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Transcript of Mid-term Review 2014
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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
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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
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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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)
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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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%
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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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:
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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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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FINA1003/1310 Review for Mid-term Exam_________________________________________________Mr. Clive Man Chung HO
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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