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# TVM, portfolio's return, bond and stock pricing

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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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#### Solution Preview

Please see the attached file.

QUESTIONS

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%

After tax return on corporate bonds= 8.5% x (1- Tax rate )
After tax return on Municipal bonds = 5.5 % (Municipal bonds are not taxed)
For indifference

8.5% x (1- Tax rate) = 5.5 %
Solving for tax rate
Tax rate = 35.29%

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%

Beta of the portfolio = 1.3 (see calculations below)

Stock Amount Invested Proportion Beta Proportion x beta
1 \$300,000 0.1875 =300000/1600000 0.6 0.1125
2 300,000 0.1875 =300000/1600000 1 0.1875
3 500,000 0.3125 =500000/1600000 1.4 0.4375
4 500,000 0.3125 =500000/1600000 1.8 0.5625
\$1,600,000 1.0000 1.3000

r = risk free rate + beta x market risk premium
12.5% = 6% + 1.3 x market risk premium
Or market risk premium = (12.5% -6%)/ 1.3 = 5%

After rebalancing the portfolio, beta becomes 1.5250

Stock Amount Invested Proportion Beta Proportion x beta
2 300,000 0.1875 =300000/1600000 1 0.1875
3 500,000 0.3125 =500000/1600000 1.4 0.4375
4 800,000 0.5 =800000/1600000 1.8 0.9
\$1,600,000 1.0000 1.5250

r = risk free rate + beta x market risk premium = 6% + 1.5250 x 5 % = 13.625%

Answer: The required return = 13.625% or rounded off to 13.63%

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

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

é 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 ...

#### Solution Summary

Answers to 6 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.

\$2.19