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# TVM , Price of bonds, Stock price

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1. Carrie Tune will receive \$19,500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for \$160,000?

2. If you owe \$40,000 payable at the end of seven years, what amount should your creditor accept in payment immediately if she could earn 12 percent on her money?

3. Wilson Oil Company issued bonds five years ago at \$1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 8 percent. This return was in line with the required returns by bondholders at that point in time as described below:

Real rate of return 2%
Total return 8%

Assume that 10 years later, due to bad publicity, the risk premium is now 6 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity. Compute the new price of the bond.

4. Haltom Enterprises has had the following pattern of earnings per share over the last five years:

Year Earnings per Share
2000 \$3.00
2001 3.18
2002 3.37
2003 3.57
2004 3.78

The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future. Dividends represent 30 percent of earnings.

1. 1. Project earnings and dividends for the next year (2005). Round all values in this problem to two places to the right of the decimal point.

2. If the required rate of return (Ke) is 10 percent, what is the anticipated stock price at the beginning of 2005?

#### Solution Preview

Note: For the following answers the abbreviations have the following meanings

PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity
FVIF= Future Value Interest Factor
FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n
FVIF( n, r%)= =(1+r%)^n
FVIFA( n, r%)= =[(1+r%)^n -1]/r%

1. Carrie Tune will receive \$19,500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for \$160,000?

Calculate the present value of annuity

n= 20
r= 10.00%
PVIFA (20 periods, 10.% rate ) = 8.513564

Annuity= \$19,500
Therefore, present value= \$166,014 =19500x8.513564

Since the present value of annuity at \$166,014 is more than \$160,000
Carrie should not sell her future rights now

2. If you owe \$40,000 payable at the end of seven years, what amount should your creditor accept in payment immediately if she could earn 12 percent ...

#### Solution Summary

The solution answers questions on Time Value of Money (TVM) Price of bonds, Stock price

\$2.19

## Multiple choice questions on tax rate at which investors would be indifferent between two bonds, portfolio's required rate of return, time value of money, bond and stock pricing

1. A corporate bond currently yields 8.5 percent. Municipal bonds with the same risk, maturity, and liquidity currently yield 5.5 percent. At what tax rate would investors be indifferent between the two bonds?

a. 35.29%
b. 40.00%
c. 24.67%
d. 64.71%
e. 30.04%

2. A money manager is holding the following portfolio:

Stock Amount Invested Beta
1 \$300,000 0.6
2 300,000 1.0
3 500,000 1.4
4 500,000 1.8

The risk-free rate is 6 percent and the portfolio's required rate of return is 12.5 percent. The manager would like to sell all of her holdings of Stock 1 and use the proceeds to purchase more shares of Stock 4. What would be the portfolio's required rate of return following this change?

a. 13.63%
b. 10.29%
c. 11.05%
d. 12.52%
e. 14.33%

3. John and Barbara Roberts are starting to save for their daughter's college education.

Assume that today's date is September 1, 1998.

College costs are currently \$10,000 a year and are expected to increase at a rate equal to 6 percent per year for the foreseeable future. All college payments are due at the beginning of the year. (So for example, college will cost \$10,600 for the year beginning September 1, 1999).

Their daughter will enter college 15 years from now (September 1, 2013). She will be enrolled for four years. Therefore the Roberts will need to make four tuition payments. The first payment will be made on September 1, 2013, the final payment will be made on September 1, 2016. Notice that because of rising tuition costs, the tuition payments will increase each year.

The Roberts would also like to give their daughter a lump-sum payment of \$50,000 on September 1, 2017, in order to help with a down payment on a home, or to assist with graduate school tuition.

The Roberts currently have \$10,000 in their college account. They anticipate making 15 equal contributions to the account at the end of each of the next 15 years. (The first contribution would be made on September 1, 1999, the final contribution will be made on September 1, 2013).

All current and future investments are assumed to earn an 8 percent return. (Ignore taxes.)

How much should the Roberts contribute each year in order to reach their goal?

a. \$3,156.69
b. \$3,618.95
c. \$4,554.83
d. \$5,955.54
e. \$6,279.54

4. Graham Enterprises anticipates that its dividend at the end of the year will be \$2.00 a share (D1) The dividend is expected to grow at a constant rate of 7 percent a year. The risk-free rate is 6 percent, the market rate is 5 percent, and the company's beta equals 1.2 What is the expected price of the stock 5 years from now?

a. \$52.43
b. \$56.10
c. \$63.49
d. \$70.49
e. \$72.54

5. The expected rate of return on the common stock of NW Corp. is 14 percent. The stock's dividend is expected to grow at a constant rate of 8 percent a year. The stock currently sells for \$50 a share. Which of the following statement is most correct?

f.the stocks dividend yield is 8%
g.the stocks dividend yield is 7%
h.the current dividend per share is \$4.00
i.the stock price is expected to be \$54 a share in one year
j.the stock price is expected to be \$57 a share in one year

6. Which of the following statements is most correct?

a. If a bond sells for less than par, then its yield to maturity is less than its coupon rate.
b. If a bond sells at par, then its current yield will be less than its yield to maturity.
c. Assuming that both bonds are held to maturity and are of equal risk, a bond selling for more than par with ten years to maturity will have a lower current yield and higher capital gain relative to a bond that sells at par.
d. Answers a and c are correct.
e. None of the answers above is correct.

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