1 Lecture Notes Lecture Four (updated: 16 Oct. 2007) FINA 521 INVESTMENT APPRAISAL

1

Lecture Notes

Lecture Four(updated: 16 Oct. 2007)

FINA 521 INVESTMENT APPRAISAL

2

Integration of Movements in

Prices, Inflation, Exchange

Rates and Interest Rates

3

1. Nominal Prices (Current prices)

P1t,P2

t, P3t……….. Pn

t

2. Price Level PL

t = in (Pi

t Wi)

Where: i = Individual good or service included in the market basket

Pit = Price of the good or service (i) at a point in time (t)

Wi = Weight given to the price of a particular good or service (i); where wi = 1

Note: it is generally useful to express the price level of a basket of goods and services at a specific point in time in terms of a price index (P )

P = P / P

Where P = Price level in period (t)

P = Price level for the base period (B)

tI

tL

tL

BL

tI

BL

4

3. Changes in Price Level (Inflation)

• Measured in terms of a price index:

gPeI = ((Pt

I - PIt-1)/(PI

t-1)) * 100

4. Real PricesPt

iR = Pti / Pt

I

Where Pti = nominal price of good or service (i) as of a point in time

(t) Pt

I = Price level index at time period (t)

5. Changes in Real Prices

Change in PtiR =

tiRP - P

t-1

iR

t-1iR

P

PtiR = Real price of good ( i ) as of a specific period

5

Example 1: Nominal Prices and Changes in Price levelAssume Year 1 is base year

Goods 1 2 3Weights 0.2 0.5 0.3

Nominal Prices Year 1: P11 =30 P2

1=100 P31=50

P L1 =0.2(30)+0.5(100)+0.3 (50)

P L1 =71

P LB= 71

Price Index P I1 =1.00


2=110 P32=40

PL2 =0.2(40)+0.5(110)+0.3(40)=

P L2 =75

P LB= 71


6

Example 1:Nominal Prices and Changes in Price Level (cont’d)

Assume Year 1 is base yearGoods 1 2 3Weights 0.2 0.5 0.3


3=108 P33=60

P L3 =0.2(35)+0.5(108)+0.3 (60)

P L3 =79


INFLATION RATE • Changes in Price Level : Measured in terms of a price index

gP I2 = ((P I

2 - P I1 )/(P I

1 )) * 100=((1.056-1.00)/1.00))*100=5.63%

gP I3 = ((P I

3 - P I2 )/(P I

2 )) * 100=((1.113-1.056)/1.056)*100=5.33%

7

EXAMPLE 2: Real Prices and Changes in Real PricesReal Prices and Changes in Real Prices Goods 1 2 3Weights 0.2 0.5 0.3


1=100 P31=50

Price Index P I1 =1

Real Prices Year 1: P1R1=30/1 P2R

1=100/1 P3R1=50/1

P1R1=30 P2R

1=100 P3R1=50


2=110 P32=40


Real Prices Year 2: P1R2=40/1.056 P2R

2=110/1.056 P3R

2=40/1.056

P1R2=37.87 P2R

2=104.13 P3R2=37.87

8

EXAMPLE 2: Real Prices and Changes in Real Prices (Cont’d)

Goods 1 2 3Weights 0.2 0.5 0.3


3=108 P33=60


Real Prices Year 3: P1R3=35/1.113 P2R

3=108/1.113 P3R3=60/1.113

P1R3=31.46 P2R

3=97.06 P3R3=53.92

Changes in Real Prices Year 2

Change in P1R2 = P1R

2 – P1R1 / (P1R

1) = ((37.80-30)/30) ( (104.13-100)/100)

((37.80-50)/50)=0.26 =0.04 =-0.24

Changes in Real Prices in Year 3

Change in P1R3 = P1R3 - P1R2 / (P1R2 ) = ((31.46-37.87)/37.87) ((97.06-104.13)/104.13) ((53.92-37.87)/37.87)

=- 0.17 =- 0.07 =0.42

9

6. Inflation Adjusted Values

= Pti*(1 + gPt

iR)*(1 + gPeI)

7. Constant Prices• Fixed set of prices at a given year t0

P = P ; P = P

Not a useful concept to use in project evaluation

t+ni

toi

t+nk

tok

t+ni

toi

t+nk

tok

= assumed growth in price level index from year t to t+1

t+1i

ti

gPtiR

eI

= estimated nominal price of good i in year t+1

= nominal price of good i in year t

= estimated growth in real price of good i

gP

P

P

t+1

i

P

= assumed growth in price level index from year t to t+1

t+1i

ti

gPtiR

eI

= estimated nominal price of good i in year t+1

= nominal price of good i in year t

= estimated growth in real price of good i

gP

P

P

t+1

i

P

t+1

i

P

10

Example: Telephone charges over time: Satellite Project

Due to changes in Technology and Deregulation real price of telephone calls are falling at 8% per year

(1) Price in year 1 for Domestic Communication = $0.033 /minute

(2) Real decrease in tariffs -8.00% -8.00% -8.00% -8.00% -8.00% -8.00%

(3) Index of real telephone charges 1.00 0.92 0.85 0.78 0.72 0.66

(4) Rate of Inflation 3.00% 3.00% 3.00% 3.00% 3.00% 3.00%

(5) General Price Index 1.00 1.03 1.06 1.09 1.13 1.16

(6) Index of inflation adjusted prices 1.00 0.95 0.90 0.85 0.81 0.76

(7) Expected real price per minute (US$) (row 1 * row 3)

$0.033 $0.030 $0.028 $0.026 $0.024 $0.022

(8) Expected nominal price per minute (US$) (row 1 * row 6)

$0.033 $0.031 $0.030 $0.028 $0.027 $0.025

11

7. Constant Prices• Fixed set of prices at a given year t0

P = P ; P = P

Not a useful concept to use in project evaluation

t+ni

t+nk

tok

t+ni

toi

t+nk

tok

12

Integrated Financial Analysis of Investments

• The market exchange rate is the current price of foreign exchange. The market rate between the domestic currency and the foreign currency can be expressed at a point in time (t) as: E = (#D/F)t

• If the price index for the domestic currency’s economy is I at the time t, and the price index for the foreign currency’s country is l , then the real exchange rate (E ) at that point in time can be expressed as:

E = (#D/F)t * (l / l )

E = E * (l / l ) E = E * (l / l )

Mt

Dt

Rt

Ft

Dt

Ft

Rt

Rt

Mt

Ft

Dt

Mt

Rt

Dt

Ft

• The market exchange rate is the current price of foreign exchange. The market rate between the domestic currency and the foreign currency can be expressed at a point in time (t) as: E = (#D/F)t

• If the price index for the domestic currency’s economy is I at the time t, and the price index for the foreign currency’s country is l , then the real exchange rate (E ) at that point in time can be expressed as:

E = (#D/F)t * (l / l )

E = E * (l / l ) E = E * (l / l )

Mt

Dt

Rt

Ft

Dt

Ft

Rt

Rt

Mt

Ft

Dt

Mt

Rt

Dt

Ft

13

EtM = 8 Rand / $US

ItD = 1.0

ItUS = 1.0

I 1.0Et

R = E = 8.0 = 8.0 Rand/$I 1.0

Example

Mt

USt

Dt

• Initial year prices indexes in both countries assumed in project analysis to be equal to 1.0.

14

Real effective Exchange Rates IF/IDItaly

Real effective Exchange Rates IF/IDFrance

Real effective Exchange Rates IF/IDGermany

Real Effective Exchange Rates of Euro

0.000

0.850

0.900

0.950

1.000

1.050

1999 2000 2001 2002 2003 2004

~~

FranceGermany

Italy

15

Integrated Financial Analysis of Investments• We can derive the market exchange rate in period t+n, E , that

is required given that the projected real exchange rate as in period t+n is (E ), and given the movement in the price levelsof the two countries between period t and t+n. It is expressed as:

lE = E

lor

( 1 + gP )iE = E (l /l )

( 1 + gP )i

• When there is uncertainty as to the timing of changes in the real exchange rate, the market exchange rate in period t+n can be expressed as:

lE = ( 1 + K ) * E

l

Where K is a random variable with a mean of 0

Mt+n

Rt+n

Mt+n

Rt+n

Mt+n

Rt+n

Ft

Dt F

Lt+i

ni=1

Dt+n

Ft+n

Rt+n

Dt+n

DLt+i

Mt+n F

t+n

Mt+n

Rt+n

Mt+n

Rt+n

Mt+n

Rt+n

Ft

Dt F

Lt+i

ni=1

Dt+n

Ft+n

Rt+n

Dt+n

DLt+i

Mt+n F

t+n

Where K is a random variable with a mean of zero

16

If gPf = 2%/p.a. Foreign rate of inflation

If gPd = 8%/p.a. Domestic rate of inflation

Idt+5

= 1 (1.08)5 = 1.47

Ift+5

= 1 (1.02)5 = 1.10

ERt+5 = 8 Rand/$

Therefore, if then:

EMt+5

= Rand/$US

Suppose that in the current year:Domestic Price Index = 1 and Foreign Price Index = 1

Therefore, in Year 0, E0M = E0

R. Suppose E0M is 8 Rand/$US and

the real exchange rate is also 8 Rand/$US. The real exchange rate remains constant.

10.65 (1.10) (1.47) 8.0

цж d

ччччч

шззззз

и

ґ f5tI

5tI R

5tEM5tE

What is market exchange rate going to be in 5 years time ?

17

Inflation and Nominal Interest Rates

• Nominal Interest Rate = (i)

• Real Interest Rate = (r)

• Risk Premium = R

• Expected Growth (inflation) in Prices = gPe

Given the factors above, nominal interest rate iscalculated as: i = r + R + (1 + R + r) gPe

18

Example

Determination of Nominal Interest Rate

By using following information:

Inflation rate ( gPe ) = 20%

Risk Premium (R) = 0Real Interest Rate (r) = 0.05

i = r + R + (1 + R + r) gPe

i = 0.05 + 0 + (1 + 0 + 0.05)* 0.20 i = 0.26

19

Inflation and its Impact on Interest and Principal Payments

Price Index1. $1000 Loan @5% Interest & No InflationLoanInterestLoan PaymentCash Flow in Year 0 PricesNet Present Value (Equilibrium Situation)

01.0

-1000

-10000

21.0

50

50

11.0

50

50

31.0

50

50

41.0

501000

1050

Price index2. $1000 Loan @5% Interest & 20% InflationLoanInterestLoan PaymentCash Flow in Current PricesCash Flow in year 0 PricesNet Present Value (Dis-Equilibrium Situation)

1.0-1000

-1000-1000

-487.24

1.44

50

5034.72

1.20

50

5041.67

1.728

50

5028.94

2.074

501000

1050506.37

Price Index3. $1000 Loan @ 26.0% Interest & 20% InflationLoanInterestLoan PaymentCash Flow in Current PricesCash Flow in year 0 Prices

Net Present Value (Equilibrium Situation)4. Undiscounted Change in Cash Flow=Case 1 - Case 3 in Year 0 Prices

1.0-1000

-1000-1000

00

1.44

260

260180.56

-130.56

1.2

260

260216.67

-166.67

1.728

260

260150.46

-100.46

2.074

2601000

1260607.64

+442.36

Period

20

Steps for Undertaking Financial Analysis

1. Estimate Real Prices, (Pit /Pt level) for project life

2. Make Assumptions about Future Inflation Rate (S)3. Calculate Changes in Inflation-Adjusted Prices4. Calculate estimated Nominal Interest Rate5. Determine Cash Requirements (Nominal)6. Determine Financing Requirements (Nominal)7. Estimate Taxable Income and Income Taxes (Nominal)8. Construct Pro-Forma Cash Flow Statement in Nominal Values9. Calculate Nominal Net Cash Flows from Different Points of View10. Deflate Nominal Value by General Price Index for Each Year to

Obtain Real Cash Flow Statements11. Calculate Debt Service Capacity Ratios for Total Investment

(Banker’s) Point of View12. Calculate NPV and IRR for Owner’s Point of View

21

Impact of Expected Change in Real Exchange Rate on Real Interest Rates

• US ($) Loan Yen (Y) LoanNominal interest rate:iUS = rUS + (1+rUS)gPUS iJ = rJ + (1+rJ)gPJ

• Market exchange rate:E0

M = (#$/Y)E0

M = E0R (I0

US/I0J)

E1M = E1

R (I1US/I1

J)

22

• Define the price indices in US and Japan so that

111 Jt

USt II

)1(

)1(

11

Jt

UStR

tMt

Jt

UStR

tMt

Rt

Mt

gP

gPEE

I

IEE

EE

23

• In equilibrium the nominal return of giving a loan to Japan in

Yen must be same as making a loan in US$ in the US.• In order to have no profits from arbitrage the following must

hold:

Rt

Rt

JUS

Jt

USt

Rt

RtJ

tJUS

tUS

Jt

UStR

tJ

tJJRt

UStUSUS

MtJM

tUS

E

Err

gP

gP

E

EgPrgPr

gP

gPEgPrr

EgPrr

EiE

i

1

1

1

1

)1()1(

)1(

)1()1)(1()1)(1(

})1(

)1(}{)1(1{

1)1(1

))(1)(1(1

)1(

24

• The return in dollars from a loan you make

to Japan is given by the real rate of

interest you earn in Japan plus any

additional (or reduction) in dollars you

receive when you convert the Yen

repayments into dollars.

25

An Example

Assume that Yen is appreciating at an annual rate of 3%

E1R = E0

R (1.03)

The $ is devaluing 3% a year relative to the Yen. Alternatively, the Yen is appreciating 3% a year.

26

• Example $ 1,000 loan

iUS = rUS + (1+rUS)gPUS

Market exchange rate:

E0M = 0.01 $/Y

r$ = 0.05

Expected rate of Inflation in US (gP$)= 0.04/year

i$ = r$ + (1+r$)gP$

i$ = 0.05 + (1+0.05) 0.04

i$ = 0.092If one year loan made to US borrower:Year 0 1Loan -1000Repayment +1000Interest 92Total -1000 +1092

27

Real Interest Rate in Yen

(1+r$) = $1/ E0R(1 + rY) (E1

R)(1+r$) = (1 + rY) (E1

R/E0R)

where E0R is the real exchange rate in year zero and E1

R is real exchange rate in year 1.

Let us assume E1R/E0

R = 1.03 i.e. the dollar is devaluing at 3 percent a year relative to the Yen.

Hence, if r$ = 0.051.05 = (1 + rY) (1.03)rY = (1.05/1.03) – 1rY = 0.019417476

28

• Expected rate of Inflation in Japan (gPJ) is 0.01/year

• Hence, the nominal interest rate in Yen is,

iY = rY + (1+rY)gPJ

iY = 0.019417476 + (1+ 0.019417476) 0.01

= 0.019417476 + 0.01019417476

iy = 0.02961165

Nominal interest rate is 2.961%.

• If US$ 1,000 loan made to Japan in Yen, US $ 1,000 is equal to 1,000/EM =

1000/0.01 = 100,000 Yen

Hence nominal interest due on 100,000 Yen loan is 2,961.165076.

If one year loan made to US borrower:

Year 0 1

Loan -100,000

Repayment +100,000

Interest 2,961

Total -100,000 +102,961

29

What will E1M be?

• Hence, the market exchange rate in year 1 is,

E1M = E1

R (I1US/I1

J)

E1R = E0

R (1.03)

E1R = 0.01 (1.03) = 0.0103

E1M = E1

R (I1US/I1

J) = 0.0103 (1.04/1.01)

= 0.010609594

• Repayment plus interest in US$ in year 1 of Yen loan,

= (102,961 Y) (0.010609594) = 1,092 US$

• This is exactly the same as if loan made in US dollars at 9.2%.

30

• Interest expense deduction if US company borrows Yen loan of 100,000 Y.

Nominal interest rate in Yen = 0.02961165

Interest expense = 2,961.17

US $ equivalent in Year 1 = 2,961.17 (E1M)

= 2,961.17 (0.01060594)

= $31.40• This is less than $92 interest expense that is allowed as tax

deduction on an equivalent US $ loan of US $ 1,000.• Need to consider exchange rate loss in US dollars when loan paid

back.• In order to pay back 100,000 Yen in year 1 the US borrower will

need 100,000 (E1M) dollar or 100,000 (0.01060594) = $1060.60.

• There has been a foreign exchange capital loss of $60.60 due to exchange rate devaluation.

• Total tax deduction should be interest expense + foreign exchange loss or 31.40 + 60.60 = $92.00.

Calculation of Income Tax Deduction for Foreign LoansBorrowing from Japan

31

Years 0 1 2 3 4Inflation Rate in USA 4% 4% 4% 4%Price Index 1.00 1.04000 1.08160 1.12486 1.16986Real Interest Rate 0.05

Nominal Interest Rate 0.09200 0.09200 0.09200 0.09200

Loan ScheduleYears 0 1 2 3 4Loan -1000Interest 92 92 92 92Repayment of Capital 1000Interest Payment in Real US$ of Year 0 88.46 85.06 81.79 78.64Principal Payment in Real US$ of Year 0 854.80

Real Value of Loan and Repayments -1000.00 88.46 85.06 81.79 933.45Present Value of Loan and Repayments @ 5% 0.00

US$ 1,000 Loan made in the USA with the Real Interest of 5%

32

Market Exchange Rate in Year 0 0.01000 $/Yen

Years 0 1 2 3 4Real Interest Rate (USA) 5.00%Real exchange devaluation of US$ 3.00% 3.00% 3.00% 3.00% 3.00%

Years 0 1 2 3 4Inflation Rate in Japan 1.00% 1.00% 1.00% 1.00%Price Index 1.00 1.01000 1.02010 1.03030 1.04060Real Interest Rate in Yen 0.019417

Nominal Interest Rate 0.02961 0.02961 0.02961 0.02961

Loan Schedule in Yen

Years 0 1 2 3 4Loan -100000Interest 2961 2961 2961 2961Repayment of Capital 100000Total Repayment of Interest+Loan (Yen) -100000 2961 2961 2961 102961

Real Exchange Rate 0.0100 0.01030 0.01061 0.01093 0.01126Nominal Exchange Rate 0.0100 0.01061 0.01125 0.01193 0.01265

Repayment of Interest rate in US $ Nominal 31.41 33.31 35.33 37.47Repayment of Loan in US $ Nominal 1265.31

Repayment of Interest rate in US $ Real 30.20 30.80 31.41 32.03Repayment of Loan in US $ Real 1081.59


US$ 1,000 Loan in equivalent to 100,000 Yen made to Japan

Japan

YearsInflation Rate in USA 4% 4% 4% 4%Price Index 1.00 1.04000 1.08160 1.12486 1.16986Real Interest Rate 0.05

Loan Schedule

Loan -1000Interest 92 92 92 92Repayment of Capital 1000


Documents

1 Lecture Notes Lecture Four (updated: 16 Oct. 2007) FINA 521 INVESTMENT APPRAISAL