The following question is based on the following information about the stocks of

Question

The following question is based on the following information about the stocks of KT Corporation, International Flavors & Fragrances, and Quality Systems. Price Dividend Yield KT (KT Corporation) $16 7% IFF (International Flavors & Fragrances) $56 2% QSII (Quality Systems) $80 2% You invested a total of $10,400 in shares of the three stocks at the given prices, and expected to earn $248 in annual dividends. If you purchased a total of 200 shares, how many shares of each stock did you purchase? KT shares IFF shares QSII shares

Explanation / Answer

(i) Let shares invested in KTT = x Also invested shares in IFF = y Shares in QSII will be = 200-x-y (ii) Also total amount invested in shares = 10400 Price x Shares Amount in KTT 16 x X Amount in IFF 56 x y Amount in QSII 80 x (200-x-y) Therefore = 16x + 56y + 16000 - 80x -80y = 10400 (80-16)x + (80-56)y = 16000-10400 64x + 24y = 5600 x + 0.375y = 87.5 (Dividing both sides by 64) x = 87.5 - 0.375 y (iii) Expected dividend = 248 Dividend per share = price x Div. Yield Stock Div per share DPS x No.of shares KTT =16*7% = 1.12 1.12x IFF =56*2% = 1.12 1.12y QSII =80*2%= 1.6 1.6(200-x-y) 1.12x + 1.12y + 1.16(200-x-y) = 248 1.12 x + 1.12 y + 232 -1.6x -1.6y = 248 - 0.48x - 0.48y = 16 -x -y = -33.3333 (Dividing both sides by 0.48) Solving equation (ii) and (iii) Putting value of x in eq iii -(87.5 - 0.375y) - y = -33.33333 -87.5 + 0.375Y -Y = -33.333 y = (-33.3333+ 87.5)/(0.375-1) y = -87.6667 Putting value in X = 87.5 - 0.375 y x = 87.5 - 0.375(-87.6667) x = 87.5 + 32.5 x = 120 Let shares invested in KTT = x 120 Also invested shares in IFF = y -87.6667 Shares in QSII will be = 200-x-y 167.6667 - sign represents short selling IFF Please provide feedback…. Thanks in advance…. :-)

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