Citibank: basic of corporate finance
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3-46 TIME VALUE OF MONEY
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ANSWER KEY
4. If you borrow $150,000 for five years at an 11.5% annual rate, compounded
monthly, payable at the end of the loan, how much will you have to pay at the end of
five years?
FV = $265,840.78
Using a financial calculator:
PV = $150,000
%
i
= 11.5
÷
12
N = 60
Compute FV
5. To calculate the present value of a bond portfolio, we apply a discount rate that
represents the (select two):
a) rate of return on the next best alternative investment.
c) investor's required rate of return.
6. XYZ Company is issuing zero-coupon bonds to fund its expansion plans. The bonds
have a face value of $100,000 and a maturity of five years. How much would an
investor requiring a 10% return be willing to pay today for one of these bonds?
$62,092.13
Using a financial calculator:
FV = $100,000
%
i
= 10
N = 5
Compute PV
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PROGRESS CHECK
(Continued)
7. Assuming the investor can purchase the bond at the price you calculated in question
6, compare the XYZ bond to a $62,000 investment in ABC Company at 10%
compounded annually for five years.
What is the return on this investment?
$_____________________
Which investment will yield more to the investor?
_____a) Loan to ABC Company
_____b) Purchase of bond from XYZ Company
8. A college graduate with a new job and a promising career devises a ten-year savings
plan. On December 31 of each year she will make the following deposits:
Years 1-3: $1,000 each year
Years 4-6: $2,000 each year
Years 7-10: $5,000 each year
If the interest on the account is locked in at 8% per annum, how much will be in the
account at the end of ten years?
$_____________________
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3-48 TIME VALUE OF MONEY
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ANSWER KEY
7. Assuming the investor can purchase the bond at the price you calculated in question
6, compare the XYZ bond to a $62,000 investment in ABC Company at 10%
compounded annually for five years.
What is the return on this investment?
$37,851.62 Using a financial calculator:
PV = $62,000
%
i
= 10
N = 5
Compute FV = $99,851.62 - 62,000 = 37,851.62
Which investment will yield more to the investor?
b) Purchase of bond from XYZ Company
ABC Company Loan: FV = $99,851.62 - 62,000 = 37,851.62
XYZ Bond: FV = $100,000 - 62,092.13 = 37,907.87
8. A college graduate with a new job and a promising career devises a ten-year savings
plan. On December 31 of each year she will make the following deposits:
Years 1-3: $1,000 each year
Years 4-6: $2,000 each year
Years 7-10: $5,000 each year
If the interest on the account is locked in at 8% per annum, how much will be in the
account at the end of ten years?
$36,927.70 Using a financial calculator (first deposit):
PV = $1,000
%
i
= 8
N = 9
Compute FV = 1,999.00
Year Deposit x FVIF = Payments
1 $1000 x (1.08)
9
= 1,999.00
2 $1000 x
(1.08)
8
= 1,850.93
3 $1000 x
(1.08)
7
= 1,713.82
4 $2000 x
(1.08)
6
= 3,173.75
5 $2000 x
(1.08)
5
= 2,938.66
6 $2000 x
(1.08)
4
= 2,720.98
7 $5000 x
(1.08)
3
= 6,298.56
8 $5000 x
(1.08)
2
= 5,832.00
9 $5000 x
(1.08)
1
= 5,400.00
10 $5000 x
(1.08)
0
= 5,000.00
FV = $36,927.70
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PROGRESS CHECK
(Continued)
9. If the investor wishes to have $40,000 at the end of ten years, and plans to invest an
equal amount on December 31 of each year at 8% p.a., what will be the amount of
the annuity payment?
$_____________________
10. An investor intends to purchase, and to hold for an indefinite period of time, shares
of Mega Company preferred stock. The stock pays an $8 annual dividend. The
investor requires a 14% return on investment. How much will the investor be
willing to pay per share for Mega Company preferred stock?
$_____________________
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3-50 TIME VALUE OF MONEY
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ANSWER KEY
9. If the investor wishes to have $40,000 at the end of ten years, and plans to invest an
equal amount on December 31 of each year at 8% p.a., what will be the amount of
the annuity payment?
$2,761.18
Using a financial calculator:
FV = $40,000
%
i
= 8
N = 10
Compute PMT = $2,761.18
10. An investor intends to purchase, and to hold for an indefinite period of time, shares
of Mega Company preferred stock. The stock pays an $8 annual dividend. The
investor requires a 14% return on investment. How much will the investor be
willing to pay per share for Mega Company preferred stock?
$57.14
PV
p
= A x (1 / R)
PV
p
= $8 x (1 / 0.14)
PV
p
= $57.14
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Unit 4
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UNIT 4: VALUING FINANCIAL ASSETS
INTRODUCTION
In Units One, Two, and Three, you learned some of the basics of financial markets, interest
rates, and the time value of money. In this unit, you will apply these concepts to calculating
the value of common financial assets. You will begin to learn how the market prices bonds,
common stock, and preferred stock securities.
UNIT OBJECTIVES
When you complete this unit, you will be able to:
• Recognize some terminology associated with bonds
• Calculate the present value of a bond
• Apply the dividend valuation model to find the present value of common stock
• Calculate the present value of preferred stock
BONDS
Debt financing
There are two major types of debt financing:
• Bank loans
• Bonds
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4-2 VALUING FINANCIAL ASSETS
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Bank loan:
agreement
between lender
and borrower
A bank loan is an agreement between a company and its bank. The bank
provides a line of credit for the company to use, and the company pays
the bank a rate of interest when it uses the credit line to borrow funds.
Bank loans are priced so that the lending bank covers the cost
of the funds and makes a profit.
Bond:
agreement
between issuer
and investor
Bonds represent loans by investors to a company. In a bond contract, the
investor purchases a certificate from the issuer in exchange for a stream
of interest payments and the return of a principal amount at the end of
the contract. In this section we will discuss the terminology of the bond
market and the methodology for calculating the price (present value) of
a bond.
Bond Terminology
There are several terms that are commonly used by investors and
issuers when dealing with bonds.
Coupon
The periodic interest payment made by the issuer.
When bonds were first developed, the bond
certificate had detachable coupons that the
investor would send to the issuer to receive each
interest payment. The term still applies to
payments, even though coupons are no longer
used to redeem them.
Coupon rate The interest rate used to calculate the coupon
amount the bond will pay. This rate is multiplied
by the face value of the bond to arrive at the
coupon amount.
Face (par) value
The amount printed on the certificate. The face
value represents the principal in the loan
agreement, which is the amount the issuer pays at
maturity of the bond.
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Maturity date
The date the loan contract ends. At this time, the
issuer pays the face value to the investor who
owns the bond.
Zero-coupon
A type of bond where the company pays no
periodic interest payments. The bond is priced at
a discount so that interest is imputed throughout
the life of the bond. At maturity, the issuer pays
the face value and the investor receives all of the
return in the form of capital gain.
Bonds are often referred to as fixed income securities because they
have a fixed payout to the investor. Since the coupon rate is set before
the sale of the bond, the investor knows the amount of the interest
payments.
Process for Issuing Bonds
A simple example will illustrate the process for issuing bonds.
Example
ABC Company needs capital to purchase a new piece of equipment
for its operations. The company meets with financial advisors and
investment bankers to discuss the possibilities of raising the necessary
capital. They decide that a bond issue is the least expensive method for
the company. The process is as follows:
Terms
1. ABC Company sets the maturity date and face value of the bonds.
The bonds will have a maturity date of ten years from the date of
issue and a face value of $1,000. The company will issue as many
bonds as it needs for the equipment purchase – if the equipment
costs $10,000,000 fully installed, then the company will issue
10,000 bonds.
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