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(Bond valuation) A company 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?

Ans: The market price of these bonds should be equal to present value of the coupon of 6.75 discounted at the rate of 8% assuming principal is returned in 8.5 years i.e. $ 91.89 (Assuming face value of $100)

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

Ans: The required return on the preferred stock on which the dividend is not growing is dividend / market price i.e. 4.5 / 65.5 i.e. 6.87%.

(Stock valuation) Let's say the 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 common stock is 14%, what is a share worth?

Ans: In case there are no growth prospects, the worth of a share is linked to the dividend that it pays and the expected return. Therefore the worth of the share of the Corporation is 5 / 14% i.e. $70.

(Interest-rate risk) A quick look at bond quotes will tell you that the company 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.

  • 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?
  • 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?
  • 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?
  • 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?

Ans:

The fair price of the bond is calculated by discounting the cash flow expected from the bond by the yield to maturity. For instance the fair price of a 7.25% coupon 2 year bond with YTM of 9% is based on discounting the 7.25 coupon for 2 years and the principal repayment in the second year at 9% discount rate. Based on this the fair price of various bonds is calculated as follows: -

2 year bond 5 year bond 10 year bond 20 year bond
a. 9% 96.92 93.19 88.77 84.03
b. 10% 95.23 89.58 83.10 76.59
c. 8% 98.66 97.01 94.97 92.64

d. we can say that the interest rate risk is a function of the maturity of the bond. Higher the matrurity of the bond, higher is its sensitivity to change in the market interest rates. This is evident from the above tables. When interest rate rises from 9% to 10% while the fair price of a 2 year bond reduces only marginally, that os a 20 year bond goes down substantially.

(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.

  1. 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?
  2. 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?

Ans:

  1. Cash flow of the bond are as follows: -

Year 0 -500

Year 1 +88

Year 2 +88

Year 2.5 +150

Based on above the realized return is (-) 17.3%

  1. Cash flow of the bond are as follows: -

Year 0 -500

Year 1-10 +88

Year 10 +1000

Based on above the realized return is (+) 21.2%

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

Ans:

If the revenue generated from this capital charge is invested at ten percent, the firm will not have enough funds available to meet its replacement cost as the amount invested (1500/12*5.33= 666.67) if invested at the end of each month will generate approximately $27854.69 which can be seen as under:

Rate of interest 1.008333
Months
1 666.67
2> 1338.896
3 2016.723
4 2700.199
5 3389.371
6 4084.285
7 4784.991
8 5491.536
9 6203.969
10 6922.339
11 7646.695
12 8377.087
13 9113.566
14 9856.183
15 10604.99
16 11360.03
17 12121.37
18 12889.05
19 13663.13
20 14443.66
21 15230.69
22 16024.29
23 16824.49
24 17631.37
25 18444.96
26 19265.34
27 20092.56
28 20926.66
29 21767.72
30 22615.79
31 23470.93
32 24333.19
33 25202.63
34 26079.32
35 26963.32
36 27854.69

If price level depreciation were used to establish the capital charge then the situation would be that each month $764.54 would be a capital charge to enable the firm have enough funds for replacement :

1 764.54
2 1535.451
3 2312.787
4 3096.6>
5 3886.945
6 4683.876
7 5487.448
8 6297.717
9 7114.738
10 7938.568
11 8769.262
12> 9606.879
13 10451.48
14 11303.11
15 12161.85
16 13027.73
17 13900.84
18 14781.22
19 15668.94
20 16564.05
21 17466.62
22 18376.72
23 19294.4>
24 20219.72
25 21152.76
26 22093.58
27 23042.23
28 23998.79
29 24963.32
30 25935.88
31 26916.56
32 27905.4
33 28902.49
34 29907.88
35 30921.65
36 31943.87

Thus it can be seen that the end of 36th month the amount is equal to the replacement cost of $ 31944.

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 yields on the portfolio was thus $5,000,000. What value would you have expected given the facts above?

Ans:

Fixed Income Mutual Fund

Proportion 60% 40%

Benchmark return 6% 10%

Expected return for the portfolio based upon benchmark weighted average return is 6%*.6 + 10%*.4 = 7.6%

Against this the portfolio return is 5%

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