1.Before the rating change:Vb = (1,000(6.75%)/2) {[1-(1/(1 + 0.082/2)2(10))]/0.082/2} + 1,000/(1 + 0.082/2)2(10) Solving for Vb, we get $902.336888.On a financial calculator: PMT = 33.75, FV = 1,000, I = 8.20/2 = 4.10, N = 10(2) = 20=> PV = -902.336888After the rating change:Vb = (1,000(6.75%)/2) {[1-(1/(1 + 0.071/2)2(10))]/0.071/2} + 1,000/(1 + 0.071/2)2(10) Solving for Vb, we get $975.2404439.On a financial calculator: PMT = 33.75, FV = 1,000, I = 7.1/2 = 3.55, N = 10(2) = 20=> PV = -975.2404439$ change in Vb = $975.2404439 - $902.336888 = $72.9035558% change in Vb = ($975.2404439 - $902.336888)/$ 902.336888 = $72.9035558/$902.336888 = 8.079%

2.You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $16,000 (.20 x $80,000) at closing and borrow $64,000 through the mortgage.a. For your mortgage:$64,000 = PMT{[1-(1/(1+.08/12)15(12))]/(.08/12)}or PMT = $64,000/{[1-(1/(1+.08/12)15(12))]/(.08/12)}therefore PMT = $64,000/104.6406 = $611.617Thus, your monthly payment is $611.62.b. The 127th payment of $611.62 is split as follows: $184.40 to interest and $427.22 to principal.c. The 159th payment of $611.62 is split as follows: $83.18 to interest and $528.44 to principal.d. The total payments over the life of the mortgage amount to payments of $110,091.60 ($611.62 x 15 x 12): $62,000 to the repayment of principal and $46,091.60 to the payment of interest.

3. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $30,000 (.20 x $150,000) at closing and borrow $120,000 through the mortgage.a. For your mortgage:$120,000 = PMT{[1-(1/(1+.0525/12)15(12))]/(.0525/12)}orPMT = $120,000/{[1-(1/(1+.0525/12)15(12))]/(.0525/12)}therefore PMT = $120,000/124.3970 = $964.6Thus, your monthly payment is $964.65.

4. You will make a down payment of 25 percent of the purchase price, or you will make a down payment of $43,750 (.25 x $175,000) at closing and borrow $131,250 through the mortgage.a. If Option 2 is chosen you pay $131,250 x .02 = $2,625 in points and receive $128,625 at closing ($131,250 - $2,625), although the mortgage principal is $131,250. To determine the best option, we first calculate the monthly payments for both options as followsOption 1: $131,250 = PMT {[1-(1/(1+.0500/12)15(12))]/(.0500/12)} => PMT = $1,037.92Option 2: $131,250 = PMT {[1-(1/(1+.0475/12)15(12))]/(.0475/12)} => PMT = $1,020.90In exchange for $2,625 up front, Option 2 reduces your monthly mortgage payments by $17.012. The present value of these savings (evaluated at 4.75 percent) over the 15 years isPV = $9.90 {[1-(1/(1+.0475/12)15(12))]/(.0475/12)} = $2,187.14Option 1 is the better choice. The present value of the monthly savings, $2,187.14, is less than the points paid up front, $2,625.B.. If Option 1 is chosen you pay $131,250 x .02 = $2,625 in points and receive $128,625 at closing ($131,250 - $2,625), although the mortgage principal is $131,250. If Option 2 is chosen you pay $131,250 x .03 = $3,937.5 in points and receive $127,312.5 at closing ($131,250 - $3,937.5). The difference in savings on the points is $1,312.5.To determine the best option, we calculate the monthly payments for both options as followsOption 1: $131,250 = PMT {[1-(1/(1+.0485/12)15(12))]/(.0485/12)} => PMT = $1,027.69Option 2: $131,250 = PMT {[1-(1/(1+.0468/12)15(12))]/(.0468/12)} => PMT = $1,016.17In exchange for $1,312.5 up front, Option 2 reduces your monthly mortgage payments by $11.52.5. a. With cumulative voting, the total number of votes available is 75,000,000 (= 15 million shares outstanding H 5 directors). If there are six candidates for the five board positions, the five candidates with the highest number of votes will be elected to the board and the candidate with the least total votes will not be elected. In this example, the minimum number of votes needed to ensure election is one sixth of the 75 million votes available, or 12,500,000 votes. If one candidate receives 12,500,000, the remaining votes together total 62,500,000. No matter how these votes are spread over the remaining 5 director candidates, it is mathematically impossible for each of the 5 to receive more than 12,500,000. This would require more than 5 x 12,500,000 votes, or more than the 62,500,000 votes that remain.b. With straight voting, the vote on the board of directors occurs one director at a time. Thus, the number of votes eligible for each director is 15,000,000, the number of shares outstanding. The minimum number of votes needed to ensure election is one half 15 million votes available, or 7.5 million.

6. You own 50,000 shares of common stock in a firm with 2.5 million total shares outstanding. The firm announces its plan to sell an additional 1 million shares through a rights offering. Thus, each shareholder will be sent 0.4 rights for each share of stock owned. One right can then be exchanged for one share of common stock in the new issue.a. Your current ownership interest is 2.0 percent (50,000/2.5 million) prior to the rights offering and you receive 20,000 rights (50,000 x 0.4) allowing you to purchase 20,000 of the new shares. If you exercise your rights (buying the 20,000 shares) your ownership interest in the firm after the rights offering is still 2 percent ((50,000 + 20,000)/(2.5 million + 1 million)).b. The market value of the common stock is $35 before the rights offering, or the total market value of the firm is $87.5 million ($35 x 2.5 million), and the 1 million new shares are offered to current stockholders at a $5 discount, or for $30 per share. The firm receives $30 million. The market value of the firm after the rights offering is $117.5 million (the original $87.5 million plus the $30 million from the new shares), or $33.571 per share ($117.5 million / 3.5 million).c. Your 50,000 shares are worth $1.75 million ($35 x 50,000) before the rights offering, and you can purchase 20,000 additional shares for $600,000 ($30 x 20,000). Thus, your total investment in the firm after the rights offering is $2.35 million, or $33.571 per share ($2.35 million / 70,000).d. Your 50,000 shares are worth $1.75 million ($35 x 50,000) before the rights offering. Since each right allows a stockholder to buy a new share for $30 per share when the shares are worth $33.571, the value of one right should be $3.571. Should you sell your rights rather than exercise them, you maintain your original 50,000 shares of stock. These have a value after the rights offering of $1.679 million (50,000 x 33.571). You also sell your rights for $0.071 million (20,000 x $3.57). You have a total of $1.75 million, or have lost no wealth.