Advanced Investment Analysis §To download lecture notes, please click to : § then click,...

Advanced Investment Analysis

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Information for BSc and select Year Two’ notes

Reminder of last year’s lecture 1) Did I meet you last year ? 2) The logic of market comparison 3) Income approach

Income Approach or Investment Method The logic of capitalising future rental values to obtain the property

value is well-recognised by the property professionals :

• "...The basic principles of property value suggest the existence of a predictable relationship between income and value. Knowing that real estate is only one of many investment opportunities, the behaviour of buyers and sellers in other investment markets should give us a clue about the income/value relationship...If a plausible relationship between income and value can be estimated when only the income is known..."

This provides a certain logic in arriving the value of the property. At least it gives a guarantee that the income to be generated from the property will be able to compensate for the cost of owning the property.

This gives a clearer picture of the relationship of the different elements in the appraisal process.

For instance, if an investor has HK$100 and he invests all of this sum into project A, the opportunity cost for this decision is the likely return he could have achieved from projects B,C or D had he chosen to do so. So long as project A compensates him enough or opportunity cost is less than return from project A, the investment is a sound one. In the present value situation, the utility of immediate consumption is always greater than deferred consumption. Hence future value is less than present value.

The second reason is the age of inflation. Future value is always readily eroded by inflation in terms of purchasing power.

In fact, the PV factor formula can be analyzed from reverse in an investment angle. For instance, if we have HK$100 today and invest this sum into a regular investment giving a 10% return per annum.

In one year’s time, we will have HK$110 (since HK$100 x (1+10%) = HK$110). In this case, 10% is our required rate of return.

Now, let’s look at this from the future. If we are given an opportunity to receive HK$110 in one year’s time, how much are we prepare to pay for such opportunity ? Since we can earn 10% from a regular investment, we will use 10% as the discount rate to find the present value. As a result, the present value of HK$110 in a year’s time is :HK$110 x 1/(1+10%) = HK$100. This illustrates the fact that the discount rate and rate of return for investment are closely related. To a certain extent, we can even assert that they are the same.

When the value of the stream of incomes (I) is fixed within the holding period, the capital value (V) of the interest in property (hence the summation of the future incomes) during the holding period then becomes :

It is also obvious that when the holding period approaches infinity, the re-sale value of the asset approaches zero, hence it becomes relatively insignificant. In infinity, PV of the reversionary capital value approaches 0 such that formula becomes :

VPV

iI

1*

VI

i

Suppose a property whose rental income per annum is HK$ 20. This amount is fixed and unchanged forever. Assuming rental income is receivable at the end of each year, and our required rate of return for property is 20%, we’ll be able to find out the value of this property by formula. Since the property is for rental forever, there is no reversionary sale price, formula becomes :

Assume year 1000 is a proxy for eternity, the summation incomes is HK$100. This is obtained either through the serial calculation or just : HK$20/20% = HK$100.

$20

(

$20

(

$20

(....

$20

($100

1 20%) 1 20%) 1 20%) 1 20%)2 3 1000

In any case, we can prove that if we pay HK$100 today, and getting HK$20 per year, it is an investment with return of 20% p.a.( i.e. return or yield is equal to annual income divided by capital value). This exactly reflects what we require before the valuation process.

Now, let’s assume a more realistic situation that rental does grow as time goes by. Assuming a 12% rental growth per year due to an upsurge of demand for this kind of property,

$20

(

$22.

(

$25

(....

$20( .

($250

1 20%)

4

1 20%) 1 20%)

1 12%)

1 20%)2 3

1000

1000

If we are patient enough, we can try to add up all these together and V will turn out to be HK$ 250. In this case, the yield has dropped to : HK$20/HK$250 = 8% ! Superficially, it does not make sense. Logically, when there is an increase in demand leading to a rise in rental income, the rate of return should increase as well ! In fact, the opposite happens. This is the case even when we assume that the increase in rental value starts immediately so that it becomes :

$22.

(

$25

(

$28

(....

$20( .

($280

4

1 20%) 1 20%) 1 20%)

1 12%)

1 20%)2 3

1000

1000

In this case, V becomes HK$280 but yield remains 8% (i.e. HK$22.4/HK$280 = 0.08).

When there is future growth in the rental income, a new definition of yield is spinned off from the general concept of the rate of return.

In fact, in both cases, we are not getting less than 20% p.a. This is because in both cases, we are using 20%, the required

rate of return to discount future values. What is different is the initial yield we are getting. As the initial income of HK$20 or HK$22.4 represents the

initial rental level only with an implication that in the future, this level will go up at a rate of about 12% p.a.

As a result, we are willing to accept a yield initially lower than what we require in the understanding that the rental income we are getting from this property will go up in the future.

Since the definition of yield is always income divided by capital value.

When there is future growth in the rental level, the initial rental income is always lower than the future rental level.

Hence, the initial yield will be lower than the expected rate of return.

In addition, there is a hidden relationship in both cases. In these two cases, we have a required rate of return of 20% p.a. and a rental growth rate of 12% p.a.

When we deduct the rental growth rate from the rate of return, it becomes 8%, which is equal to the initial yield ! As a result, initial yield may be applied to future inflated income etc.

The traditional approach of investment method of valuation tends to rely on initial income and the market yield to carry out capitalisation process.

The market property yield, which is commonly derived from the relationship between the current open market rent and the current market value of similar properties, has itself carried an implication of future rental growth potential (or diminution).

This is because the open market rent at any time represents the maximum initial rental receivable.

Under most of the circumstances, rental value will vary with the economic environment and the property market sentiment.

If we take a very long span of time, say 50 years, rental value should have a positive growth rate per year, on average.

This is the point which most valuers will find puzzled when trying to adopt a suitable discount rate for future incomes. Traditional text books teach us that it is the market property yield that should be used in the capitalisation process, regardless of the implications of the future incomes.

A more reasonable in adopting the rate is to look at the potential movement of these future incomes.

If the capitalisation process takes into account of the current market rent only, then the current market yield should be used. Where we are capitalising a stream of fixed future values, the discount rate, taking into account of the expected rate of return, opportunity cost and the risk premium should be used.

Example 1:Mortgage Valuation using Investment

Model : ( could negative asset have been avoided in 1997 ?)

Case 1 : Taikoo Shing Tower TH 20/F825 sqft. With seaview

Sold in Dec, 1996 - HK$6.5mMarket rental estimated to be :$19,000/mth

Simulation of Mortgage Valuation by Investment Model of appraisal :

HK$19,000 x 12 months /market yield

= HK$228,000/5.2% (RV data in 1996)=HK$4.38m

Similar units sold for HK$3.8m (Dec. 2001 value)

Case 2 : South Horizons Tower X 20/F1078 sq.ft. With seaview




= HK$258,000/5.2% (RV data in 1996)=HK$4.96m


Case 3 : Kingswood Villa KW Court 20/F811 sq.ft.




= HK$78,000/5.2% (RV data in 1996)=HK$1.5m


Example 2 :Advise your client on the investment value

for the following real estate :120-124, Charter Road is a 4-storey

building for commercial/residential use held under single ownership by Mr. Rich. Each floor has an area of 240 sq.m. Ground floor is a retail shop Me-2. The first floor is used as office. The second floor is residential floor with two units of equal size. Mr. Rich occupies the top floor.

The tenancies are as follows :

-Ground Floor : Retail shop held under long lease with 15 years

to go at HK$650,000 p.a. with 3-yearly rent review. Current market OMR for similar shops is about HK$850,000 p.a. The next rent review is two years from now. Expected growth rate of rent is about 8% p.a. All risk yield for retail shops in the neighbourhood is about 6%.

-First floor :Divided into two units. Unit A (120 sq.m.

in gross floor area) is occupied by a trading company with 7 years to go with no rent review at HK$350,000 p.a. Current OMR is about HK$450,000. Expected growth rate of rent is about 6% p.a. All risk yield for offices in the neighbourhood is about 8%. Unit B is currently empty (120 sq.m.) and expected to be rented out in 6 months’ time

-2nd floor Wong’s Family on Flat A (120 sq.m. in

gross floor area) just moved in two days ago paying HK$ 220,000 p.a. The tenancy agreement contains normal rent review pattern. Dum’s Family next door (120 sq.m. in gross floor area) is having a long lease with 7 years unexpired. The lease contains no rent review. Dum’s Family is now paying HK$ 135,000 p.a. Expected growth rate of rent is about 5% p.a. All risk yield for residential in the neighbourhood is about 9%.

-3rd floor.Occupied by Mr. Rich

In this example, we have both the properties with vacant possession ready (unit B on the first floor and the whole of third floor), and properties with sitting tenants paying less than open market rent. When we apply investment appraisal to value this real estate, we will separate the treatment for these two kinds of interests.

First of all, we can always be able to find the value of a property if we have the initial annual rental income and the all risk yield of this class of property.

For properties with sitting tenant paying less than market rent, under the British appraisal system, we have the Term and Reversion Method.

Under this method, we separate the rental income into term income and reversionary income.

Term income refers to the income receivable during the contract term with the sitting tenant before the expiry date of the tenancy or the next rent review date.

Reversionary income refers to the rental income achievable in the open market when either the occupation right reverts back to the landlord for another tenant or when the landlord is free to set a new open market rent at rent review date.

G/F : Term : HK$650,000 x YP @6% 2 yrs. = HK$650,000 x 1

1

1 6%

6%

2

= HK$650,000 x 1.83 = HK$1,189,500.

Reversion : HK$850,000 x YP 6% in perpetuity x PV6% 2 yrs.

= HK$850,000 x 1

6% x

1

1 6%2

= HK$850,000 x 16.67 x 0.89= HK$ 12,610,855

Value : = HK$1,189,500 + HK$ 12,610,855= HK$13,800,355

1st /F : Unit A

Term : HK$350,000 x YP 8% 7 yrs. = HK$350,000 x 1

1

1 8%

8%

7

= HK$350,000 x 5.21 = HK$1,823,500


= HK$450,000 x 1

8% x

1

1 8%7

= HK$450,000 x 12.5 x 0.58= HK$ 3,262,500

Value : = HK$1,823,500 + HK$ 3,262,500= HK$5,086,000

1st /F : Unit BHK$450,000 x YP 8% in perpetuity x PV8% 0.5 yr

= HK$450,000 x 18% x

1

18%05 .

= HK$450,000 x 12.5 x 0.962Value : = HK$ 5,411,250

2nd /F : Unit AHK$220,000 x YP 9% in perpetuity

= HK$220,000 x 19%

= HK$220,000 x 11.11Value : = HK$ 2,444,200

2nd /F : Unit BTerm : HK$135,000 x YP 9% 7 yrs.

= HK$135,000 x 1

1

1 9%

9%

7

= HK$135,000 x 5.033 = HK$679,455


= HK$220,000 x 1

9% x

1

1 9%7

= HK$220,000 x 11.11 x 0.55= HK$ 1,344,310

Value : = HK$1,344,310 + HK$ 679,455= HK$2,023,765

3rd /F : HK$440,000 x YP 9% in perpetuity

= HK$440,000 x 1

9%= HK$440,000 x 11.11

Value : = HK$ 4,888,400

Total investment value of 120-124, Charter Road is : = HK$ 33,653,970

G/F :

Term : HK$650,000 x YP @14% 2 yrs. = HK$650,000 x 1

1

1 14%

14%

2

= HK$650,000 x 1.65 = HK$1,072,500.

Reversion : HK$850,000 x 1 8%2 x YP 6% in perpetuity x PV14% 2 yrs.

= HK$850,000 x 1.166 x 1

6% x

1

1 14%2

= HK$991,440 x 16.67 x 0.769= HK$ 14,819,274

Value : = HK$1,072,500 + HK$ 14,819,274= HK$15,891,774

1st /F : Unit A

Term : HK$350,000 x YP 14% 7 yrs. = HK$350,000 x 1

1

114%

14%

7

= HK$350,000 x 4.288 = HK$1,500,907

Reversion : HK$450,000 x 16%7 x YP 8% in perpetuity x PV14% 7 yrs.

= HK$450,000 x 1.5 x 18% x

1

114%7

= HK$675,000 x 12.5 x 0.4= HK$ 3,375,000

Total Value : = HK$1,500,907 + HK$ 3,375,000= HK$4,875,907

1st /F : Unit BHK$450,000 x YP 8% in perpetuity x PV8% 0.5 yr

= HK$450,000 x 1

8% x

1

1 8%0 5 .

= HK$450,000 x 12.5 x 0.962Value : = HK$ 5,411,250

2nd /F : Unit AHK$220,000 x YP 9% in perpetuity

= HK$220,000 x 1

9%= HK$220,000 x 11.11

Value : = HK$ 2,444,200

2nd /F : Unit BTerm : HK$135,000 x YP 14% 7 yrs.

= HK$135,000 x 1

1

1 14%

14%

7

= HK$135,000 x 3.75 = HK$506,250

Reversion : HK$220,000 x 1 5% x YP 9% in perpetuity x PV14% 7 yrs.

= HK$220,000 x 1.41 x 1

9% x

1

1 14%7

= HK$310,200 x 11.11 x 0.4= HK$ 1,378,529

Value : = HK$1,378,529 + HK$ 506,250= HK$1,884,779

3rd /F : HK$440,000 x YP 9% in perpetuity

= HK$440,000 x 1

9%= HK$440,000 x 11.11

Value : = HK$ 4,888,400

Total Value : = HK$ 35,396,310

The traditional wisdom of using the years’ purchase factor for both eternally receivable incomes and fixed period incomes therefore attracts the problem of this yield choosing criteria.

A relatively simple solution to this yield choosing problem is to turn to discounted cash flow model (D.C.F.) where only the discount rate for future values is to be used.

However, as with other financial analytical techniques, the D.C.F. model is itself not without drawbacks.

Criticisms have been raised by various authorities on different aspects of the model.

These cautious notes include the need to consider the relationship of risk as it applies to the discount rate as opposed to the capitalisation rate in the D.C.F. model, the lack of substantial proof that the use of D.C.F. model actually improves an investor’s performance and the reasonableness in setting the various assumptions in the D.C.F. model.

Nevertheless, compared to the conventional capitalisation process for varying incomes, the D.C.F. model can avoid the problem of defining and justifying the use of market yield in various stages of the valuation.

In a D.C.F. model, the discount rate is simply the required rate of return. What we need to focus on is the rate of compensation for future cash flows at different points of time in the future. Deriving from this, we may even have different discount rates for different stages of future incomes, depending on the risk premium required for each stage of the cash flow.

office property renting at HK$2088000 per year (3000 sq. ft.) (or HK$58/sq. ft.)rental expected to grow at 8% p.a. until six years later at 12% p.a.expected rate of return : 0.14Purchase Price : 45,000,000$ What is the NPV ?

Discounted Cash Flow (D.C.F.) Analysis :

Year rental Expenses Net Income YP P.V. Total 1 2,088,000$ 200,000$ 1,888,000$ 1 0.8771930 1,656,140$ 2 2,088,000$ 220,000$ 1,868,000$ 1 0.7694675 1,437,365$ 3 2,088,000$ 242,000$ 1,846,000$ 1 0.6749715 1,245,997$ 4 2,628,792$ 266,200$ 2,362,592$ 1 0.5920803 1,398,844$ 5 2,628,792$ 292,820$ 2,335,972$ 1 0.5193687 1,213,231$ 6 2,628,792$ 322,102$ 2,306,690$ 1 0.4555865 1,050,897$ 7 3,311,489$ 354,312$ 2,957,177$ 1 0.3996373 1,181,798$ 8 3,311,489$ 389,743$ 2,921,746$ 1 0.3505591 1,024,244$ 9 3,311,489$ 428,718$ 2,882,772$ 1 0.3075079 886,475$

10 4,652,311$ 471,590$ 4,180,722$ 1 0.2697438 1,127,724$ : : : : : : :: : : : : : :

80 11,574,793,556$ 372,436,403$ 11,202,357,153$ 1 0.0000280 313,994$ 81 11,574,793,556$ 409,680,043$ 11,165,113,513$ 1 0.0000246 274,518$ 82 16,261,427,467$ 450,648,047$ 15,810,779,420$ 1 0.0000216 341,001$ 83 16,261,427,467$ 495,712,852$ 15,765,714,615$ 1 0.0000189 298,271$ 84 16,261,427,467$ 545,284,137$ 15,716,143,330$ 1 0.0000166 260,819$

85+ 22,845,679,448$ 599,812,551$ 22,245,866,898$ 12.5 0.0000146 4,048,060$

Total Value : 58,954,626$ NPV : 13,954,626$

Investment appraisal based on D.C.F. Prime office building investment

Data : office GFA : 212500 sf.ft. (8500 sq.ft. / floor , and 25 storey high)OMR : $ 75.00 psf/monthcontract rent $ 55.00 psf/month next rent review : 2 years laterexpected holding period : 5 years market rent review pattern 3-yearlyexpected rate of return : 15%market yield : 8%expected growth rate : 7% p.a.management cost : 4.5 psf/month (rises by 8% p.a.)

D.C.F. analysis :PV factor

Year Rental cost net income @15% PV1 $ 140,250,000.0 $ 11,475,000.0 $ 128,775,000.0 0.869565 $ 111,978,260.92 $ 140,250,000.0 $ 12,393,000.0 $ 127,857,000.0 0.756144 $ 96,678,260.93 $ 218,962,125.0 $ 13,384,440.0 $ 205,577,685.0 0.657516 $ 135,170,664.94 $ 218,962,125.0 $ 14,455,195.2 $ 204,506,929.8 0.571753 $ 116,927,500.95 $ 218,962,125.0 $ 15,611,610.8 $ 203,350,514.2 0.497177 $ 101,101,144.8

6* $ 268,238,018.5 $ 16,860,539.7 $ 251,377,478.8 6.214709 $1,562,237,928.1Total : $2,124,093,760.3

* : sale price at the beginning of year 6 is equal to :OMR at year 6 divided by market yield (assumed to be 8% as well) but discounted for FIVE yearshence : $251,377,478.8 x (1/0.08 x 0.497177) = $1,562,237,928.1

Compared this with traditional approach of Term and Reversion :

Term income : $ 140,250,000.0 x YP @8% 2 years = $ 250,107,825.00

Reversion : $ 191,250,000.0 x YP @8%, PV 2 years $2,049,568,875.0

Total : $2,299,676,700.0

Furthermore, D.C.F. makes realistic assumption to the valuation, especially on the part of property finance.

If we accept that most property investments are carried out with property finance, or on a mortgage-backed system, the value of this real estate should in fact be composed of two elements in terms of property rights, namely the part that belongs to the equity investor and the part that belongs to the lender, or the bank. Hence, the value of real estate on a mortgage-equity situation will be equal to :

equitymortgage VVV

When we further break down these two components, we may see that the value of the mortgage is made up of the total discounted value of the debt service (i.e. total periodic loan repayments made) and the mortgage balance(residual amount of the mortgage loan at the point of re-sale); and the total discounted rental cash flow plus the net equity reversion (net sale proceed to the equity investor after deducting the mortgage balance) receivable at the point of re-sale. Hence :

)(4)(3)(2)(1 nerdsdrcfm VVVVV

Where : V1(m) = mortgaged value of the real estate

V2(drcf) = total discounted rental cashflow

V3(ds) = discounted values of total debt service or re-paid mortgage loan

V4(ner) = net equity reversion, or disposal value minus mortgage balance

Assuming a property will give the following schedule of incomes for the five-year holding period :

Year One HK$120,000 Year Two HK$120,000 Year Three HK$150,000 Year Four HK$150,000 Year Five HK$150,000

In addition to this expected cash flow, the investor expects an average annual capital growth rate of 5% per year. In using a 20% discount rate for his expected rate of return, he is taking out a mortgage from his banker at a mortgage rate of 11.75% p.a. or 0.98% per month for a maximum loan term of 25 years at 70% of the value of the property. He can utilize the above mortgage-equity model to estimate the value of this property by the following steps :

1) V1(m) - mortgaged value of the real estate = 0.7 x V

2) V2(drcf) - total discounted rental cashflow = $402,758.49

3) V3(ds) - discounted values of total debt service =

Mortgaged value times annual mortgage constant times YP factor @ investor’s discount rate :

%20%)201(

11

12

%)98.01(1

1

%98.07.0

5

300

)(1

xxxVxV ds

Hence :

We may notice that if we calculate the annual mortgage constant from the annual mortgage rate instead of the monthly rate, the constant would become 0.125.

VV

xxVxV

ds

ds

26.0

99.212426.07.0

)(1

)(1

V4(ner) - net equity reversion = disposal value minus mortgage balance

Where : mortgage balance at the point of re-sale = This is the ratio annual mortgage constant on the original term

of loan to the annual mortgage constant on the remaining term of loan at the point of re-sale, times the mortgaged value of the real estate :

VV

xVxV

xVxV

mb

mb

mb

67.0108.0

0104.07.0

%)98.01(1

1

%98.0

%)98.01(1

1

%98.07.0

)(

)(

240300

)(

Hence the value of this real estate is :

281.620,258,1$

49.758,402$32.0

49.758,402$068

24.026.049.758,402$7.0

)(4)(3)(2)(1

V

V

VV

VVVV

VVVVV nerdsdrcfm

This can be compared with a less complicated example below using a finance-explicit D.C.F. model incorporated with the above mortgage assumption. By this D.C.F. model, the financial market is more closely and easily linked to the property market.

The value of the property based on this D.C.F. model is assessed at $1,275,915.03. The apparent difference with the above figure of $1,258,620 is due to rounding problem in the computer calculation. We may further analyse the mechanism of this model by looking at the individual components of the model. Option (a) gives the same assumptions as above while option (b) shows that the model is easy to cope with variations in these assumptions. In option (b), rental variation is assumed to be downward adjusted after two years.

D.C.F. model of Valuation with Finance Option (a)mortgageratio :

70% rate of return:

20%

mortgagerate p.a. :

11.75% term of loan : 25 years

mortgagerate p.m. :

0.98% term of loan : 300 months

expected valuegrowth p.a. :

5%

Year mortgagebalance

Income p.a. resale income Mortgagerepayment p.a.

net income p.a. PV factor discountedincomes

1 $ 120,000.00 $ 110,906.42 $ 9,093.58 0.833333333 $ 7,577.982 $ 120,000.00 $ 110,906.42 $ 9,093.58 0.694444444 $6,314.983 $ 150,000.00 $ 110,906.42 $ 39,093.58 0.578703704 $ 22,623.604 $ 150,000.00 $ 110,906.42 $ 39,093.58 0.482253086 $ 18,853.005 $

852,832.12 $ 150,000.00 $

1,628,426.82 $ 110,906.42 $ 814,688.28 0.401877572 $ 327,404.95

plus :mortaged value : $ 893,140.52

property value : $1,275,915.03

D.C.F. model of Valuation with Finance Option (b)mortgageratio :

70% rate of return : 20%

mortgagerate p.a. :

11.75% term of loan : 25 years

mortgagerate p.m. :

0.98% term of loan : 300 months

expected valuegrowth p.a. :

5%

Year mortgagebalance

Income p.a. resale income Mortgage repaymentp.a.

net incomep.a.

PV factor discountedincomes

1$120,000.00

$84,723.36 $ 35,276.64 0.833333333 $ 29,397.20

2$120,000.00

$ 84,723.36 $ 35,276.64 0.694444444 $ 24,497.67

3 $ 85,000.00 $ 84,723.36 $ 276.64 0.578703704 $ 160.094 $ 85,000.00 $ 84,723.36 $ 276.64 0.482253086 $ 133.415

$651,493.38 $ 85,000.00 $1,243,983.74 $ 84,723.36

$592,767.010.401877572 $ 238,219.76

plus :mortagedvalue :

$682,285.67

propertyvalue :

$ 974,693.81

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