FINA1310FGH Corporate Finance
Semester 2 2020-2021
Assignment 1
Due on 17/3 (Wed) at 17:00. No late submission will be accepted. Both typed and
hand-written works are acceptable. Please scan your work properly and combine them
into one consolidated pdf file. Each group needs to submit once only. Do not forget
to indicate your name, email, UID, and subclass clearly.
Group
Name
Member
01
Email
UID
Subclass
02
03
04
05
Calculation Questions (200 points)
Workings should be submitted for all questions requiring calculations. Please round
off all answers to 4 decimal places.
Question 1 (12 points)
Your company plans to provide you a bonus as a reward for your hard work this year.
They offered to give you either $7,000 today or $13,000 in 8 years.
a. If the interest rate is 7% compounded annually, which option is preferable? (4
points)
b. What interest rate (APR compounded annually) would make the two options
indifferent? (4 points)
c. Suppose your company also provide you the third option of giving you $1,300 per
year for 8 years. If the interest rate remain unchanged at 7% compounded
annually, which option is preferable? (4 points)
Question 2 (6 points)
You would like to buy a car that cost $300,000. You expected to receive a windfall of
$240,000 from an investment you made in a friend’s business in 3 years. In how many
years from now will you have enough to buy the car if you invest the whole windfall
amount in the Bank at 8% compounded annually? (6 points)
Question 3 (26 points)
Your bank sells you an annuity that pays $2,800 every month from the end of Nov
2020 to the end of Jan 2025 with annual interest rate 6% compounded monthly.
a. What’s the price of this annuity on Nov 1, 2020? (5 points)
b. What’s the price of this annuity on Apr 1, 2021? (Hint: Imagine today is Apr 1,
2021, how much are you willing to buy this annuity which has already made
several payments in the past months?) (5 points)
c. What’s the future value of this whole annuity at the end of Jan 2025? (5 points)?
d. What’s the future value of all the payments at the end of Sept 2025 (assume the
interest rate stays the same after the end of Jan 2025)? (5 points)
Suppose your bank also sells you an annuity product that pays $3,100 at the beginning
of each month from the beginning of Aug 2021 to the beginning of Jun 2024 with
annual interest rate 8% compounded monthly.
e. What is the price of this annuity due at the beginning of Aug 2021? (6 points)
Question 4 (14 points)
Fredrick wants to have $1,600,000 when he retires in 32 years.
a. How much does he have to save each quarter if he can earn an APR of 14%
compounded quarterly? (8 points)
b. Fredrick needs to finance his retirement consumption for 18 years after he retired
using the $1,600,000 he have at retirement. Thereafter, his son will support his
retirement consumption. How much can he consume each quarter during the 18
years retirement? (assume the interest rate stays the same) (6 points)
Question 5 (14 points)
You are planning to move your money to another bank. There are three investments
you are considering:
Investment 1: Invest in High Growth Bank that offers a weekly interest rate of
0.31% compounded weekly.
Investment 2:
Investment 3:
Invest in Superior Bank that offers a monthly interest rate of 1.4%
compounded monthly.
Invest in Exceptional Bank that offers to pay 16.7% compounded
annually.
a. What are the APRs for the three investment options? (3 points)
b. What are the EARs for the three investment options? (6 points)
c. Which investment option should you choose? (1 points)
d. Now suppose you planned to move your money to High Growth Bank as it locates
nearest to your home. Knowing your plan, your current bank’s manager offers to
match the rate you have been offered by High Growth Bank. The account at your
current bank would pay interest every six months. What APR with semiannual
compounding your current bank must offer you to be indifferent with High
Growth Bank’s offer? (4 points)
Question 6 (10 points)
Your rich relative has just bequeathed you an insurance policy that will make
quarterly payment of $4,200 for the first 8 years. Thereafter, the insurance policy will
start making payment of $1,200 every quarter forever. If the interest rate is 12%
compounded quarterly. What is the value of the insurance policy today? (10 points)
Question 7 (14 points)
Blake has just taken a $540,000, 6 years loan at 3% with a fixed amount of principal
to be repaid every year.
a. What is the total amount that he will need to pay at the end of year 5? (Prepare an
amortization table)(6 points)
Year
Beginning
Principal Balance
1
$540,000
Total
Payment
Interest
Payment
Principal
Repayment
Ending
Principal
Balance
2
3
4
5
6
$0
If Blake renegotiated the loan term with the bank and he is allowed to repay the loan
with equal annual payment over 6 years and the same interest rate.
b. How much interest is paid in the fifth year? (Prepare an amortization table) (8
points)
Year
Beginning
Principal Balance
1
$540,000.00
Total Payment
Interest
Payment
Principal
Repayment
Ending
Principal
Balance
2
3
4
5
6
$0
Question 8 (26 points)
You just bought two different bonds today. Bond A offers 13% coupon. Bond B
offers 5% coupon. Both bonds make annual payments, have a YTM of 8%, and have
10 years to maturity.
a. What are the bond prices this year? What type of bond A and B are respectively?
(i.e. whether it is a Par Bond, Discount Bond or Premium Bond) (6 points)
b. What are the current yields for the bonds this year? (4 points)
c. If the YTM for both bonds remain unchanged, what are the expected bond prices 3
years later? (6 points)
d. Explain the price-time relationship for bond selling at premium or discount based
on the previous parts findings, assuming the interest rate remain unchanged (Hint:
How the price change across time? And at maturity?) (4 points)
e. Suppose that 3 years have passed, and the YTM for Bond B has increased to 10%.
You decide to sell Bond B today. What is the holding period return from holding
Bond B in these 3 years? (6 points)
Question 9 (20 points)
You would like to pursue further studies after you completed your undergraduate
degree in 4 years. You are able to save $46,000 in real dollar (i.e. in today’s value)
each year for the next 4 years. The nominal return on your saving is 6.6% and the
inflation rate is 2.5%.
a. What real amount would you have saved to achieve your goal in 4 years? (6
points) (Hint: What is the total future value in real term?)
b. What nominal amount would you have saved to achieve your goal in 4 years? (6
points)
c. What are the values of the real cash flows today? (4 points)
d. What are the values of the nominal cash flows today? (4 points)
Question 10 (20 points)
You are considering the following two different bonds to add to your investment
portfolio.
•
•
Everrich Bond has a face value of $40,000 and pays $800 every quarter.
MaxWealth Bond is a 16% coupon bond with a face value of $40,000. Its
coupons will be paid on a quarterly basis.
Everrich Bond has a maturity of 15 years and MaxWealth Bond has a maturity of 10
years. Both bonds currently have a rating of AA from Standard and Poor’s.
The following table summarizes the yield to maturity for bonds with various ratings:
Rating
AAA
AA
A
BBB
BB
Yield (APR compounded quarterly)
6.2%
6.8%
7.8%
9%
10%
a. What are the prices of the bonds if they maintain a rating of AA? (6 points)
b. What will the price of the bonds be if they are downgraded to a rating of A? (6
points)
c. Please explain which bond has higher interest rate risk (Price risk)? (4 points)
d. Suppose you are also considering another bond, Superior Bond. The price of bond
currently is $44,369.8356. The bond has a face value of $40,000, a maturity of 8
years and pays $1,200 every quarter. What is the likely rating of the bond? (4
points)
Question 11 (18 points)
Summerset Corporation is a multinational conglomerate. It is expected that it can
distribute stable dividends with a growth rate of 0.8% every year and the market
expects it can generate 4% return on the common stock. The dividends of the
common stock just distributed were $5 per share.
a. What is the common stock price today and what is the theoretical common stock
price 4 years later? (6 points)
b. Now suppose Summerset Corporation planned to invest in new capital and
decided not to distribute dividends in the next 5 years. The company will
distribute a $6.5 per share dividend in 6 years with a growth rate of 1.6% every
year thereafter and the market expects it can generate 5% return on the common
stock. What is the common stock price today? (6 points)
c. Summerset Corporation also issued preferred shares (constant dividends paid
every year forever) with a stated value of $100 each with 5.2% dividends 3 years
ago. The next dividend will be paid today and you will receive the next dividend.
The required return on the preferred stock is 4%. What is the price of the preferred
stock today before the dividend paid today? (6 points)
Question 12 (20 points)
Sanderson Inc., a high tech firm, is experiencing rapid growth. The company just paid
a dividend of $7 per share. The dividends are expected to grow at 20% for the next
four years and then level off to 6% growth rate indefinitely.
a. If the required return is 10%, what is the stock price of the company today? (10
points)
Now suppose Sanderson Inc. planned to retain some earnings for research and
development and would like reduce the dividend payout gradually. The company just
paid a dividend of $7 per share. The dividends are expected to decrease by $0.5 per
share for each of the next four years and then level off to 3% growth rate indefinitely.
b. If the required return is 10%, what is the stock price of the company today? (10
points)