Análisis del modelo y programa

Directions: Select the one best answer for each question, unless otherwise indicated. Check your responses with the Answer Key on the next page.

1. ABC Bank receives a loan payment of $1,000 principal and interest from a

customer. The bank loans the $1,000 to another customer for one year at the rate of 6.25% per annum. The second customer will pay $1,062.50 to the bank. This

amount represents the:

_____ a) loan made to the second customer discounted to its present value on the maturity date.

_____ b) compounded value of the first customer's payment after it was loaned to customer two.

_____ c) future value of the loan payment received from the first customer calculated on a simple interest basis.

_____ d) simple interest future value of the amount of the loan made to the first customer.

2. In the future value formula FV_{T = P (1 + R/M)}T x M_{, if:}

_____ a) M equals two, interest is compounded semi-annually for each year in the period.

_____ b) T equals one and M equals twelve, interest is compounded once during each twelve month period.

_____ c) T equals three, interest is compounded every four months.

_____ d) T equals five and M equals one, simple interest is calculated once each year for five years.

3. In the formula FV_{T = P x e}RT_{, e}RT_represents:

_____ a) the future value interest factor for a discrete number of compounding periods.

_____ b) the future value interest factor for an infinitely large number of compounding periods.

_____ c) simple interest calculated on a continuous basis for a specified period of time.

_____ d) interest factor compounded for a discrete period (e) at a certain rate (R) for a specific amount of time (T).

ANSWER KEY

1. ABC Bank receives a loan payment of $1,000 principal and interest from a

customer. The bank loans the $1,000 to another customer for one year at the rate of 6.25% per annum. The second customer will pay $1,062.50 to the bank. This

amount represents the:

c) future value of the loan payment received from the first customer calculated on a simple interest basis.

2. In the future value formula FV_{T = P (1 + R/M)}T x M_{; if:}

a) M equals two, interest is compounded semi-annually for each year in the period.

3. In the formula FV_{T = P x e}RT_{, e}RT_represents:

b) the future value interest factor for an infinitely large number of compounding periods.

PROGRESS CHECK

(Continued)

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?

$_____________________

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.

_____ b) reciprocal value of an interest rate on a comparable investment. _____ c) investor's required rate of return.

_____ d) investor's return on the bond portfolio.

_____ e) risk factor associated with the bond portfolio.

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?

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

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?

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 = 5,400.00

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?

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

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

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.

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: