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A3. (Bond valuation) General Electric made a coupon payment yesterday on its 6.75% bonds that mature in 8.5 years. If the required return on these bonds is 8% APR, what should be the market price of these bonds?

.0675 x 6 + 1/1.08^8.5 = ..405 +.52 = ..925 or 92.5% of par value should be the fair price.

A13. (Required return for a preferred stock) Sony $4.50 preferred is selling for $65.50. The preferred dividend is nongrowing. What is the required return on Sony preferred stock?

4.50/65.5 = 6.875 %

A15. (Stock valuation) Let's say the Mill Due Corporation is expected to pay a dividend of $5.00 per year on its common stock forever into the future. It has no growth prospects whatsoever. If the required return on Mill Due's common stock is 14%, what is a share worth?

5/.14 = $35.71

B15. (Interest-rate risk) A quick look at bond quotes will tell you that GMAC has many different issues of bonds outstanding. Suppose that four of them have identical coupon rates of 7.25% but mature on four different dates. One matures in 2 years, one in 5 years, one in 10 years, and the last in 20 years. Assume that they all made coupon payments yesterday. a. If the yield curve were flat and all four bonds had the same yield to maturity of 9%, what would be the fair price of each bond today? b. Suppose that during the first hour of operation of the capital markets today, the term structure shifts and the yield to maturity of all these bonds changes to 10%. What is the fair price of each bond now? c. Suppose that in the second hour of trading, the yield to maturity of all these bonds changes once more to 8%. Now what is the fair price of each bond? d. Based on the price changes in response to the changes in yield to maturity, how is interest-rate risk a function of the bond's maturity? That is, is interest-rate risk the same for all four bonds, or does it depend on the bond's maturity?

|  |2 |5 |10 |20 |

|Coupon rate |0.0725 |0.0725 |0.0725 |0.0725 |

|a  |  |  |  |  |

|Value at 9% | 1.76 | 3.89 | 6.42 | 9.13 |

|PV of interest |0.1276 |0.282025 |0.46545 |0.661925 |

|  |  |  |  |  |

|PV of principal |0.84168 |0.649931 |0.422411 |0.178431 |

|  |  |  |  |  |

|Expected price |0.96928 |0.931956 |0.887861 |0.840356 |

|  |  |  |  |  |

| b |  |  |  |  |

|Value at 10% | 1.74 | 3.79 | 6.14 | 8.51 |

|PV of interest | 0.1262 | 0.2748 | 0.4452 | 0.6170 |

|  |  |  |  |  |

|PV of principal |0.826446 |0.620921 |0.385543 |0.148644 |

|  |  |  |  |  |

|Expected price |0.952596 |0.895696 |0.830693 |0.765619 |

| c |  |  |  |  |

|Value at 8% | 1.78 | 3.99 | 6.71 | 9.82 |

|PV of interest |0.12905 |0.289275 |0.486475 |0.71195 |

|  |  |  |  |  |

|PV of principal |0.857339 |0.680583 |0.463193 |0.214548 |

|  |  |  |  |  |

|Expected price |0.986389 |0.969858 |0.949668 |0.926498 |

d

It is quite obvious that the price is also affected by the maturity period, you can see that at all percentages the expected value of bond is decreasing over the time period.

B17. (Default risk) You buy a very risky bond that promises an 8.8% coupon and return of the $1,000 principal in 10 years. You pay only $500 for the bond. a. You receive the coupon payments for two years and the bond defaults. After liquidating the firm, the bondholders receive a distribution of $150 per bond at the end of 2.5 years. What is the realized return on your investment? b. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?

a

|Received for 3 years |176 | |

|after 2.5 years |150 | |

|total |326 | |

|Investment |-500 | |

|Loss on investment |-174 | |

| | | |

|total return |-34.8 |% |

|Average yearly retrun |-13.92 |% |

b

|Received for 10 years |880 |

|after 10 years |1000 |

|total |1880 |

|investment |-500 |

|Profit |1380 |

|  |  |

|total return |376% |

|Annual return |37.6% |

C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here. a. Calculate the expected returns on the stock market and on Chicago Gear stock. b. What is Chicago Gear's beta? c. What is Chicago Gear's required return according to the CAPM? REALIZED RETURN

State of the Market Probability that State Occurs Stock Market Chicago Gear

Stagnant 0.20 (10%) (15%)

Slow growth 0.35 10 15

Average growth 0.30 15 25

Rapid growth 0.15 25 35

A

Stock market

.2x .1 + .35 x .1 +.3 x .15 + .15 x .25 = 13.75%

.2x .15 + .35 x .15 +.3 x .25 + .15 x .35 = 21%

B

|  |1 |2 |3 |4 |5 |6 |

|  |Stock |Chicago |Dveiation |Deviaton |Square 3 |3 x 4 |

|  |0.1 |0.15 |-0.05 |-0.075 |0.0025 |0.00375 |

|  |0.1 |0.15 |-0.05 |-0.075 |0.0025 |0.00375 |

|  |0.15 |0.25 |0 |0.025 |0 |0 |

|  |0.25 |0.35 |0.1 |0.125 |0.01 |0.0125 |

|Total |0.6 |0.9 |0 |0 |0.015 |0.02 |

|  |  |  |  |  |  |  |

|Average |0.15 |0.225 |  |  |  |  |

|  |  |  |  |  |  |  |

|  |  |  |  |  |  |  |

|Beta |1.333333 |  |  |  |  |  |

C

Expected return = .06 + 1.33 (.1375-.06) = 16.31%

4. A home health care firm has purchased five automobiles. Each automobile costs $24,000 and has an estimated useful life of three years. Each year, the replacement cost of the automobiles is expected to increase ten percent. At the end of the third year, the replacement cost would be $31,944 per vehicle. The firm anticipates that each automobile will be used to make 1500 patient visits per year. If the firm prices each visit to recover just the historical cost of the automobiles, it will include a capital cost of $5.33 per visit ($24,000 divided by 4500 total visits). Assuming the revenue generated from this capital charge is invested at ten percent, will the firm have enough funds available to meet its replacement cost?

4500 x 5.33 = 24000 x 3.31 = 79440

Less required

31944 x 3 =95832

No the fund will have a shortage of $16392

How would this situation change if price level depreciation were used to establish the capital charge?

The company needs 95832, therefore it should cover 95832/3.31 = 28952

The company should charge = 28952/4500 = $6.433 should be charged .

5. Your firm's investment portfolio was valued at $100,000,000 at the beginning of the year. Approximately 60 percent of the portfolio was invested in fixed-income securities, primarily U.S. government bonds. The remaining 40 percent was invested in mutual funds selected by your firm's portfolio manager. During the year, the U.S. government bonds yielded 6.0 percent, and the change in the Standard and Poor's 500 index was 10.0 percent. Reported investment income during the year was $6,000,000, including realized gains. The firm also reported an unrealized loss of $1,000,000. Total yield on the portfolio was thus $5,000,000. What value would you have expected given the facts above?

60 million x .06 = $3.6 million

40 million x .1 =$4 million

Total expected return should be = $7.6 million

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