quiz3 - solutions

MATH1119 - Quiz 3 1. Mr. Bartlett’s will specified that, upon liquidation of any asset, the proceeds be divided among his wife, his son, and his sister in the ratio of 7 : 5 : 3. a. (3 points) If the son received $9500 from the sale of securities, what amounts did Bartlett’s wife and sister receive? b. (3 points) What amount would the sister receive from the sale of the deceased’s boat for $27,000? Let W, N, and S represent the wife's, son's, and sister’s shares in any allocation. Then W:N:S = 7:5:3 a. With N = $9500, and Then and 𝑆 = 3 5 ($9500) = $5700 Hence, Mr. Bartlett’s wife received $13,300 and his sister received $5700. b. The sister received 0.2($27,000) = $5400. 2. Geological Consultants Ltd. is a private company with four shareholders: W, X, Y, and Z. The following table shows their respective shareholdings. X is retiring and has agreed to sell his shares to the other three shareholders for $175,000. The agreement calls for the 500 shares to be purchased and allocated among W, Y, and Z in the same ratio as their present shareholdings. The shares are indivisible, and consequently the share allocation must be rounded to integer values. Partner Number of shares owned W 300 X 500 Y 350 Z 400 5 7 9500 W = $ 3 5 S 9500 = $ ( ) $13,300 $9500 W 5 7 = = 2 0 5 1 15 3 3 5 7 3 000 27 S . , $ = = = + + =

a. (3 points) What implied value does the transaction place on the entire company? b. (3 points) How many shares will W, Y, and Z each own after the buyout? c. (3 points) What amount will W, Y, and Z each contribute toward the $175,000 purchase price? Prorate the $175,000 on the basis of the allocation of the shares in part (b). Total number of outstanding shares = 1550 a. Value of X's shares : Value of company = Shares owned by X : Total number of shares Value of company = $175,000 = $542,500 b. Number of shares already owned by W, Y, and Z is 1050. From the 500 shares owned by X, W’s allocation : 500 = W's current shares : Total of W, Y, and Z W’s allocation = = 142.9 shares Similarly, Y’s allocation = = 166.7 shares Z’s allocation = = 190.48 shares After the buy-out, W will own 300 + 143 = 443 shares Y will own 350 + 167 = 517 shares, and Z will own 400 + 190 = 590 shares c . W’s contribution : $175,000 = W's allocation : 500 W’s contribution = = $50,050 Similarly, Y’s contribution = = $58,450 Z’s contribution = = $66,500 3. A basket of goods and services representative of the CPI cost $2750 when the CPI stood at 118.3. a. (2 points) What did the basket of goods cost 10 years earlier, when the CPI was at 93.1? b. (3 points) What was the overall percent inflation experienced by consumers for the entire 10-year period 1550 500 company of Value 000 175 = , $  500 1550 500 1050 300  500 1050 350  500 1050 400  000 175 500 143 , $  000 175 500 167 , $  000 175 500 190 , $ 