advanced corporate finance lecture 1

8/12/2019 Advanced Corporate Finance Lecture 1

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FINA0304 Advanced Corporate Finance

Prof. Keith K. P. Wong

Fall 2013

Course Objective:The objective of this course is to developtheoretical and practical tools for corporatefinancial decisions. Topics covered include:discounting and compounding, valuation ofbonds and stocks, pricing options andderivatives, capital budgeting, capital structure,and real options.Subtle elements of asymmetric information andconflict of interests among various claimants areemphasized.


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ReferencesBrealy, R. A., S. C. Myers, and F. Allen, 2006,Corporate Finance , 8th ed., McGraw-Hill.Shockley, R. L., 2007, An Applied Course in RealOptions Valuation. Thomson South-Western.

Grading:The course grade is made up as follows:Mid-Term Test October 24 (Thursday) 30%Homework Biweekly 10%Final Exam To Be Announced 60%

Office: KK930 Tel.: 2859-1044 E-mail: [email protected]

Office hrs: 2:00p.m. 3:00p.m., Friday


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The study of corporate finance Capital budgeting

Process of planning and managing a firmsinvestment in fixed assets.

Capital structureMix of debt and equity used by a firm.

Working capital managementManaging short-term assets and liabilities of afirm.

Balance-sheet model of a firm

Current liabilitiesCurrent assets

Fixed assetsTangible assetsIntangible assets

Long-term debt

Shareholdersequity

Total value of assets Total value of thefirm to investors

Net working capital


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Goal of financial management Profit maximization?

Current profits or future profitsProfits can be calculated in different ways.

Maximize the market value of shareholdersclaimsCurrent stock priceForward looking objective

Separation of ownership and control

Principal-agent relationship betweenshareholders (principals) and management(agents).Diffuse shareholder ownership makes effectivecontrol of management difficult.

Control devices used by shareholders to alignmanagements interest with theirs:(i) Board of directors(ii) Managerial compensation contracts(iii) Takeovers(iv) Labor market competition


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Lecture note 1

Discounting and Compounding

Time Value of Money

A dollar today is worth more than a dollar later. Present dollars and future dollars are different

kinds of money, e.g., HK$ vs. US$.

To compare present and futures dollars, weneed some exchange rates. Compounding: e.g., US$1 = HK$7.8 Discounting: e.g., HK$1 = US$0.13


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The One-Period Case In the one-period (two dates, 0 and 1) case,

Present cash flow ( C 0) Future value ( FV )

0 1

the formula for the future value at date 1 can bewritten as

where r is the appropriate interest rate for thatperiod. (1 + r ) is referred to as the compoundfactor.

The formula for present value ( PV ) at date 0 canbe written as

Present value ( PV ) Future cash flow ( C 1)

0 1

1/(1+ r ) is referred to as the discount factor.


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The Multiperiod Case Compound interest vs. simple interest The general formula for the future value over T

periods can be written as

Example:

Suppose that you invest $10,000 at 5% interest,compounded annually, for three years. What isthe total amount due at the end of theinvestment?

Cash flow of the investment

Year 0 Year 1 Year 2 Year 310,000 10,000 10,000 10,000

Interest 500 500 500500 500

interest on interest 25 25500

2525

1.25Total amount after 3 years 11,576.25


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Solution:

By the general formula, we obtain the sameanswer:

FV = $10,000 (1 + 5%) 3 = $11,567.25

The general formula for the present value over T periods can be written as

Example:Suppose that you want to prepare $10,000 topay the school fee 3 years later. The bank offers5% interest, compounded annually. How muchdo you need to deposit in the bank?


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SolutionLet PV be the amount of deposit.By the general formula,PV = $10,000/(1.05) 3 = $8,638.38

Cash flow of the deposit

Year 0 Year 1 Year 2 Year 3

8,638.38 8,638.38 9,070.29 9,523.81Interest 431.92 453.51 476.19Total amount after 3 years 10,000

Compounding Periods

Compounding an investment m times a year forT years provides for future value of wealth:

where r is the stated annual interest rate(i.e., rate before considering any compoundingeffects).


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Discounting an investment m times a year for T years provides for present value of wealth:

Example (Your school fee again):Suppose that the bank offers 5% interest,compounded quarterly, this time. How much doyou need to deposit in the bank?

Solution Annual interest rate: r = 5%Number of compounding periods a year:

m = 1

4 = 4Total number of years: T = 3The amount of the deposit= $10,000/(1 + 5%/4) 4 3 = $8,615.09

< $8,638.38


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A Comparison Compounding effects

After 5 years, the payouts are 1.276,1.2801 and1.284 respectively.

Continuous Compounding

In the limiting case of continuous compounding,the formula for the future value in year t is

where e = 2.7182818 Proof. Note that


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Applying lHpitals rule, we have

Hence, we have

The formula for the present value in continuousdiscounting is


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Effective Annual Interest Rates The Effective Annual Interest Rate ( EAR ) is the

annual interest rate that would give us the sameend-of-investment wealth:

where the equality holds when m = 1 or r = 0.

Example:Suppose that you invest $10,000 for 3 years at12% compounded monthly. What is the EAR on

this investment? Solution:r = 12%, m = 1 12 = 12EAR = (1 + 12%/12) 12 1 = 12.68%


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The Multiple Cash-Flow Case The general formula for the future value of a

stream of cash flows,

C 0 C 1 C 2 C 3 .. C N ... FV

0 1 2 3 N T

over T N periods can be written as

The general formula for the future value of astream of cash flows,

C 0 C 1 C 2 C 3 .. C N

0 1 2 3 N

can be written as


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Simplifications Perpetuity: A constant stream of cash flow, C ,

that lasts forever.

The formula for the present value of a perpetuityis:

Proof: Buy the perpetuity for one period and thensell, you get C in the holding period.

PV C + PV

0 1


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Growing perpetuity: A stream of cash flows, C ,that grows at a constant rate, g , forever.

The formula for the present value of a growingperpetuity is:

if g < r .

Proof:

C C (1 + g ) ..

0 1 2

C (1 + g ) C (1 + g )2 ..

0 1 2 3


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PV C + PV (1 + g )

0 1

Annuity: A stream of constant cash flows, C , thatlasts for a fixed number of periods.

PV C C C . C

The formula for the annuity is:


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Proof:T -period annuity

C C C .. C

0 1 2 3 T Perpetuity

C C C .. C C ..

0 1 2 3 T T + 1

PV of T-period annuity= PV of perpetuity

0 0 0 .. 0 C ..

0 1 2 3 T T + 1

=


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Growing annuity: A stream of cash flows thatgrows at a constant rate for a fixed number ofperiods.

The formula for the present value of an annuity

is :

ExampleMr. Wong has recently bought a tiny apartmentat a price of $ 3 million dollars. Hang Seng Bankoffers a 70% 10-year mortgage at an interest

rate of prime minus 2.5%. The current prime rateis 5%.1. What is the installment amount?2. What will be the interest paid and principal

paid in the 60th installment payment?3. What will be the outstanding balance at that

time?


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Solution1. Interest rate = 5% 2.5% = 2.5%

Amount borrowed = $3m 70% = $2.1mNo. of installments = 10 12 = 120Monthly payment = P

=> Annuity with 120 periods

2. The balance right after the 59th installment= PV of the annuity with 61 periods= [$19,796.68/(2.5%/12)]

[1 1/(1+2.5%/12) 61]= $1,132,908.20


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3. Interest paid= $1,132,908.2 (2.5%/12) = $2,360.23Principal paid= $19,796.68 $2,360.23 = $17,436.45Outstanding balance= $1,132,908.20 $17,432.45= $1,115,475.75

Net Present Value (NPV) Rule

A project requires an investment of I at t = 0 andgenerates a certain cash flow of CF t at t = 1,2, , T .

The projects NPV is given by

where r is the riskless rate of interest. If the stream of cash flows are risky, r would be

the risk-adjusted required return.


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The NPV rule: Accept a project if its NPV > 0.

Accepting positive NPV projects maximizesshareholders wealth.

How to cash in the future cash flows of theproject today?

Year 0 1 2 3 T Project I CF 1 CF 2 CF 3 CF T

Borrow CF 1 0 0 0

for 1 year Borrow 0 CF 2 0 0for 2 years

Borrow 0 0 0 CF T for T years


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Net cash flow at date 0

=

= NPV (Cash in pocket)

Ranking criteria:Choose the project with the highest NPV.Year 0 1 2 T

Project A I A CF 1 A CF 2 A CF TAProject B I B CF 1B CF 2B CF TBIf NPV A > NPV B, project A is preferred toproject B.

Objective:Replicate the future cash flows of project B usingproject A and riskless borrowing and lending.


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Example:Project A requires $1.5 million to yield $0.2million in next year and $2 million two yearslater. Project B requires $2 million to yield$1.25 million each year in the next two years.Both projects are risk-free. Your boss likesthe constant cash flow of project B. How areyou going to persuade him/her that project Bis in fact dominated by project A? Theriskless rate of interest is 10%.NPV(A) = $0.34m NPV(B) = $0.17m

Year 0 1 2

Project A 1.5 0.2 2

Lend 0.95for 1 year 0.95 1.05 0Borrow 0.62

for 2 years 0.62 0 0.75Total 1.83 1.25 1.25Project B 2 1.25 1.25


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Investment vs. Consumption

Some people prefer to consume now. Someprefer to invest now and consume later.

How do we know all shareholders prefer theNPV rule as their investment rule?

As long as capital markets are complete,investment and consumption decisions are

separable.

Example:Individual A wants to consume now. IndividualB wants to wait and consume later. Each ofthem has $185 that can be consumed rightaway or invested in a project that returns $210at the end of the year. The rate of return on theproject is 13.5%.(1) Capital markets are incomplete in that A

and B cannot borrow and lend.(2) Capital markets are complete in that A and

B can borrow and lend at 5%.


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185 DollarsNow

DollarsNext Year

210

B invests $185 now andconsumes $210 nextyear

A consumes$185 now.

185 200 DollarsNow

DollarsNext Year

210

194

B invests $185 now andconsumes $210 nextyear

A invests $185 now,borrows $200 andconsumes now.

advanced corporate finance lecture 1

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