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

2. 2 Integration of Movements in Prices, Inflation, Exchange Rates and Interest Rates

3. 3 1. Nominal Prices (Current prices) P 1 t,P 2 t, P 3 t ……….. P n t 2. Price Level P L t =  i n (P i t W i ) Where: i = Individual good or service included in the market basket P i t = Price of the good or service (i) at a point in time (t) W i = Weight given to the price of a particular good or service (i); where  w i = 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) tItI tLtL tLtL BLBL tItI BLBL

4. 4 3. Changes in Price Level (Inflation) Measured in terms of a price index: gP e I = ((P t I - P I t-1 )/(P I t-1 )) * 100 4. Real Prices P t iR = P t i / P t I Where P t i = nominal price of good or service (i) as of a point in time (t) P t I = Price level index at time period (t) 5. Changes in Real Prices Change in P t iR = t iR P- P t-1 iR t-1 iR P P t iR = Real price of good ( i ) as of a specific period

5. 5 Example 1: Nominal Prices and Changes in Price level Assume Year 1 is base year Goods 123 Weights0.20.50.3 Nominal Prices Year 1:P 1 1 =30 P 2 1 =100 P 3 1 =50 P L 1 =0.2(30)+0.5(100)+0.3 (50) P L 1 =71 P L B= 71 Price Index P I 1 =1.00 Nominal Prices Year 2:P 1 2 =40 P 2 2 =110 P 3 2 =40 P L 2 =0.2(40)+0.5(110)+0.3(40)= P L 2 =75 P L B= 71 Price Index P I 2 =1.056

6. 6 Example 1:Nominal Prices and Changes in Price Level (cont’d) Assume Year 1 is base year Goods123 Weights0.20.50.3 Nominal Prices Year 3:P 1 3 =35 P 2 3 =108 P 3 3 =60 P L 3 =0.2(35)+0.5(108)+0.3 (60) P L 3 =79 Price Index P I 3 =1.113 INFLATION RATE Changes in Price Level : Measured in terms of a price index gP I 2 = ((P I 2 - P I 1 )/(P I 1 )) * 100=((1.056-1.00)/1.00))*100=5.63% gP I 3 = ((P I 3 - P I 2 )/(P I 2 )) * 100=((1.113-1.056)/1.056)*100=5.33%

7. 7 Real Prices and Changes in Real Prices EXAMPLE 2: Real Prices and Changes in Real Prices Goods123 Weights0.20.50.3 Nominal Prices Year 1:P 1 1 =30P 2 1 =100 P 3 1 =50 Price Index P I 1 =1 Real Prices Year 1: P 1R 1 =30/1 P 2R 1 =100/1P 3R 1 =50/1 P 1R 1 =30 P 2R 1 =100P 3R 1 =50 Nominal Prices Year 2:P 1 2 =40 P 2 2 =110 P 3 2 =40 Price Index P I 2 =1.056 Real Prices Year 2: P 1R 2 =40/1.056 P 2R 2 =110/1.056 P 3R 2 =40/1.056 P 1R 2 =37.87 P 2R 2 =104.13 P 3R 2 =37.87

8. 8 EXAMPLE 2: Real Prices and Changes in Real Prices (Cont’d) Goods123 Weights0.20.50.3 Nominal Prices Year 3:P 1 3 =35 P 2 3 =108 P 3 3 =60 Price Index P I 3 =1.113 Real Prices Year 3: P 1R 3 =35/1.113 P 2R 3 =108/1.113 P 3R 3 =60/1.113 P 1R 3 =31.46 P 2R 3 =97.06 P 3R 3 =53.92 Changes in Real Prices Year 2 Change in P 1R 2 = P 1R 2 – P 1R 1 / (P 1R 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 P 1 R 3 = P 1 R 3 - P 1 R 2 / (P 1 R 2 ) = ((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. 9

10. 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

11. 11 7. Constant Prices Fixed set of prices at a given year t 0 P = P ; P = P Not a useful concept to use in project evaluation t+n i k to k t+n i to i t+n k to k

12. 12 Integrated Financial Analysis of Investments

13. 13 E t M =8 Rand / $US I t D = 1.0 I t US = 1.0 I 1.0 E t R = E  = 8.0  = 8.0 Rand/$ I 1.0 Example MtMt US t DtDt Initial year prices indexes in both countries assumed in project analysis to be equal to 1.0.

14. 14 Real effective Exchange Rates I F /I D Italy Real effective Exchange Rates I F /I D France Real effective Exchange Rates I F /I D Germany France Germany Italy

15. 15 Integrated Financial Analysis of Investments Where K is a random variable with a mean of zero

16. 16 If g P f = 2%/ p.a. Foreign rate of inflation If g P d = 8%/ p.a. Domestic rate of inflation I d t+5 = 1 (1.08) 5 = 1.47 I f t+5 = 1 (1.02) 5 = 1.10 E R t+5 = 8 Rand/$ Therefore, if then: E M t+5 = Rand/$US Suppose that in the current year: Domestic Price Index = 1 and Foreign Price Index = 1 Therefore, in Year 0, E 0 M = E 0 R. Suppose E 0 M is 8 Rand/$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   d               ґ    f 5t I 5t I R 5t E M 5t E What is market exchange rate going to be in 5 years time ?

17. 17 Inflation and Nominal Interest Rates Nominal Interest Rate = (i) Real Interest Rate = (r) Risk Premium = R Expected Growth (inflation) in Prices = gP e Given the factors above, nominal interest rate is calculated as:i = r + R + (1 + R + r) gP e

18. 18 Example Determination of Nominal Interest Rate By using following information: Inflation rate ( g P e ) = 20% Risk Premium (R) = 0 Real Interest Rate (r) = 0.05 i = r + R + (1 + R + r) g P e i = 0.05 + 0 + (1 + 0 + 0.05)* 0.20 i = 0.26

19. 19 Inflation and its Impact on Interest and Principal Payments Price Index 1. $1000 Loan @5% Interest & No Inflation Loan Interest Loan Payment Cash Flow in Year 0 Prices Net Present Value (Equilibrium Situation) 0 1.0 -1000 0 2 1.0 50 1 1.0 50 3 1.0 50 4 1.0 50 1000 1050 Price index 2. $1000 Loan @5% Interest & 20% Inflation Loan Interest Loan Payment Cash Flow in Current Prices Cash Flow in year 0 Prices Net Present Value (Dis-Equilibrium Situation) 1.0 -1000 -487.24 1.44 50 34.72 1.20 50 41.67 1.728 50 28.94 2.074 50 1000 1050 506.37 Price Index 3. $1000 Loan @ 26.0% Interest & 20% Inflation Loan Interest Loan Payment Cash Flow in Current Prices Cash 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 0 1.44 260 180.56 -130.56 1.2 260 216.67 -166.67 1.728 260 150.46 -100.46 2.074 260 1000 1260 607.64 +442.36 Period

20. 20 Steps for Undertaking Financial Analysis 1. Estimate Real Prices, (P i t /P t level) for project life 2. Make Assumptions about Future Inflation Rate (S) 3. Calculate Changes in Inflation-Adjusted Prices 4. Calculate estimated Nominal Interest Rate 5. 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 Values 9. Calculate Nominal Net Cash Flows from Different Points of View 10. Deflate Nominal Value by General Price Index for Each Year to Obtain Real Cash Flow Statements 11. Calculate Debt Service Capacity Ratios for Total Investment (Banker’s) Point of View 12. Calculate NPV and IRR for Owner’s Point of View

21. 21 Impact of Expected Change in Real Exchange Rate on Real Interest Rates US ($) LoanYen (Y) Loan Nominal interest rate: i US = r US + (1+r US ) g P US i J = r J + (1+r J ) g P J Market exchange rate: E 0 M = (#$/Y) E 0 M = E 0 R (I 0 US /I 0 J ) E 1 M = E 1 R (I 1 US /I 1 J )

22. 22 Define the price indices in US and Japan so that

23. 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:

24. 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. 25 An Example Assume that Yen is appreciating at an annual rate of 3% E 1 R = E 0 R (1.03) The $ is devaluing 3% a year relative to the Yen. Alternatively, the Yen is appreciating 3% a year.

26. 26 Example $ 1,000 loan i US = r US + (1+r US ) g P US Market exchange rate: E 0 M = 0.01 $/Y r $ = 0.05 Expected rate of Inflation in US ( g P $ )= 0.04/year i $ = r $ + (1+r $ ) g P $ i $ = 0.05 + (1+0.05) 0.04 i $ = 0.092 If one year loan made to US borrower: Year 0 1 Loan-1000 Repayment+1000 Interest 92 Total-1000+1092

27. 27 Real Interest Rate in Yen (1+r $ ) = $1/ E 0 R (1 + r Y ) (E 1 R ) (1+r $ ) = (1 + r Y ) (E 1 R /E 0 R ) where E 0 R is the real exchange rate in year zero and E 1 R is real exchange rate in year 1. Let us assume E 1 R /E 0 R = 1.03 i.e. the dollar is devaluing at 3 percent a year relative to the Yen. Hence, if r $ = 0.05 1.05 = (1 + r Y ) (1.03) r Y = (1.05/1.03) – 1 r Y = 0.019417476

28. 28 Expected rate of Inflation in Japan ( g P J ) is 0.01/year Hence, the nominal interest rate in Yen is, i Y = r Y + (1+r Y ) g P J i Y = 0.019417476 + (1+ 0.019417476) 0.01 = 0.019417476 + 0.01019417476 i y = 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/E M = 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. 29 What will E 1 M be? Hence, the market exchange rate in year 1 is, E 1 M = E 1 R (I 1 US /I 1 J ) E 1 R = E 0 R (1.03) E 1 R = 0.01 (1.03) = 0.0103 E 1 M = E 1 R (I 1 US /I 1 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. 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 (E 1 M ) = 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 (E 1 M ) 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 Loans Borrowing from Japan

31. 31 US$ 1,000 Loan made in the USA with the Real Interest of 5%

32. 32 US$ 1,000 Loan in equivalent to 100,000 Yen made to Japan Japan