used

 Difficult to ensure consistency of basis with that of liability valuation

 Value reflects position of marginal investor rather than the individual

 May not be realisable value on sale

• Can be subject to considerable fluctuation
• Argued that use of market value depends on vagaries of the market and obscures underlying or intrinsic value of the asset
• Counter argument is using another valuation method to try identifying intrinsic worth of asset involves investment call as to the direction the market in that asset will move
• In practice other factors would be taken into account before making buying or selling decisions:

 Nature, term, certainty and currency of investor’s liabilities

 Investor’s tax position

 Investor’s risk appetite

 Regulatory restrictions

 Dealing costs

 Temporary inefficiencies in the market

• If market value not used, then it is important to make implications of this clear to client
• E.g. if discounted cashflow approach used then the client needs to be aware that this is not necessarily value that would be obtained on sale of assets
• Particularly true when short-term solvency is being considered
• E.g. discounted value may make it appear that client is solvent but if assets were realized at their market value, they would be insufficient to cover cost of liabilities

Question 14

How are equities valued?

Answer 14

1. Market value
2. Dividend discount model
3. Net asset value per share
4. Value added measures
5. Other equity valuation methods

Question 15

How are equities valued? - Market value

Answer 15

Market value

• Starting point for valuation of an equity – if there is a suitable market
• Simple and objective means of valuation – for most shares

Question 16

How are equities valued? - Dividend discount model

Answer 16

Dividend discount model

• Discounted cashflow calculation can be carried out to value shares, if investors want to:

 Value unlisted shares

 Check whether market value is reasonable or under- or over-priced

• DDM derives the value of a share as the discounted value of the estimated future dividend stream
• Close attention paid to assumptions used in order to appreciate limitations of DDM

General Model:

• V = SUM(from t=1 to infinity) Dt*v(t)
• Where:

 V is the value of the share

 Dt is the gross amount of the t-th dividend payment

 v(t) is the discounted factor applied between time 0 and time of the t-th dividend payment

Simplified model

• A simplified equation obtained by assuming:

 Dividends are payable annually, with next payment in one year’s time

 Dividends grow at a constant rate, g, per annum

 The required rate of return, i, is independent of the time at which payments are received

 i > g

 i and g are defined consistently – e.g. both include inflation or are net of inflation

 dividend proceeds can be reinvested at i p.a.

 not tax and expenses

 shares are held forever

• The equation is then:

V=Do(1+g)/(i-g)

• Where Do is the most recent dividend received

Question 17

What are some of the issues that need to be considered when

Answer 17

Issues to be considered when applying the simplified model

1. Do not know the value of i to use in the model

 Assumption of constant required rate of return i over time might not be appropriate when yield curve is steeply sloping upwards or downwards

 To calculate a value necessary to decide on appropriate required rate of return

 Often calculated as yield on long-term government bonds plus appropriate addition for riskiness of income stream

 Require higher return from equities than from government bonds to compensate for the:

• Risk of dividends being reduced or even not paid and loss of capital on wind up
• Uncertainty or return and volatility of share price
• Lower marketability and higher dealing costs
  2. Do not know what the growth rate g should be

 Investors with real liabilities might start from an index-linked government bond yield and estimate the real (rather than nominal) rate of dividend growth

 Value g used will reflect the investor’s estimates of the future dividend growth of the company

 This in turn will reflect investor’s view of the company’s future profitability

 Constant dividend growth might not be realistic assumption in practice

 Alternative approach would be to use dividends based on profit forecasts for first few years,

 then apply a short-term rate of growth for a period until growth rates settled down to long-term average

3. Results obtained are very sensitive to assumed level of i-g
4. The equation ignores tax

 tax-paying investors should use net dividends received and suitable after-tax rate of return

 also ignores expenses

5. Model assumes annual dividend payments even though payments might be half-yearly on individual shares
6. Model is of no use unless i > g

Question 18

What are some of the issues that need to be considered when using the simplified DDM?

Answer 18

Issues to be considered when applying the simplified model

1. Do not know the value of i to use in the model

 Assumption of constant required rate of return i over time might not be appropriate when yield curve is steeply sloping upwards or downwards

 To calculate a value necessary to decide on appropriate required rate of return

 Often calculated as yield on long-term government bonds plus appropriate addition for riskiness of income stream

 Require higher return from equities than from government bonds to compensate for the:

• Risk of dividends being reduced or even not paid and loss of capital on wind up
• Uncertainty or return and volatility of share price
• Lower marketability and higher dealing costs
  2. Do not know what the growth rate g should be

 Investors with real liabilities might start from an index-linked government bond yield and estimate the real (rather than nominal) rate of dividend growth

 Value g used will reflect the investor’s estimates of the future dividend growth of the company

 This in turn will reflect investor’s view of the company’s future profitability

 Constant dividend growth might not be realistic assumption in practice

 Alternative approach would be to use dividends based on profit forecasts for first few years,

 then apply a short-term rate of growth for a period until growth rates settled down to long-term average

3. Results obtained are very sensitive to assumed level of i-g
4. The equation ignores tax

 tax-paying investors should use net dividends received and suitable after-tax rate of return

 also ignores expenses

5. Model assumes annual dividend payments even though payments might be half-yearly on individual shares
6. Model is of no use unless i > g

Question 19

How are equities valued? - Net asset value per share

Answer 19

Net asset value per share

• Adopted for companies with significant tangible assets
• Similar approach adopted to shares of property investment company – valued as sum of value of building and land that it owns less liabilities
• Approach would not give realistic value for companies whose value comprises of intangible assets
• Might be used to value an investment trust company where underlying assets may have valuations in their own rights
• Investment trusts comprise several holdings in other assets – although investment trust itself is a company
• Shares of an investment trust will trade at price set by market following principles of supply and demand and shareholder perceptions of risk and future of company
• Possible to determine market price or proxy for each shareholding in the investment trust
• These can be aggregated and divided by number of shares in issue to give a NAV per share
• This is what investor would receive less expenses – if wound up, all assets sold, and proceeds distributed to shareholders
• Investment trusts frequently quoted as the market price being at % premium or discount to NAV

Question 20

How are equities valued? - Other equity valuation methods

Answer 20

Other equity valuation methods

• Where companies are not making profits and NAV is not appropriate other methods have to be used if a calculated valuation is required
• Methods already discussed implicitly assume at least one:

 Company is declaring dividends

 Making profits

 NAV is suitable

• Not always the case
• Methods often involve determining a relevant and measurable key factor for company’s business
• Relationship between this factor and market price of other quoted companies is used as basis for valuation
• Factor used will depend on business of company
• Will also depend up exactly what info in available
• May be either qualitative or quantitative

Question 21

How are equities valued? - Other equity valuation methods

Answer 21

Other equity valuation methods

• Where companies are not making profits and NAV is not appropriate other methods have to be used if a calculated valuation is required
• Methods already discussed implicitly assume at least one:

 Company is declaring dividends

 Making profits

 NAV is suitable

• Not always the case
• Methods often involve determining a relevant and measurable key factor for company’s business
• Relationship between this factor and market price of other quoted companies is used as basis for valuation
• Factor used will depend on business of company
• Will also depend up exactly what info is available
• May be either qualitative or quantitative

Question 22

How is property valued?

Answer 22

Property valuations

• True market value is only known when there is transaction that equates willing buyer with willing seller
• Indications of value can be taken from similar recent transactions, but uniqueness of each property means that skill is needed to assess property market values
• Such valuations regarded as valuer’s opinion rather than fact
• Property can be valued using explicit discounted cashflow approach – but now more common to use market-consistent valuation of liabilities
• Cashflows discounted should be net of all outgoings and make explicit allowance for expected rental increases
• Property rental increases are stepped (equity dividend growth smooth) – level for a period and then step changes to new level
• Allowance needs to be made if passing rent is different from current open market rental value
• Current rent level will be valued to next rent review and after the open market rental value is valued
• When current rent > than open market rental value (over rented property) then necessary to know whether terms of lease allow downward rent reviews

Question 23

How are is property valued? - Discounted cashflow formula

Answer 23

Discounted cashflow formula

• Consider freehold property that is let on commercial lease
• Can value this by applying discounted cashflow approach, assume for simplicity:

 Rents payable in perpetuity

 Rents quoted are net of expenses and tax

 Rents quoted are net of any costs of modernising or refurbishing property

• Discounted rate used depends on riskiness of investment
• Could be based on yield on bond of suitable term + margins for factors such as risk and lack of marketability

Question 24

How is the variability of asset prices allowed for when valueing assets?

Answer 24

Allowing for the variability of asset prices

• Volatility of asset value is often the main problem with market value of assets
• Arguable that stability is not a desirable feature of asset valuation and consistency overrides stability
• Volatility of asset value not a problem in itself – volatile asset value may correctly reflect underlying reality
• But comparing volatile asset values with value of liabilities calculated using stable interest rate is potentially misleading
• Thus, the problem with a market value of assets is not the volatility of asset valuation but inconsistency of asset and liability valuation bases
• Key aim: create consistent approach to the valuation of assets and liabilities so that appropriate conclusion can be drawn
• Stability can be desirable feature of valuation in some situations
• Unstable value of assets may make results harder to communicate and interpret
• May be difficult in practice to establish a market-consistent value of liabilities
• Solution is to modify the method of valuing assets to make value more stable and hence more consistent with value of liabilities calculated using stable assumptions
• Smoothed market value is often seen as solution to problem with market values
• Smoothing, however, does create major problem
• Very hard to know what should be taken as consistent rate of interest for the purpose of valuing liabilities