9 - Price Changes

Engineering EconomicsECO 1192

Lecture 9: Decision-making with Price Changes

Claude Théoret

University of Ottawa

9. Price Changes 2

Recommended Reading

Fraser et al. Chapter 9 Newnan et al. chapter 14

3

Before- and After-Tax Cash Flows END OF YEAR

0 1 2 3 4Annual revenues (AR) (Actual $)

Annual costs (AC) (Actual $)

1. BTCF "Operations" (Actual $) AA BB

2. BTCF "SV" (Actual $) CC

3. BTCF "Working Capital" (Actual $)

4. Total BTCF (Actual $) DD

5. BTCF "Operations" (Constant $) EE

6. BTCF "SV" (Constant $) FF

7. BTCF "Working Capital" (Constant $)

8. Total BTCF (Constant $)

9. Annual Depreciation GG HH

10. Interest on loan II

11. Taxable Operating Income

12. Taxes on Operating Income JJ

13. Capital gains KK

14. Taxes on capital gains

15. Recaptured depreciation LL

16. Taxes on recaptured dep. MM

17. ATCF "Operations" (Actual $) NN

18. ATCF "Operations" (Constant $)

19. ATCF "SV" (Actual $)

20. ATCF "SV" (Constant $)

21. ATCF "Working Capital" (Actual $)

22. ATCF "Working Capital" (Constant $)

23. Total ATCF (Actual $) OO

24. Total ATCF (Constant $) PP QQ

25. (=R10.) Interest on loan RR

26. Loan repayment SS

27. CFOE (Actual $) TT

28. CFOE (Constant $) UU

9. Price Changes 4

Introduction

In all project analyses thus far, the prices of all goods and services were constant.

In the real world, prices are not constant, sometimes increasing (inflation) and sometimes decreasing (deflation)

Price changes can have significant effects on the value or worth of an investment; hence, they must be factored in an engineering economic study

9. Price Changes 5

Measuring Inflation

Consumer Price Index basket of consumer goods and services used

to track changes in prices on a monthly basis Wholesale Price Index (tracks the prices of

wholesale goods) GDP Implicit Price Deflator (tracks price

changes for all final goods and services produced by an economy) Published quarterly and annually

Consumer Price Index (CPI)

9. Price Changes 6

Your house ….

1. Purchased in 1990 for $150,000

2. Market value in 2005 (15 years later) is $225,000

3. The annual inflation rate has been, on average, 2%.

4. Did your purchasing power increase between 1990 and 2005? Real value of your house in 2005 in 1990 dollars

= $225,000(1+inflation rate)-15

= $225,000(1+0.02)-15 = $167,178

Answer: YES (real value in 2005 > real value in 1990).

9. Price Changes 7

9. Price Changes 8

Example: John and Mary

John and Mary married five years ago following their graduation from U of O.

Their joint income in their first year as a couple was $80,000. the CPI for that year was (hypothetically)

105.8 Five years later, the CPI reached 133.9. What

must be the joint income of the couple to maintain the purchasing power of 5 years earlier?

9. Price Changes 9

Bonds and Inflation

$60,000 10-year Canada bonds are currently on sale by Speedy Brokers Inc.

The rate of interest is 8% annually, payable semiannually.

Bondholders expect A return of 6% per year compounded semiannually Inflation to be constant at 2% every 6 months.

How much should a purchaser pay Without any adjustment for inflation When inflation is considered

9. Price Changes 10

Example: Bond Rates of Return

A corporate bond has a current price of $90,000 pays $10,000 annually for 10 years

If inflation is expected to be 5% forever1. What is the bond’s actual before-tax rate of return?2. What is the bond’s actual after-tax rate of return if the

tax rate is 30%?3. What is the bond’s real before-tax rate of return? 4. What is the bond’s real after-tax rate of return if the

tax rate is 30%?

9. Price Changes 11

Causes of Inflation

Money supply Growth in the money supply (currency and bank

deposits) exceeds the growth of goods and services Exchange rates

Value of one currency in terms of another currency; changes may affect the cost of purchasing goods and services from other countries

Cost-push inflation Increases in production costs (wages) higher prices

Demand –pull inflation the demand for goods and services grows faster than

their production

9. Price Changes 12

Why bother with inflation?

Repercussions on the purchasing power of money purchasing power (or value) of money declines if

prices increase and cash flows (including weekly wages) are not fully responsive (do not grow at the same rate as prices)

future dollars are less valuable than today or present dollars

• $100 today will have a purchasing power of $90.91 in 1 year if prices increase by 10 per

cent during the year or $62.10 in 5 years

9. Price Changes 13

Why bother with inflation? Investors are not satisfied with keeping pace with inflation A successful investment must result in a net gain in buying

power (i.e., must exceed inflation) Investors who purchase a corporate bond or make a

physical investment (such as a restaurant) must account for the impact of price changes in their decision-making

Two rates of return are important in an investment decision: Total or combined rate = real rate + rate of inflation Real (inflation-free rate)

Of course, an investor should not forget the impact of income taxes on the return on investment must determine her/his rate of return after adjusting for price changes AND after accounting for income taxes.

9. Price Changes 14

Is Inflation problematic?

Yes. Unpredictable changes in the inflation rate redistribute income in arbitrary ways between employers and workers, between borrowers and lenders ...

A high inflation rate is problematic because it diverts resources from productive activities to the unproductive activity of forecasting inflation

• An engineer allocates much of her time to forecasting inflation instead of producing the goods and services to meet the needs of society.

9. Price Changes 15

Rates of interest

Nominal (or actual) Combination of the real rate and the rate of

inflation Real (or constant)

Inflation-free rate of interest In a zero (no) inflation world, the minimum rate

required for you to substitute future consumption for current consumption

• Save now to increase future consumption• About 2%

9. Price Changes 16

Real rate of interest

Important to state future $ in terms of a base or reference year

Note that base year dollars can be stated as real or constant dollars (for example, year 2000 dollars)

Non base-year dollars (such as year 2001 dollars) can be stated as nominal or current dollars

For the base year, the PW of real dollars (inflation-free dollars) will equal the PW of nominal dollars (dollars containing inflation)

See next slide for the conversion of nominal dollars for any year (other than the base year) to equivalent real dollars (i.e., inflation-free dollars)

9. Price Changes 17

Real rate of interest

Let $F be the future worth of $P today(containing both inflation and a real rate of return) To remove inflation from these future dollars ($F):

F' = F/(1+f) where f is the inflation rate To bring these dollars to now or today $ adjust as follows

P = F'/(1+ir)Therefore, the current (i.e., now) real dollars are given by

P = F/{(1+f)(1+ir)}

where (1+ic) = (1+f)(1+ir) or ic = (1+f)(1+ir)-1 Therefore,

ir = {(1 +ic) /(1 + f)} - 1

f = inflation rate; ir = real rate; ic = market rate

9. Price Changes 18

Real (constant) and current (actual) $

You invested $1,000 in a GIC from the Trust Me Company exactly five years ago today.

No annual interest was paid to you over the years as the interest income was reinvested automatically by the financial institution.

Today, you received a cheque for $1,500 which represents The reimbursement off the $1,000 invested 5 years ago Interest income generated by your $1,000 investment

If inflation was 4% throughout the 5 years, what is the purchasing power of the $1,500 today relative to their purchasing power 5 years ago?= 1,500(P/F,inflation rate, 5) = 1,500(P/F,4%,5) = $1,232.89 $1,500 is required today to buy what $1,232.89 could buy 5 years

ago (or about 83%); or $1,217 is required today to buy what $1,000 could buy 5 years ago.

9. Price Changes 19

MARR and Cash Flows

Given: Annual inflation rate = 3% Nominal interest rate without risk = 5% First cost (P) = $3,000 on January 1, 2001 (same as

December 31, 2000) Cash flows in January 1, 2001 dollars (i.e., real or

constant dollars) Real interest rate

= 5% - 3% = 2%

December 31

Cash Flows

2000 -3 000

2001 +1 500

2002 +1 500

2003 +1 500

2004 +1 500

MARR and Cash Flows

Given: Annual inflation rate = 3% Nominal interest rate without risk = 5% First cost (P) = $3,000 on January 1, 2001 (same as

December 31, 2000) Cash flows in actual dollars (i.e., at the prevailing price of

each year)

December 31

Cash Flows

2000 -3 000

2001 +1 500 (1.03)= 1 545

2002 +1 500 (1.03)2 = 1 591

2003 +1 500 (1.03)3 = 1 639

2004 +1 500 (1.03)4

= 1 6899. Price Changes 20

9. Price Changes 21

Example

An investor wants a real return (i.e., inflation-free return) of 4% on a $1,000 investment when the annual rate of inflation is 10% $1,000 now must grow to $1,100 in one year just to

maintain today's purchasing power In addition, there must be a 4% rate of return on the $1,100 to

meet the investor’s rate of return objective The total rate of return for one year becomes

F = P(1+f)N(1+ir)N

= 1000(1.10)(1.04) = $1,144 (anything less would represent a return on investment less than 4% in real terms)where f = inflation rate ir = real rate of return ic= combined rate (rate with inflation)

9. Price Changes 22

Example: DVD Purchases

Johnny loves classical music and, on a recent birthday, received a $1,000 gift which could be used for investment purposes or to purchase DVDs DVDs currently sell for $20 The local bank pays 5.5% interest

compounded annually Inflation (f) is expected to be 2% annually for

the next 10 years.

9. Price Changes 23


What is the market (or combined) interest rate (iC)? (Bank rate = Market rate = 5.5%)

What is the real (inflation-free) interest rate (ir)?

(1+ic) = (1+ir)(1+f); (1+ir) = (1+ic)/(1+f)

ir = (1+ic)/(1+f) – 1

= [(1+0.055)/(1+0.02)] - 1

= 0.0343 or 3.43% (precise rate)

9. Price Changes 24


How many DVDs could Johnny purchase today? $1,000/$20 = 50 DVDs

How many DVDs could Johnny purchase in 1 year? {1,000(F/P,5.5%,1)}/{20(F/P,f=2%,1)} 1055/20.40 = 51.71 DVDs

Since the nominal interest rate (5.5%) > inflation rate (2%), the purchasing power of the $1,000 (in terms of purchasing DVDs) would grow during the year.

Note that the percentage increase in the capacity to purchase DVDs is (51.71-50)/50 = 0.0343 or 3.43% (= inflation-free rate)

Discount Rate and Cash Flows

Discount Rate (%)

Accurate Approximate

Current = (1+f)(1+r) – 1 = r + f

Constant= [(1+c)/(1+f)] -1 = c – f

Cash Flows

Current $ Constant $

Discount Rate (%)

Current(nominal)

X

Constant(real) X

9. Price Changes 25

8. VAN, flux monétaires et taux d'actualisation 26

Your turn!!!!

Determine the rate of inflation during a decade if the price of a computer (driven exclusively by inflation) doubled during the decade?

27

Your turn!!!!

Determine the rate of inflation during a decade if the price of a computer (driven exclusively by inflation) doubled during the decade?

F = P(1+i)N

2P = P(1+i)10

2 = (1+i)10

20.1 = (1+i)10/10

i = 0.0718 7.18 %


Your turn!!!!

During a specific 5-year period, the market rate of interest was 12% and the rate of inflation was 5%.

How many dollars would be required after 5 years to maintain the purchasing power of $2,000 at the beginning of the 5-year period?


Your turn!!!!

During a specific 5-year period, the market rate of interest was 12% and the rate of inflation was 5%.

How many dollars would be required after 5 years to maintain the purchasing power of $2,000 at the beginning of the 5-year period? F = P(1+i)N

F = 2,000(1+0.05)5

F = 2,552 dollars

9. Price Changes 30

Example 1

P = 1,000; F = 2,000; N = 4 years;

f = 10% (inflation rate); tax rate (t) = 0 (No taxes)

Find ic and ir

From F = P(1+ic)N

2000/1000 = (1+ic)4

Solve for ic: ic = 0.189 or 18.9% (with inflation)

From ir = [(1 +ic) /(1 + f)] - 1

= [(1+0.189)/(1+0.1)] - 1 = 0.081 or 8.1% (inflation-free)

9. Price Changes 31

Example 2

Assume that $5,000 is deposited each year-end in anaccount earning interest at 10 percent per yearover a 5-year period. During this period, inflation isexpected to remain at 6 percent per year.

Determine the dollar amount in the fund at the endof five years (the future worth after five years inactual dollars)?

Future Worth = 5000(F/A,10%,5) = $30,525 (actual or current dollars i.e., in dollars 5

years from now)

9. Price Changes 32

Example 2 (cont’d)

Given the eroding effect of inflation on

purchasing power, what is the value of this fund

in constant (real) dollars after five years?

$30,525(P/F,inflation,5)

= 30,525(P/F,6%,5)

= $22,810 [inflation-free dollars]

9. Price Changes 33


What is the real (inflation-free) rate of return on this investment?Real interest rate = ir = [(1 +ic)/(1 + f)] - 1

= [(1+0.1)/(1+0.06)] - 1

= 0.03774 or 3.774%

(the rate at which the investor’s purchasing power increased during the 5-year period)

9. Price Changes 34

Example 3

Engineering Press is offering several subscription packages to its influential Journal of Engineering Economics: 1 year for $40 2 years for $74 3 years for $109

Inflation is expected to be 5% annually for the next decade. You are an avid reader of this Journal and plan to purchase it

forever. What’s the best subscription deal if current market rates are

10% compounded annually and a subscription MUST be paid in full at the beginning of a subscription period?

Year Option 1 Option 2 Option 3

1 40 74 109

2 42 -- --

3 44.10 81.59 --

4 46.31 -- 126.18

5 48.62 89.95 --

6 51.05 -- --


9. Price Changes 35

9. Price Changes 36


Find the PW of each subscription option: Annual subscription : 40+42(P/F,10%,1)

+44.102(P/F,10%,2)+46.31(P/F,10%,3)+48.62(P/F,10%,4)+51.05(P/F,10%,5)= $214.32 (most expensive as expected)

Two-year subscription: 74 +81.59(P/F,10%,2)+89.95(P/F,10%,4)= $202.87 (best deal)

Three-year subscription: 109+126.18(P/F,10%,3)= $203.80

9. Price Changes 37

Example 4

Exactly 75 years ago today, Farmer Billy Cash stored $1,000 (in dollar bills) in a bag of wheat. During these years, inflation was 5% annually.

What are their actual- and real-dollar values today? Actual dollar value = $1,000 Real-dollar value = 1,000(P/F,5%,75)= $25.75($1,000 today can buy what $25.75 could buy

75 years ago)

9. Price Changes 38


Instead of “storing” $1,000 in a bag of wheat, Farmer Bill could have purchased a GIC from the TRUST ME Co. which paid 6% per year. What would be the actual and real dollar equivalents of the $1,000? [Inflation is still 5% annually] Actual dollar value = $1,000(F/P,6%,75)

= $79,057 Real-dollar value = 79,057(P/F,inflation,75)

= $2,036 [Which is much better than $25.75]

GIC ≡ Guaranteed Investment Receipt

9. Price Changes 39


Instead of “storing” the $1,000 in a bag of wheat or purchasing a GIC, Farmer Bill could have invested in a stock market index fund that grew by 12% annually during this period. What would be the actual and real dollar equivalents of the $1,000 invested in a stock index fund? [Inflation is 5% annually] Actual dollar value = $1,000(F/P,12%,75)

= $4,913,056 Real-dollar value = 4,913,056(P/F,inf,75)= $126,519

[Which is much better than $25.75 in the bag of wheat and $2,036 in a GIC]

9. Price Changes 40

Cash Flows

Key issue: are cash flows Annual receipts Annual operating and maintenance costs

fully or partially responsive to inflation i.e., do they grow in whole or in part with inflation? Fully

• Cash flows grow at the inflation rate. Partially

• cash flows grow by a fraction of the inflation rate Cash flows are independent of the inflation

rate.

9. Price Changes 41

Example 5

• Annual Interest Income = 1,000@15% = $150

• Inflation is 10% annually• $1,000 bond investment is fully refunded

(without risk of default) after 3 years• N = 3 years

Find ic and ir

9. Price Changes 42


Using the Present Worth Approach:

1000 = 150(P/A,i*,3)+ 1000(P/F,i*,3)

Solve for i*: i* = 15% (=ic)

From ir = [(1 +ic) / (1 + f)] – 1, ir

= [(1 +0.15) / (1 + 0.1)] – 1

= 0.0455 or 4.55%

9. Price Changes 43

Example 5 (with 30% tax rate)

Solve for ic and ir

Using the Present Worth Approach

1000 = 150 (1-0.3)(P/A,i*,3)+ 1000(P/F,i*,3)

i* = 10.5% (=ic)

From ir = (1 +ic) /(1 + f) - 1

ir = (1 +0.105) /(1 + 0.1) - 1

ir = 0.0045 or 0.45%

(compare with 4.55% on previous slide)

9. Price Changes 44

Example 6

A = Annual interest income is fully responsive to inflation

Inflation (f) = 10% P = $1,000 which is also fully responsive to

inflation F = $1,000 N = 3 years Find ic and ir

9. Price Changes 45

Example 6 cont’d

Using the Present Worth Approach

1000 = 150(1+f)(P/F,i*,1)

+ 150(1+f)2(P/F,i*,2)

+ 150(1+f)3(P/F,i*,3) + 1000(1+f)3(P/F,i*,3)

Solve for i*: i* = 26.5% (=ic)

From ir = (1 +ic) /(1 + f) - 1

ir = (1 +0.265) /(1 + 0.1) - 1

= 0.15 or 15.0%

9. Price Changes 46

Example 7 – Education Fund

You wish to set up an education fund TODAY for a child who will attend college in 10 years.

Each of the 4 college years will cost $9,000 in today dollars. Annual college costs are fully responsive to price changes and

inflation is projected to be 8% per year for the next 50 years. The education fund is expected to earn 12% interest

compounded annually. Assume that annual college payments are made in a lump sum

at the beginning of each of the four (4) academic years.How much money must you deposit in the education fund at the end of each of the next 10 years (with the first deposit in one year from today)?

Example 7 – Education Fund

College Year

Cost of College(Actual College Year

Dollars)

PW (at the beginning of the First

College Year)

First 9000(F/P,8%,10) = $19,431 19,431(P/F,12%,0) = $19,431

Second 9000(F/P,8%,11) = 20,985 20,985(P/F,12%,1) = 18,737

Third 9000(F/P,8%,12) = 22,664 22,664(P/F,12%,2) = 18,068

Fourth 9000(F/P,8%,13) = 24,477 24,477(P/F,12%,3) = 17,422

TOTAL = $87,557 TOTAL = $73,658

The 10-year annuity becomes: A = F(A/F,12%,10)73,658(0.057) = $4,199

9. Price Changes 47

9. Price Changes 48

Your new job

You are graduating this Fall and have been to several job interviews with potential employers.

You received three (3) job offers in today’s mail (starting date is January 3, 2007 in each case) Offer A: $50,000 annually in January 3, 2008

purchasing power Offer B: $49,000 the first year followed by

annual increases of $3,000 Offer C: $55,000 annually for the next 5 years

9. Price Changes 49

Your new job

Economic intelligence tells you that inflation will be 6% annually for the next 10 years.

If you are seeking a real MARR = 8%, which plan would you select based on A 4-year period of analysis A fully-paid salary on May 1 of the next four (4)

years

9. Price Changes 50

Your new job

Offer A

PW(iC = 14.48%) = 50,000

+ 50,000(F/P,6%,1)(P/F,14.48%,1)

+ 50,000(F/P,6%,2)(P/F,14.48%,2)

+ 50,000(F/P,6%,3)(P/F,14.48%,3)

+ 50,000(F/P,6%,4)(P/F,14.48%,4)

= $188,335

If inflation=6% and you are seeking an 8% real increase, theniC = (1+f)(1+ir) – 1 = (1.06)(1.08) - 1 = 0.1448

9. Price Changes 51

Your new job

Offer B

PW(iC = 14.48%) = 49,000

+ 49,000(P/A,14.48%,3)

+ 3,000(P/G,14.48%,3)

= $183,929

9. Price Changes 52

Your new job

Offer C

PW(iC = 14.48%)

= 55,000 + 55,000(P/A,14.48%,4)

= $186,661

Summary:

PW (Offer A) = $188,335

PW (Offer B) = $183,929

PW (Offer C) = $186,661

9. Price Changes 53

Project Analysis – Example 1

1. Annual inflation (f) = 10%

2. No debt capital (r=0)

3. Straight line depreciation

4. SV = 0

5. Cash flows are fully responsive to inflation

(i.e., they increase by 10% each year)

Year

BTCFnominal

BTCFreal

Intereston

Debt

AED TaxableIncome

IncomeTaxes

ATCFnominal

ATCFreal

0-2991 -2991

NODEBT

-- -- -- -2991 -2991

1 1100 1000 598 502 251 849 771.7

2 1210 1000 598 612 306 904 747.1

3 1331 1000 598 733 367 964 724.3

4 1464 1000 598 866 433 1031 704.2

5 1611 1000 598 1013 507 1104 685.5


AED = Annual Equivalent Depreciation9. Price Changes 54

9. Price Changes 55


Annual inflation = 10%; Debt capital; debt Capital is 30% of P paid

back in 5 equal instalments Interest on unpaid debt = 12%. Depreciation Method: Straight Line SV = $0


Year BTCF nom

(1)

BTCFReal(2)

Int.on

Debt(3)

AnnualDep.(4)

TI(5)

IT(6)

ATCFNom.

(7)

ATCFReal(8)

Debt +

Princ(9)

CFOENom(10)

CFOEReal(11)

0 -2991 -2991 -- -- -- -- -2991 -2991 -- -2093.7

-2093.7

1 1100 1000 107.64 598 394 197 903 820.9 287 616 560

2 1210 1000 86.11 598 526 263 947 782.6 265 682 563

3 1331 1000 64.58 598 668 334 997 749.1 244 753 566

4 1464 1000 43.06 598 823 412 1052 718.5 222 830 567

5 1611 1000 21.53 598 991 496 1115 692.3 201 914 568

TI = Taxable Income; IT = Income Taxes9. Price Changes 56

9. Price Changes 57

Project Analysis – Example 2 Six (6) rates of return (%)

A. Before tax nominal rate of return = 32% Real rate of return = 20%

B. After-tax nominal rate of return = 19% Real rate of return = 8%

C. Owner Equity Nominal rate of return = 22% Real rate of return = 11%

Debt Ratio and Return on Equity

Rate of returnon equity

Debt Ratio0

See row 10. of table on next slide.

Debt Ratio0.10.20.30.40.50.6 19.2

9.310.912.815.5

Rate of ReturnCFOE8

9. Price Changes 58

Scenario #1 #2 #3 #4 #5 #6 #7 #8 #9 #10

1.Inflation 0 10 10 0 10 10 10 10 10 10

2.Responsive NO NO YES NO YES YES YES YES YES YES

3.debt ratio (r;%)

0 0 0 0.3 0.1 0.2 0.3 0.4 0.5 0.6

4.t=tax rate 50 50 50 50 50 50 50 50 50 50

5.BTRR nom 20 20 32 20 32 32 32 32 32 32

6.BTRR real 20 9.1 20 20 20 20.0 20 20 20 20

7.ATRR nom 10.5 10.5 17.7 12.2 18.3 18.8 19.2 19.8 20.3 20.9

8.ATRR real 10.5 0.45 7 12.2 7.5 8.0 8.4 8.9 9.5 9.9

9.CFOE nom 10.5 10.5 17.7 12.3 18.8 20.2 21.9 24 27 31.2

10.CFOE real 10.5 0.45 7 12.3 8.0 9.3 10.9 12.8 15.5 19.2

9. Price Changes 59

9. Price Changes 60

Investment Project

A firm is considering the purchase of a truck for $300,000 fully installed.

The truck is expected to last 3 years with a salvage value of $100,000 at that time.

Revenues from operations will be $250,000each year and operating and maintenance

costs will be $75,000 each year

9. Price Changes 61

Investment Project

1. Depreciate the truck using the DB method (d=25%)

2. The half-year rule does not apply.

3. Before-tax with inflation interest rate = 20%.

4. Before-tax inflation-free interest rate = 15%.

5. After-tax with inflation interest rate = 10%.

6. After-tax inflation-free interest rate = 5%.

7. Annual inflation rate = 5%.

8. Tax rate = 50%

9. The firm gets a $100,000 loan (at a 10% rate of interest) which is repaid as follows: next slide

9. Price Changes 62

Investment Project

The firm gets a $100,000 loan (at a 10% rate of interest) which is repaid as follows:

Year-end Repayment Year 1 : 30% Year 2 : 30% Year 3 : 40%

Years

Item 0 1 2 3

1. BTCF (Actual $) ‑300,000 175,000 175,000 175000+100000

2. BTCF (Constant $) ‑300,000 166,667 158,730 237,555

3. Interest on Loan 10,000 7,000 4,000

4. Depreciation 75,000 56,250 42,188

5. Taxable Income 90,000 111,750 128,812

6. Taxes Payable 45,000 55,875 64,406

7. ATCF (Actual $) ‑300,000 130,000 119,125 110,594+71,093.7=181,687.7

8. ATCF (Constant $) ‑300,000 123,810 108,050 156,948.7

9. Repayment of Loan 30,000 30000 40,000

3. Interest on Loan 10,000 7000 4,000

10. CFOE (Actual $) ‑200,000 90,000 82125 112,948.7

11. CFOE (Constant $) ‑200,000 85,714 74,490 97,569.39. Price Changes 63

Table Rows (previous slide) for Rate of Return Calculations

Rate of Return Calculations ROW

Current $ Before-Tax Cash Flow 1

Constant $ Before-Tax Cash Flow 2

Current $ After-Tax Cash Flow 7

Constant $ After-Tax Cash Flow 8

Current $ Owner Equity 10

Constant $ Owner Equity 11

1. BTCF (Actual $)

2. BTCF (Constant $)

3. Interest on Loan

4. Depreciation

5. Taxable Income

6. Taxes Payable

7. ATCF (Actual $)

8. ATCF (Constant $)

9. Repayment of Loan

3. Interest on Loan

10. CFOE (Actual $)

11. CFOE (Constant $)

9. Price Changes 64

9. Price Changes 65

Problem: Investment Project

After-tax inflation-free NPW of projectFrom the ATCF real dollar row (row 8):

-300,000 + 123,810(P/F,5%,1)

+ 108,050(P/F,5%,2) + 156,948.7(P/F,5%,3)

= $51,490

Owner Equity NPW in after-tax inflation-free dollars

From the CFOE real dollar row (row 11):

= -200,000 + 85,714(P/F,5%,1)

+ 74,490(P/F,5%,2) + 97,569.3(P/F,5%,3)

= $33,477

Problem: Investment Project

Rates of Return

Cash Flow IRR (%)

BTCF (nominal or actual) 43

BTCF (constant or real) 37

ATCF (nominal or actual) 19

ATCF (constant or real) 14

CFOE (nominal or actual) 19

CFOE (constant or real) 14

9. Price Changes 66

Example: John and Mary

John and Mary married five years ago following their graduation from U of O.

Their joint income in their first year as a couple was $80,000. the CPI for that year was (hypothetically) 105.8

Five years later, the CPI reached 133.9. What joint income must the couple have to maintain the purchasing power of 5 years earlier?

Their combined currentincome must be:

= 80,000(133.9/105.8)= $101,248

9. Price Changes 67

Bonds and inflation

$60,000 10-year Canada bonds are currently on sale by Speedy Brokers Inc.

The rate of interest is 8% annually, payable semiannually. Bondholders expect

A return of 6% per year compounded semiannually Inflation at 2% every 6 months.

How much should a purchaser pay for a $60,000 bond Without any adjustment for inflation? Adjusted for inflation?

Without inflation adjustment

Semi-annual interest =$2,400 Number of 6-month periods

= 10(2) = 20 PW=2,400(P/A,3,20)

+ 60,000(P/F,3,20) = $68,928

With inflation adjustment

ic= r+f+rf= 0.03+0.02+0.03(0.02)= 0.0506

PW=2,400(P/A,5.06%,20)+ 60,000(P/F,5.06%,20) = $52,114

9. Price Changes 68

Bond Rates of Return

Year Before-tax actual Before-tax real After-tax actual After-tax real0 -$90,000 -$90,000 -$90,000 -$90,0001 $10,000 $9,524 $7,000 $6,6672 $10,000 $9,070 $7,000 $6,3493 $10,000 $8,638 $7,000 $6,0474 $10,000 $8,227 $7,000 $5,7595 $10,000 $7,835 $7,000 $5,4856 $10,000 $7,462 $7,000 $5,2247 $10,000 $7,107 $7,000 $4,9758 $10,000 $6,768 $7,000 $4,7389 $10,000 $6,446 $7,000 $4,51210 $100,000 $61,391 $97,000 $59,550

ROR = 11.11% 5.82% 7.78% 2.65%

Bondholders have a 30% income tax rate9. Price Changes 69

Mary’s Financial Investments

1. Mary bought a five-year $10,000 Guaranteed Income Certificate (GIC) on January 1, 2007 (for which she paid $10,000).

2. The GIC pays $1,000 in interest income each year on December 31, 2007 to December 31, 2011 giving Mary a 10% rate of return on her investment.

3. On December 31, 20011 (the GIC’s maturity date), Mary will receive, in addition to her last interest payment of $1,000, the full amount (i.e, $10,000) that she invested on January 1, 2007.

4. During this period, inflation is expected to be 5 percent per year.

9. Price Changes 70


What is the combined (i.e., market interest) rate

of interest (to 2 decimals) on the GIC?

1. 5.00%; 2. 4.76%; 3. 10.00%

4. 15.00%; None of the above answers

Answer: Market Interest Rate = 10%1. Mary bought a five-year $10,000 Guaranteed Income Certificate (GIC) on January 1, 2007 (for which

she paid $10,000). 2. The GIC pays $1,000 in interest income each year on December 31, 2007 to December 31, 2011

giving Mary a 10% rate of return on her investment. 3. On December 31, 20011 (the GIC’s maturity date), Mary will receive, in addition to her last interest

payment of $1,000, the full amount (i.e, $10,000) that she invested on January 1, 2007. 4. During this period, inflation is expected to be 5 percent per year.

9. Price Changes 71


What is the real (inflation-free) rate of interest (to 2 decimals) on the GIC?

1. 5.00%; 2. 4.76%; 3. 5.24%; 4. 10.00%

5. None of the above answers

Ans. iR = [(1+IC)/(1+f)] – 1= [1.10/1.05] – 1 = 0.0476





9. Price Changes 72


If Mary can reinvest the interest income from the GIC at10% each year, what will be the future worth (onDecember 31, 2009; to the nearest $100) of the$10,000 investment (principal and interest income) inconstant (i.e., real or January 1, 2007 dollars)?$16,100; 2. $12,600; 3. $11,500; 4. $10,0005. None of the above answersAns. $10,000[1.13/1.053] = $11,498 or $11,500

OR $10,000(1.0476)3 = $11,498 or $11,500





9. Price Changes 73


If Mary can reinvest the interest income from the GIC at 10% each year, what will be the present worth (to the nearest dollar) of the $10,000 investment in actual dollars on January 1, 2007?

1. $16,672; 2. $10,000; 3. $11,513; 4. $0

5. None of the above answers.

Ans. $10,000[(1.1)5/(1.1)5] = $10,0001. Mary bought a five-year $10,000 Guaranteed Income Certificate (GIC) on January 1, 2007 (for which




9. Price Changes 74


What is the actual dollar value of the 3rd $1000 interest payment (i.e., the payment that Mary received on December 31, 2009)?

1. $1000; 2. $952.38; 3. $907.03; 4. $540.77


Ans. $10001. Mary bought a five-year $10,000 Guaranteed Income Certificate (GIC) on January 1, 2007 (for which she paid $10,000).




9. Price Changes 75


What is the real or constant dollar value (i.e., in January 1, 2007 dollars) of the 4th $1000 interest payment?

1. $1000; 2. $823; 3. $907; 4. $541


Ans. 1000(P/F,5%,4) = $822.70 1. Mary bought a five-year $10,000 Guaranteed Income Certificate (GIC) on January 1, 2007 (for which




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9. Price Changes 77

Next Week: Lecture 10

Project Management Fraser et al.* chapter 11

Engineering EconomicsECO 1192

Lecture 9: Decision-making with price changes

Claude Théoret

University of Ottawa

Documents

9 - Price Changes