mid-term review 2014

THE UNIVERSITY OF HONG KONG

FACULTY OF BUSINESS AND ECONOMICS

FINA1003/1310A/B/C Corporate Finance

FIRST SEMESTER, 2014-2015

Review for Mid-term Exam

Date: 29 Oct (Wednesday)

Time: 7-9pm; Venue: MWT2; T4; T6 (Refer to the Room Allocation on Moodle)

Coverage: Chapter 1, 5-8, 12

Format: Part (A): MCQ 45%; Part (B): Long Numerical Questions 55%

Round off your answers to 2 decimal points

Part (A) MCQ

1. When the management of a business is conducted by individuals other than the

owners, the business is more likely to be a:

A. Corporation

B. Sole Proprietorship

C. Partnership

D. General Partnership

E. Limited Partnership

2. Which of the following are advantages of the corporate form of business

ownership?

I. Limited liability for firm debt

II. Double taxation

III. Ability to raise capital

IV. Unlimited firm life

A. I and II only

B. B. III and IV only

FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO

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C. I, III, and IV only

D. II, III, and IV only

E. I, II, III, and IV

3. Clives Pawn Shop charges an interest per month on loans to its customers. Like

all lenders, Clive must report an APR to consumers. If the effective annual rate

is 213.84%, what APR should the Clive report?

A. 213.84%

B. 17.82%

C. 120%

D. 10%

E. 615.53%

EAR = 213.84% = [(1 + r/12)12 1] 100

4. A loan where the borrower pays interest each period, and repays some of the

principal of the loan over time is called a(n) _____ loan.

A. Continuous

B. Pure Discount

C. Amortized

D. Interest-Only

E. None of Above


3

5. Dexter Mills issued 20-year bonds a year ago at a coupon rate of 11.4%. The

bonds make semiannual payments. The yield-to-maturity on these bonds is

9.2%. What is the current bond price?

A. $985.55

B. $991.90

C. $1,192.16

D. $1,195.84

E. $1,198.00

6. Which one of the following bonds is the least sensitive to interest rate risk?

A. 3-year; 4 percent coupon

B. 3-year; 6 percent coupon

C. 5-year; 6 percent coupon

D. 7-year; 6 percent coupon

E. 7-year; 4 percent coupon

7. A stock pays a constant annual dividend and sells for $31.11 a share. If the rate

of return on this stock is 9%, what is the dividend amount?

A. $1.40

B. $1.80


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C. $2.20

D. $2.40

E. $2.80

$31.31 = X / 0.09

8. High Country Builders currently pays an annual dividend of $1.35 and plans on

increasing that amount by 2.5% each year. Valley High Builders currently pays

an annual dividend of $1.20 and plans on increasing its dividend by 3% annually.

Given this information, you know for certain that the stock of High Country

Builders' has a lower ______ than the stock of Valley High Builders.

A. market price

B. dividend yield

C. capital gains yield

D. total return

E. The answer cannot be determined based on the information provided.

9. Which of the following statements is correct in relation to a stock investment?

I. The capital gains yield can be positive, negative, or zero.

II. The dividend yield can be positive, negative, or zero.

III. The total return can be positive, negative, or zero.

IV. Neither the dividend yield nor the total return can be negative.

A. I only

B. I and II only

C. I and III only

D. I and IV only

E. IV only

10. Calculate the standard deviation of the following rates of return:


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A. 10.79 %

B. 12.60 %

C. 13.48 %

D. 14.42 %

E. 15.08 %

Average return = (0.07 + 0.25 + 0.14 - 0.15 + 0.16)/5 = 0.094

Standard deviation = [1/(5 - 1)] [(0.07 - 0.094)2 + (0.25 - 0.094)2 +(0.14 - 0.094)2

+(-0.15 - 0.094)2 + (0.16 - 0.094)2] = 15.08 %

Part (B) Long Numerical Questions

Question 1

Consider a 6% semi-annual coupon bond, 10 years to maturity, with the following

prices given different YTM:

YTM = 5% YTM = 6% YTM = 15% YTM = 16%

Bond Price $1,077.95 $1,000.00 $541.25 $509.09

Calculate the percentage change in bond price and explain their different levels of

price risk using the following 2 cases:

(1) If required yield increases from 15% to 16%

(2) If required yield increases from 5% to 6%


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(1) The bond price falls (in percentage) is: $509.09 $541.25$541.25

= 0.059409

(2) The bond price falls (in percentage) is: ($1,000.00 $1,077.95) / $1,077.95 =

0.072310

We can conclude that there is more volatility in a low-interest-rate environment

because there was a greater fall (7.23% versus 5.94%).

Question 2

Clive Inc., has 11% coupon bonds making annual payments with a YTM of 8.5%.

The current yield on these bonds is 9.06%. How many years do these bonds have

left until they mature?

Current yield = 0.0906 = $110/P0

P0 = $110/.0906 = $1,214.13

P0 = $1,214.13 = $110[(1 (1/1.085)t ) / 0.085 ] + $1,000/1.085t

t = 15.96 16 years

Question 3

The current dividend yield on Clayton's Metals common stock is 2.5%. The company

just paid a $1.48 annual dividend and announced plans to pay $1.54 next year. The

dividend growth rate is expected to remain constant at the current level. What is the

required rate of return on this stock?


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Chapter 6 Discounted Cash Flow Valuation

Annuities

Annuities: A series of equal periodical cash flow that occur at regular interval. Two

types of Annuity:

(1) Ordinary Annuity: Each cash flow is at the end of each period

(2) Annuity Due: Each cash flow is at the beginning of each period

Present Value of Annuity

PV Annuity Factor (PVA): Present Value of a t-year annuity of $1

)2()1(

...)1(1

)1(

)1()1(

...)1()1(1

12

32

+++

++

++=+

+++

++

++

+=

n

n

r

C

r

C

r

CCrPVA

r

C

r

C

r

C

r

CPVA

(2) - (1)

+=

nrr

CPVA

)1(

11

Future Value of Annuity

+=

+

+=

+=

r

rCFVA

rrr

CFVA

rPVAFVA

n

n

n

n

1)1(

)1()1(

11

)1(

Annuity Due

An annuity for which cash flows occur at the beginning of the period

Annuity Due = Ordinary Annuity (1 + r)


8

Concept Check: All other things being equal, will the present value of an

annuity due and present value of an ordinary annuity be the same?

APR vs EAR

APR: Annualized interest rate based on simple interest

APR = periodic rate m

EAR: Annualized interest rate based on compound interest; actual rate interest

earned/paid

EAR = (1+APR/m)m -1

Example:

A credit card charges 18% APR compounded monthly; What is the EAR?

APR = 18%, and m = 12, so periodic rate = 15% / 12 = 1.5%

EAR = (1+1.5%)12 1 = 19.56%


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Example: A check-cashing store is in the business of making personal loans to

walk-up customers. The store makes only 1-week loans at 7% interest per week.

(a) What APR must the store report to its customers? APR = 52(7%) = 364%

(b) What EAR are customers actually paying? EAR = (1 + .07)52 1 = 3,273.53%

Things to Remember:

You ALWAYS need to make sure that the interest rate and the time period match:

(1) If you are looking at annual periods, you need an annual rate.

(2) If you are looking at monthly periods, you need a monthly rate.

*If you have an APR based on monthly compounding but your cash flow periods are

not monthly, you can first convert APR to EAR and then get the appropriate periodic

rate

HW#1 Question 5

Assume that you are planning to save for the education for your child. You

want to let your child study in US when he gets to high school at the age

of 15 that is exactly 10 years from today. You expect your child will stay

and study overseas for 7 years. You estimate that he needs to withdraw

$400,000 per year for 7 years beginning on his 15th birthday to cover tuition

and living expenses. You intend to invest in a mutual fund which offers 9%

APR compounded semi-annually.

(a) If you have decided to make one lump sum payment today to get enough

money for your child, how much should you invest today? (Convert it

to EAR first)

(b) If you make semi-annual contribution starting six months from now,

how many contributions will you make? How much should you invest

each time? Assume that you will make the last contribution when your

son turns 15. (Apply 9%, which is also the periodic rate)


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(c) If you make monthly contribution starting today, what amount should

you deposit each time? Assume that you will make the last contribution

when your son turns 15. (Convert it to EAR first)

Loan Types

(i) Pure Discount loan

Pays the lump sum on expiration, no periodical payment; e.g. T-bills

(ii) Interest-only loan

Pays interests in each period and principal on expiration; e.g. corporate bonds, T-

bonds

(iii) Amortized loan

Amortizing the principal into the same periodical payments; the total payment in

each period is reducing over time

- Fixed amount of principal

- Fixed amount of total payments (principal and interest) each period, e.g.

Personal Loans & Mortgages

Example: Yare hired as a financial planner. Please work out an amortization

schedule for a nine-year loan of $90,000 which requires equal annual payments. The

interest rate is 4.5% per year.

Year

Beginning

Balance

Total

Payment

Interest

Payment

Principal

Payment

Ending

Balance

1 90,000.00 12,381.70 4,050.00 8,331.70 81,668.30

2 81,668.30 12,381.70 3,675.07 8,706.63 72,961.67

3 72,961.67 12,381.70 3,283.28 9,098.43 63,863.24

4 63,863.24 12,381.70 2,873.85 9,507.86 54,355.39

5 54,355.39 12,381.70 2,445.99 9,935.71 44,419.68


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6 44,419.68 12,381.70 1,998.89 10,382.82 34,036.86

7 34,036.86 12,381.70 1,531.66 10,850.04 23,186.81

8 23,186.81 12,381.70 1,043.41 11,338.30 11,848.52

9 11,848.52 12,381.70 533.18 11,848.52 0.00

Chapter 7 Interest Rates and Bond Pricing

Annuities and Bond Pricing

t

t

r

CFV

r

C

r

CPV

)1(...

)1()1( 21 +

+++

++

+=

Present Value Annuity Factor (PVA): Present Value of a t-year annuity of $1

+=

nrr

CPVA

)1(

11

Present Value of Bond: Present Value of a n-year annuity of $Coupon paid

annually, i.e. m =1, plus the Present Value of Face Value:

tnr

Face

rr

CouponPV

)1()1(

11

++

+=

Given that bond make annual coupon payment periodically, i.e. m 1, the bond

pricing formula becomes:

(1) Par Bond: Bond sells at a face value (of $1,000) if coupon rate = market

interest rate


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(2) Discount Bond: Bond sells at a discount if coupon rate < market interest rate

(3) Premium Bond: Bond sells at a premium if coupon rate > market interest rate

Bond Yields

Current Yield

Annual coupon payments divided by bond price.

Yield to Maturity (YTM)

(i) Interest rate for which the present value of bond equal the market price

(ii) Total annual expected return if you buy the bond today and hold to maturity

Holding Period Returns (HPY) / Realized Returns

(1) The yield-to-maturity on a bond is the interest rate you earn until the maturity if

interest rates do not change.

(2) If you actually sell the bond before it matures, your realized return is known as

the Holding Period Return.

Real Rate of Returns

A bond that pays interest annually yields a 7.25% rate of return. The inflation rate

for the same period is 3.5%. What is the real rate of return on this bond?

Using Fisher Equation:

(1 + .0725) = (1 + r) (1 + .035) r = 3.62%


13

Interest Rate Risks of Bond Pricing

First Fundamental Properties: Bond Price changes in the opposite direction from

the change in the required yield

Second Fundamental Properties: The rate of Bond Price decreases is faster for

low yields than it is for high yield bond

Price-Yield Relationship for a 20-year 10% coupon bond

Chapter 8 Stock Valuation

Stock Valuation: Some Simplifying Assumptions

To make above equation more applicable, some simplifying assumptions about the

pattern of dividends are necessary.

Three different assumptions can cover most growth patterns:

(1) Zero-growth rate: Dividend payments remain constant over time; that is, they

have a growth rate of zero.

(2) Constant Growth: Dividends have a constant-growth rate g.


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(3) Supernormal growth: Dividends have a mixed growth rate pattern; that is,

dividends have one payment pattern then switch to another.

Zero-Growth Dividend Model

The dividend payment pattern remains constant over time:

D1 = D2 = D3 = . . . = D

In this case the dividend-discount model becomes:

If we forecast no growth for the stock (i.e. dividends keep constant forever), the

stock will become a perpetuity:

R

DP =0

Constant-Growth Dividend Model

Dividends expected far in the future have a smaller present value than dividends

expected in the next few years, and so they have less effect on the price on the stock.

If we take D0 to be the dividend just paid and g to be the constant growth rate, the

value of a share of stock can be written as:

As long as the growth rate, g, is less than the discount rate, R, the present value of

this series of cash flows can be written as:


15

In other words, the constant-growth dividend model tells us that the current price of

a share of stock is the next period dividend divided by the difference between the

discount rate and the dividend growth rate.

This constant growth model or the Gordon model is used to find the value of a

stock whose dividend is expected to grow at a constant rate (g) forever. The value

obtained, P0, is the theoretical or intrinsic value of the stock.

The basic assumption for the model to hold requires R > g. Why do we assume

that R > g?

(1) R may be less than g in the short-run. The supernormal growth problem is an

example of this situation.

(2) In equilibrium, high returns on investment will attract capital which, in the

absence of technological change, will ensure that in succeeding periods, higher

returns cannot be earned without taking greater risk. But taking greater risk will

increase R, so g cannot be increased without raising R.

Supernormal non-constant Growth Model

Two Stages of growth:


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During the early part of their lives, very successful firms experience a super-normal

rate of growth in earnings.

- Given that growth rate cannot exceed the required return indefinitely, but it

certainly could do so for some number of years.

- To avoid the problem of having to forecast and discount an infinite number of

dividends, we will require that the dividends start growing at a constant rate

sometime in the future.

- 3-Steps Valuation:

- Estimate the dividend during non-constant growth period

- Estimate the PV of the constant growth dividends at the end of non-constant

growth period which is also the beginning of the constant growth period

- Get the present value of the above two values

Example: The growth rate for firm ABC is expected to be 20% for next two

years, and 6% thereafter. The current dividend is $1.60, and the firms required

rate of return is 10%. Whats stock worth today?


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Components of Required Rate of Return

Rearrange P0 = D1 / (R g) to find R:

R = (D1 / P0 ) + g

(1) D1 / P0 = Dividend yield

(2) g = Capital gains yield or percentage increase in stock price

R = dividend yield + capital gains yield

Example: The next dividend payment by Carroll, Inc., will be $1.90 per share. The

dividends are anticipated to maintain a 5.5 percent growth rate, forever. If the stock

currently sells for $47.00 per share, what is the dividend yield? What is the expected

capital gains yield?

(1) Dividend yield = D1 / P0

Dividend yield = $1.90 / $47.00 = 4.04%

(2) Capital gains yield = 5.5%

The total (expected) return on the stock:

R = D1 / P0 + g = 4.04% + 5.50% = 9.54%


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Summary of Topics in first half of the Course

(List provided here is by no means of exclusive for the Mid-term Exam)

Chapter 1 - What is Corporate Finance?

Financial Manager

Corporate Structure

The Goal of the Financial Management

Agency Problem

Financial Markets

Chapter 5 Time Value of Money

Calculate simple interest

Calculate compound interest

Calculate Present Value (PV)

Calculate Future Value (FV)

Calculate rate of return

Calculate number of periods or the length of time needed to grow the

investment

Problem Solving: Simple vs Compound Interest; Calculating Number of Periods

Chapter 6 Discounted Cash Flow Valuation

PV and FV of multiple cash flows

Level Cash Flows: Annuity and perpetuity

Annuity due and perpetuity due

Growing annuity and perpetuity

Interest Rates: APR, APY and EAR

Loan types and loan amortizations

Problem Solving: Annuity; Perpetuity; Conversion of APR, APY and EAR;

Mortgages and Amortization


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Chapter 7 Interest Rate and Bond Valuation

Bond basics and valuation

Interest Rate Risk

Current yield, YTM and HPR

More about Bond (read the book)

Interest Rate and Inflation

Interest rate determinants

Problem Solving: Computation of Bond Price, Current Yield, Capital Gain Yield;

Real rate and Inflation rate (Fisher Equation)

Chapter 8 Stock Valuation

Features of common stocks and preferred stocks

Valuation of common stocks and preferred stocks

Stock Market

Problem Solving: Constant Growth, Supernormal Growth Model; Computation of

Dividend Yield; Dividend Growth Rate

Chapter 12 Some Lessons from Capital Market History

Calculate percentage and dollar returns

Historical return and risk by different types of assets

Market efficiency

Problem Solving: Computation of Average Return; Standard Deviation

mid-term review 2014

Documents

dividend yield

year bonds

percent coupon

coupon rate

constant annual dividend

capital iv

stock of high country

stock of valley high