lecture 1 managerial finance fina 6335 ronald f. singer

Lecture 1Lecture 1

Managerial FinanceManagerial Finance

FINA 6335FINA 6335

Ronald F. SingerRonald F. Singer

FinanceFinance

The study of resource allocation under The study of resource allocation under conditions of conditions of uncertainty.uncertainty.

Merges:Merges:– Economics.Economics.– Accounting.Accounting.– Statistics.Statistics.

AreasAreas

Corporate FinanceCorporate FinanceFrom the viewpoint of the Financial ManagerFrom the viewpoint of the Financial Manager

– Capital BudgetingCapital Budgeting– Dividend PolicyDividend Policy– Capital StructureCapital Structure

InvestmentsInvestmentsFrom the viewpoint of individual and institutional From the viewpoint of individual and institutional

investorsinvestors– RiskRisk– ReturnReturn– Portfolio DecisionsPortfolio Decisions

Types of Financial SecuritiesTypes of Financial Securities

Equity CapitalEquity Capital– Common StockCommon Stock

– PreferredPreferred StockStock

Debt CapitalDebt Capital– BondsBonds

Hybrid SecuritiesHybrid Securities – Why hold Securities?Why hold Securities?

The Rewards and Risks to The Rewards and Risks to Security HoldersSecurity Holders

The RewardsThe Rewards– To StockholdersTo Stockholders– To BondholdersTo Bondholders

The Risks:The Risks:– To StockholdersTo Stockholders

– To BondholdersTo Bondholders

The Goal of Financial The Goal of Financial ManagementManagement

What should be the goal?What should be the goal?

Possible measures of performance of Possible measures of performance of financial managersfinancial managers

How do managers achieve their objectives?How do managers achieve their objectives?Make Decisions thatMake Decisions that

InvestmentInvestment

The ProblemThe ProblemHow can we determine if a project How can we determine if a project will make will make

stockholders’ better or worse off???stockholders’ better or worse off???

What is an Investment?What is an Investment?Current Cash Expenditures which are Current Cash Expenditures which are

expected to generate cash inflows sometime expected to generate cash inflows sometime in the futurein the future

How to Make a Decision?How to Make a Decision?

Inflow Inflow

Benefits vs. CostsBenefits vs. Costs

ComplicationsComplications

Uncertainty Future FlowsUncertainty Future Flows

Digression on Digression on Conventions of TimeConventions of Time

Cash Inflows

Cash Outflows

ExampleExample

• For current Investment of $10,000, receive $5,000 For current Investment of $10,000, receive $5,000 within 1 year, $6,000 in years 3 through 5.within 1 year, $6,000 in years 3 through 5.

5000 6000 6000 6000.5000 6000 6000 6000.

0.0.

1 2 3 4 51 2 3 4 5

10000.10000.

• Observations:Observations:

1.1. t = 0 current time.t = 0 current time.

2.2. Everything happens at the end of a period unless Everything happens at the end of a period unless specified otherwise.specified otherwise.

Using Market Prices Using Market Prices to Determine Cash Valuesto Determine Cash Values

Suppose a jewelry manufacturer has the Suppose a jewelry manufacturer has the opportunity to trade 10 ounces of platinum opportunity to trade 10 ounces of platinum and receive 20 ounces of gold today. To and receive 20 ounces of gold today. To compare the costs and benefits, we first compare the costs and benefits, we first need to convert them to a common unit.need to convert them to a common unit.

Using Market Prices Using Market Prices to Determine Cash Values to Determine Cash Values

(cont'd)(cont'd) Suppose gold can be bought and sold for a Suppose gold can be bought and sold for a

current market price of $250 per ounce. current market price of $250 per ounce. Then the 20 ounces of gold we receive has Then the 20 ounces of gold we receive has a cash value of:a cash value of:

– (20 ounces of gold) ($250/ounce) = $5000 (20 ounces of gold) ($250/ounce) = $5000 todaytoday


(cont'd)(cont'd) Similarly, if the current market price for Similarly, if the current market price for

platinum is $550 per ounce, then the 10 platinum is $550 per ounce, then the 10 ounces of platinum we give up has a cash ounces of platinum we give up has a cash value of:value of:

– (10 ounces of platinum) ($550/ounce) = $5500(10 ounces of platinum) ($550/ounce) = $5500


(cont'd)(cont'd) Therefore, the jeweler’s opportunity has a Therefore, the jeweler’s opportunity has a

benefit of $5000 today and a cost of $5500 benefit of $5000 today and a cost of $5500 today. In this case, the net value of the today. In this case, the net value of the project today is:project today is:

– $5000 – $5500 = –$500$5000 – $5500 = –$500

Because it is negative, the costs exceed the Because it is negative, the costs exceed the benefits and the jeweler should reject the benefits and the jeweler should reject the trade.trade.

Example 3.1Example 3.1

Example 3.1 (cont'd)Example 3.1 (cont'd)

Present ValuePresent Value

The The present valuepresent value of receiving $1,000, one year of receiving $1,000, one year from today?from today?

$1000$1000

0 10 1

It is : What $1000 received one year from It is : What $1000 received one year from today is worth today.today is worth today.

Present ValuePresent Value

Present Value is:Present Value is:– How much someone would lend me on that claimHow much someone would lend me on that claim– How much I could sell the claim forHow much I could sell the claim for– How much it would cost to engage in a "similar" How much it would cost to engage in a "similar"

investmentinvestment

What is the Answer?What is the Answer?– In order to answer that question we have to know In order to answer that question we have to know

what “interest rate” is assumed.what “interest rate” is assumed.– Assume that the interest rate is 25%?Assume that the interest rate is 25%?– Thus, you pay $200 Thus, you pay $200 interestinterest to borrow $800 now to borrow $800 now

The Market Rate of InterestThe Market Rate of Interest

In this case, the initial amount is In this case, the initial amount is also the present value also the present value

OROR

0.25 =

800

200 =

Amount Initial

Interest =

Amount Initial

Amount) Initial - Amount (Future = R

0.25 =

800

200 =

Amount Initial

Interest =

Amount Initial

Amount) Initial - Amount (Future = R

1 - Value Present

Amount Future = R 1 -

Value Present

Amount Future = R

800. = 1.25

1000 =

R + 1

Amount Future = Value Present

800. = 1.25

1000 =

R + 1

Amount Future = Value Present

1/1+R 1/1+R is called the Discount Factoris called the Discount Factor Present Value = Future amount x Discount FactorPresent Value = Future amount x Discount Factor

If R is 25 % Discount Factor isIf R is 25 % Discount Factor is

and PV (1,000; 25%; 1 yr)and PV (1,000; 25%; 1 yr)

= = 1 1 [1000] [1000]

1.251.25

= 0.80 [1000]= 0.80 [1000]

= 800= 800

0.80 = 1.25

1 =

R + 1

1 0.80 = 1.25

1 =

R + 1

1

3.2 Interest Rates 3.2 Interest Rates and the Time Value of Moneyand the Time Value of Money

Time Value of MoneyTime Value of Money

– Consider an investment opportunity with the Consider an investment opportunity with the following certain cash flows.following certain cash flows. Cost: $100,000 todayCost: $100,000 today

Benefit: $105,000 in one yearBenefit: $105,000 in one year

– The difference in value between money today The difference in value between money today and money in the future is due to the time value and money in the future is due to the time value of money.of money.

The Interest Rate: The Interest Rate: An Exchange Rate Across TimeAn Exchange Rate Across Time

– Suppose the current annual interest rate is 7%. Suppose the current annual interest rate is 7%. By investing or borrowing at this rate, we can By investing or borrowing at this rate, we can exchange $1.07 in one year for each $1 today.exchange $1.07 in one year for each $1 today.

– Is the above investment worthwhile?Is the above investment worthwhile?

What is $105,000 worth today (What is $105,000 worth today ( i.e.i.e. its Present Value)? its Present Value)?

It is Worth $105,000 divided by 1.07 = $98,130.84It is Worth $105,000 divided by 1.07 = $98,130.84

– So is it worth giving up $100,000 to receive the So is it worth giving up $100,000 to receive the equivalent of $98,130.84 today?equivalent of $98,130.84 today?


ProblemProblem

– The cost of replacing a fleet of company trucks The cost of replacing a fleet of company trucks with more energy efficient vehicles was $100 with more energy efficient vehicles was $100 million million in 2007. in 2007.

– The cost is estimated to rise by 8.5% in 2008. The cost is estimated to rise by 8.5% in 2008.

– If the interest rate were 4%, what was the If the interest rate were 4%, what was the cost of a delay in terms of dollars in 2007?cost of a delay in terms of dollars in 2007?


SolutionSolution

– If the project were delayed, it’s cost in 2008 would be:If the project were delayed, it’s cost in 2008 would be: $100 million $100 million × (1.085) = $108.5 million× (1.085) = $108.5 million

– Compare this amount to the cost of $100 million in Compare this amount to the cost of $100 million in 2007 using the interest rate of 4%:2007 using the interest rate of 4%: $108.5 million $108.5 million ÷÷ 1.04 = $104.33 million in 2007 dollars. 1.04 = $104.33 million in 2007 dollars.

– The cost of a delay of one year would be:The cost of a delay of one year would be: $104.33 million $104.33 million –– $100 million = $4.33 million in 2007 $100 million = $4.33 million in 2007

dollars.dollars.

Future Value versus Present Value Future Value versus Present Value

We compared the cost of replacing the fleet today with the We compared the cost of replacing the fleet today with the Present Value of replacing it in the future. Present Value of replacing it in the future.

Alternatively we could find the Future Value of replacing it Alternatively we could find the Future Value of replacing it today, compared with the value of replacing it in the future. today, compared with the value of replacing it in the future.

Thus, the Future Value of replacing it today is: $100 million Thus, the Future Value of replacing it today is: $100 million times (1.04) = $104 million times (1.04) = $104 million – Comparing that with the actual cost of replacing it one year in the Comparing that with the actual cost of replacing it one year in the

future gives a benefit of future gives a benefit of The benefit in future value terms is thus: The benefit in future value terms is thus:

$108.5 million - $104 million or $4.5 million $108.5 million - $104 million or $4.5 million Note that in present value terms the present value of $4.5 million is:Note that in present value terms the present value of $4.5 million is:

$4.5 million divided by 1.04 or $4.33 million!!!$4.5 million divided by 1.04 or $4.33 million!!!

Figure 3.1 Converting Between Figure 3.1 Converting Between Dollars Today and Gold, Euros, or Dollars Today and Gold, Euros, or

Dollars in the Future Dollars in the Future

3.3 Present Value 3.3 Present Value and the NPV Decision Ruleand the NPV Decision Rule

The The net present value (NPV)net present value (NPV) of a project or of a project or investment is the difference between the investment is the difference between the present value of its benefits and the present present value of its benefits and the present value of value of its costs.its costs.– Net Present Value Net Present Value

(Benefits) (Costs) NPV PV PV

(All project cash flows)NPV PV

The NPV Decision Rule (cont'd)The NPV Decision Rule (cont'd)

Accepting or Rejecting a ProjectAccepting or Rejecting a Project

– Accept those projects with positive NPV Accept those projects with positive NPV because accepting them is equivalent to because accepting them is equivalent to receiving their NPV in cash today.receiving their NPV in cash today.

– Reject those projects with negative NPV Reject those projects with negative NPV because accepting them would reduce the because accepting them would reduce the wealth of investors.wealth of investors.

Choosing Among ProjectsChoosing Among Projects

Choosing Among Projects Choosing Among Projects (cont'd)(cont'd)

All three projects have positive NPV, and we All three projects have positive NPV, and we would accept all three if possible. would accept all three if possible.

If we must choose only one project, Project If we must choose only one project, Project B has the highest NPV and therefore is the B has the highest NPV and therefore is the best choice.best choice.

NPV and Individual PreferencesNPV and Individual Preferences

Although Project B has the highest NPV, Although Project B has the highest NPV, what if we do not want to spend the $20 for what if we do not want to spend the $20 for the cash outlay? Would Project A be a the cash outlay? Would Project A be a better choice? Should this affect our choice better choice? Should this affect our choice of projects?of projects?

NO! As long as we are able to borrow and NO! As long as we are able to borrow and lend at the risk-free interest rate, Project B is lend at the risk-free interest rate, Project B is superior whatever our preferences regarding superior whatever our preferences regarding the timing of the cash flows.the timing of the cash flows.

NPV and Individual Preferences NPV and Individual Preferences (cont'd)(cont'd)

NPV and Individual Preferences NPV and Individual Preferences (cont'd)(cont'd)

Regardless of our preferences for cash Regardless of our preferences for cash today versus cash in the future, we should today versus cash in the future, we should always maximize NPV first. We can then always maximize NPV first. We can then borrow or lend to shift cash flows through borrow or lend to shift cash flows through time and find our most preferred pattern of time and find our most preferred pattern of cash flows.cash flows.

WealthWealth

Wealth is the present value of all Wealth is the present value of all CurrentCurrent and and FutureFuture income.income.

Suppose that an individual has $1,000 in his/her Suppose that an individual has $1,000 in his/her pocket and has a claim on $1,000 one year from pocket and has a claim on $1,000 one year from now. What is his wealth if the interest rate is now. What is his wealth if the interest rate is 20%?20%?

$1,000 in his/her pocket is worth $1,000. $1,000 in his/her pocket is worth $1,000. $1,000 one year from now is worth $1,000 one year from now is worth $833.33 = 1,000/(1 +R) $833.33 = 1,000/(1 +R) = 1000/(1.20) = 1000/(1.20) Therefore, his/her Therefore, his/her WealthWealth is $1,833.33. is $1,833.33. You have to convert all future income to You have to convert all future income to Present Present

ValuesValues before you can add them up before you can add them up

Market Opportunity LineMarket Opportunity Line

The Market Opportunity Line The Market Opportunity Line shows how an individual can shows how an individual can exchange current for future exchange current for future consumption. consumption.

22502250

22002200

16251625

10001000

375375

500 1000 1833500 1000 1833

Possible Alternatives

EndowmentEndowment 10001000 NowNow 10001000 Next Next YearYear

How? How? 500500 ““ 16001600 ““

How?How? ZeroZero ““ 22002200 ““

WealthWealth 18331833 ““ ZeroZero ““

15001500 ““ ?? ““

Wealth and the NPV of a ProjectWealth and the NPV of a Project

Now suppose the investor has the Now suppose the investor has the opportunity to invest in only one of the three opportunity to invest in only one of the three projects: Project Aprojects: Project A

232023202292229222002200

16251625

10001000

375375 500 1000 1833 1910 1933500 1000 1833 1910 1933

Wealth and the NPV of a ProjectWealth and the NPV of a Project

Now suppose the investor has the Now suppose the investor has the opportunity to invest in only one of the three opportunity to invest in only one of the three projects: Project Bprojects: Project B

232023202292229222002200

16251625

10001000

375375 500 1000 1833 1910 1933500 1000 1833 1910 1933

Market Opportunity LineMarket Opportunity Line

Notice that this individual's wealth is indicated by the Notice that this individual's wealth is indicated by the horizontal intercept.horizontal intercept.

The Wealth is the maximum an individual can consume The Wealth is the maximum an individual can consume today by borrowing against all of his/her future incometoday by borrowing against all of his/her future income

0

33

1.2

$1,000 + $1,000=

R+1

$1,000 + $1,000=

$1,8 = Wealth

Factor countIncomexDis Future + Income Current = Wealth

Market Opportunity LineMarket Opportunity Line The slope of the market opportunity line is:The slope of the market opportunity line is:

- (1 + R)- (1 + R)

Slope = Rise/RunSlope = Rise/Run = (= (Principal + Interest)Principal + Interest) - Principal- Principal = -( 1 + = -( 1 + InterestInterest ) ) PrincipalPrincipal = -(1 + R)= -(1 + R) If you give up $500 now, you can get:If you give up $500 now, you can get: 500 X (1 + R) = 500(1.20) = $600 more next year.500 X (1 + R) = 500(1.20) = $600 more next year. If you want to get $800 more now, you must give up: If you want to get $800 more now, you must give up: 800 X (1.20) or $960 next year800 X (1.20) or $960 next year

Bottom LineBottom Line

1.1. Wealth is the Wealth is the PRESENT VALUEPRESENT VALUE of income of income streamstream

2.2. All individuals are unambiguously better off All individuals are unambiguously better off when their wealth increases.when their wealth increases.

3.3. The net present value of an investment The net present value of an investment project is the amount investors' wealth would project is the amount investors' wealth would increase (decrease) if the project were increase (decrease) if the project were undertaken.undertaken.

Lecture 2Lecture 2

Managerial FinanceManagerial Finance

FINA 6335FINA 6335

Ronald F. SingerRonald F. Singer

3.4 Arbitrage and the Law of One 3.4 Arbitrage and the Law of One PricePrice

ArbitrageArbitrage

– The practice of buying and selling equivalent goods The practice of buying and selling equivalent goods in different markets to take advantage of a price in different markets to take advantage of a price difference. An difference. An arbitrage opportunity arbitrage opportunity occurs when occurs when it is possible to make a profit without taking any risk it is possible to make a profit without taking any risk or making any investment.or making any investment.

Normal MarketNormal Market

– A competitive market in which there are no A competitive market in which there are no arbitrage opportunities.arbitrage opportunities.

3.4 Arbitrage and the Law of 3.4 Arbitrage and the Law of One Price (cont'd)One Price (cont'd)

Law of One PriceLaw of One Price

– If equivalent investment opportunities trade If equivalent investment opportunities trade simultaneously in different competitive markets, simultaneously in different competitive markets, then they must trade for the same price in both then they must trade for the same price in both markets.markets.

3.5 No-Arbitrage and Security 3.5 No-Arbitrage and Security PricesPrices

Valuing a SecurityValuing a Security

– Assume a security promises a risk-free payment Assume a security promises a risk-free payment of $1000 in one year. If the risk-free interest rate of $1000 in one year. If the risk-free interest rate is 5%, what can we conclude about the price of is 5%, what can we conclude about the price of this bond in a normal market?this bond in a normal market?

Price(Bond) = $952.38Price(Bond) = $952.38

3.5 No-Arbitrage and 3.5 No-Arbitrage and Security Prices (cont'd)Security Prices (cont'd)

Valuing a Security (cont’d)Valuing a Security (cont’d)

– What if the price of the bond is What if the price of the bond is notnot $952.38? $952.38? Assume the price is $940.Assume the price is $940.

– The opportunity for arbitrage will force the price of the The opportunity for arbitrage will force the price of the bond to rise until it is equal to $952.38.bond to rise until it is equal to $952.38.

3.5 No-Arbitrage and 3.5 No-Arbitrage and Security Prices (cont'd)Security Prices (cont'd)

Valuing a Security (cont’d)Valuing a Security (cont’d)

– What if the price of the bond is What if the price of the bond is notnot $952.38? $952.38? Assume the price is $960.Assume the price is $960.

– The opportunity for arbitrage will force the price of the The opportunity for arbitrage will force the price of the bond to fall until it is equal to $952.38.bond to fall until it is equal to $952.38.

Determining the No-Arbitrage Determining the No-Arbitrage PricePrice

Unless the price of the security equals the Unless the price of the security equals the present value of the security’s cash flows, present value of the security’s cash flows, an arbitrage opportunity will appear.an arbitrage opportunity will appear.

No Arbitrage Price of a SecurityNo Arbitrage Price of a Security

Price(Security) (All cash flows paid by the security) PV

Determining the Interest Rate Determining the Interest Rate From Bond PricesFrom Bond Prices

If we know the price of a risk-free bond, we If we know the price of a risk-free bond, we can use can use

to determine what the risk-free interest rate to determine what the risk-free interest rate must be if there are no arbitrage must be if there are no arbitrage opportunities.opportunities.

Price(Security) (All cash flows paid by the security) PV

Determining the Interest Rate Determining the Interest Rate From Bond Prices (cont'd)From Bond Prices (cont'd)

Suppose a risk-free bond that pays $1000 in Suppose a risk-free bond that pays $1000 in one year is currently trading with a one year is currently trading with a competitive market price of $929.80 today. competitive market price of $929.80 today. The bond’s price must equal the present The bond’s price must equal the present value of the $1000 cash flow it will pay.value of the $1000 cash flow it will pay.

Determining the Interest Rate Determining the Interest Rate From Bond Prices (cont'd)From Bond Prices (cont'd)

The risk-free interest rate must be 7.55%.The risk-free interest rate must be 7.55%.

$929.80 today ($1000 in one year) (1 $ in one year / $ today) fr

$1000 in one year1 1.0755 $ in one year / $ today

$929.80 today fr

The NPV of Trading SecuritiesThe NPV of Trading Securities

In a normal market, the NPV of buying or In a normal market, the NPV of buying or selling a security is zero.selling a security is zero.

(Buy security) (All cash flows paid by the security) Price(Security)

0

NPV PV

(Sell security) Price(Security) (All cash flows paid by the security)

0

NPV PV

The NPV of Trading Securities The NPV of Trading Securities (cont’d)(cont’d)

Separation PrincipleSeparation Principle

– We can evaluate the NPV of an investment We can evaluate the NPV of an investment decision separately from the decision the firm decision separately from the decision the firm makes regarding how to finance the investment makes regarding how to finance the investment or any other security transactions the firm is or any other security transactions the firm is considering.considering.

Example 3.7 Example 3.7

Valuing a PortfolioValuing a Portfolio

The Law of One Price also has implications for The Law of One Price also has implications for packages of securities.packages of securities.– Consider two securities, A and B. Suppose a third Consider two securities, A and B. Suppose a third

security, C, has the same cash flows as A and B security, C, has the same cash flows as A and B combined. In this case, security C is equivalent to a combined. In this case, security C is equivalent to a portfolio, or combination, of the securities A and B.portfolio, or combination, of the securities A and B.

Value AdditivityValue Additivity

Price(C) Price(A B) Price(A) Price(B)

Example 3.8 Example 3.8

3.6 The Price of Risk3.6 The Price of Risk

Risky Versus Risk-free Cash FlowsRisky Versus Risk-free Cash Flows

– Assume there is an equal probability of either a weak Assume there is an equal probability of either a weak economy or strong economy.economy or strong economy.

3.6 The Price of Risk (cont'd)3.6 The Price of Risk (cont'd)

Risky Versus Risk-free Cash Flows (cont’d)Risky Versus Risk-free Cash Flows (cont’d)

– Expected Cash Flow (Market Index)Expected Cash Flow (Market Index) ½ ($800) + ½ ($1400) = $1100 ½ ($800) + ½ ($1400) = $1100

Although both investments have the same expected value, Although both investments have the same expected value, the market index has a lower value since it has a greater the market index has a lower value since it has a greater amount of risk.amount of risk.

Price(Risk-free Bond) PV(Cash Flows)

($1100 in one year) (1.04 $ in one year / $ today)

$1058 today

Risk Aversion and the Risk Risk Aversion and the Risk PremiumPremium

Risk AversionRisk Aversion– Investors prefer to have a safe income rather than a Investors prefer to have a safe income rather than a

risky one of the same average amount.risky one of the same average amount.

Risk PremiumRisk Premium– The additional return that investors expect to earn to The additional return that investors expect to earn to

compensate them for a security’s risk.compensate them for a security’s risk.

– When a cash flow is risky, to compute its present When a cash flow is risky, to compute its present value we must discount the cash flow we expect on value we must discount the cash flow we expect on average at a rate that equals the risk-free interest rate average at a rate that equals the risk-free interest rate plus an appropriate risk premium.plus an appropriate risk premium.

Risk Aversion Risk Aversion and the Risk Premium (cont’d)and the Risk Premium (cont’d)

– Market return if the economy is strongMarket return if the economy is strong (1400 – 1100) / 1100 = 40%(1400 – 1100) / 1100 = 40%

– Market return if the economy is weakMarket return if the economy is weak (800 – 1000) / 1000 = –20%(800 – 1000) / 1000 = –20%

– Expected market returnExpected market return ½ (40%) + ½ (–20%) = 10%½ (40%) + ½ (–20%) = 10%

Expected Gain at end of yearExpected return of a risky investment

Initial Cost

The No-Arbitrage Price of a The No-Arbitrage Price of a Risky SecurityRisky Security

– If we combine security A with a risk-free bond that pays $800 in If we combine security A with a risk-free bond that pays $800 in one year, the cash flows of the portfolio in one year are identical one year, the cash flows of the portfolio in one year are identical to the cash flows of the market index.to the cash flows of the market index.

– By the Law of One Price, the total market value of the bond and By the Law of One Price, the total market value of the bond and security A must equal $1000, the value of the market index. security A must equal $1000, the value of the market index.

The No-Arbitrage Price The No-Arbitrage Price of a Risky Security (cont'd)of a Risky Security (cont'd)

Given a risk-free interest rate of 4%, the market Given a risk-free interest rate of 4%, the market price of the bond is:price of the bond is:

– ($800 in one year) / (1.04 $ in one year/$ today) = $769 ($800 in one year) / (1.04 $ in one year/$ today) = $769 todaytoday

– Therefore, the initial market price of security A is Therefore, the initial market price of security A is $1000 – $769 = $231.$1000 – $769 = $231.

Risk Premiums Depend on RiskRisk Premiums Depend on Risk

If an investment has much more variable If an investment has much more variable returns, it must pay investors a higher risk returns, it must pay investors a higher risk premium.premium.

Risk Is Relative to the Overall Risk Is Relative to the Overall MarketMarket

The risk of a security must be evaluated in The risk of a security must be evaluated in relation to the fluctuations of other investments relation to the fluctuations of other investments in the economy. in the economy.

A security’s risk premium will be higher the A security’s risk premium will be higher the more its returns tend to vary with the overall more its returns tend to vary with the overall economy and the market index. economy and the market index.

If the security’s returns vary in the opposite If the security’s returns vary in the opposite direction of the market index, it offers insurance direction of the market index, it offers insurance and will have a negative risk premium.and will have a negative risk premium.

Risk Is Relative Risk Is Relative to the Overall Market (cont'd)to the Overall Market (cont'd)

Risk, Return, and Market PricesRisk, Return, and Market Prices

When cash flows are risky, we can use the When cash flows are risky, we can use the Law of One Price to compute present values Law of One Price to compute present values by constructing a portfolio that produces by constructing a portfolio that produces cash flows with identical risk.cash flows with identical risk.

Figure 3.3 Converting Between Figure 3.3 Converting Between Dollars Today and Dollars in One Dollars Today and Dollars in One

Year with Risk Year with Risk Computing prices in this way is equivalent to Computing prices in this way is equivalent to

converting between cash flows today and the converting between cash flows today and the expected cash flows received in the future using a expected cash flows received in the future using a discount rate discount rate rrss that includes a risk premium that includes a risk premium

appropriate for the investment’s risk:appropriate for the investment’s risk:

( risk premium for investment ) s fr r s

Figure 3.3 Converting Between Figure 3.3 Converting Between Dollars Today and Dollars in One Dollars Today and Dollars in One

Year with RiskYear with Risk

3.7 Arbitrage with Transactions 3.7 Arbitrage with Transactions CostsCosts

What consequence do transaction costs What consequence do transaction costs have for no-arbitrage prices and the Law of have for no-arbitrage prices and the Law of One Price?One Price?

– When there are transactions costs, arbitrage When there are transactions costs, arbitrage keeps prices of equivalent goods and securities keeps prices of equivalent goods and securities close to each other. Prices can deviate, but not close to each other. Prices can deviate, but not by more than the transactions cost of the by more than the transactions cost of the arbitrage.arbitrage.

Problem of the DayProblem of the Day

Find the Wealth of an individual who will Find the Wealth of an individual who will earn $500,000 over the current year and who earn $500,000 over the current year and who has $2,000,000 equity in assets (such as a has $2,000,000 equity in assets (such as a home, a car, cash, etc.). Assume the home, a car, cash, etc.). Assume the interest rate is 8%interest rate is 8%

Find the wealth of the same individual who Find the wealth of the same individual who also can invest up to $200,000 in a machine also can invest up to $200,000 in a machine which will produce widgets. The rate of which will produce widgets. The rate of return for this investment is 17%.return for this investment is 17%.

Questions?Questions?

lecture 1 managerial finance fina 6335 ronald f. singer

Documents

contd slide

future slide

singer slide

cash values contd

current cash expenditures

present value present

market prices

ounces of platinum