dont understand computation for profit and why is the pv(k) over 1.005^2 and not dividends if its asking for 6 months

10 20 30 40 b) (2 points) Compute your profit if you buy this portfolio today and in 6 months OldSystem's stock equals 39. Solution: Using the Put-Call parity: 7A Puto = Callo - S. + PV(DPS) + PV(k) o = (1.0201505)4 - 1 = 0.5% 43 1.005 S 1.005 20 k-10: Puto = 19.42 - 30+ k=20: Puto = 13.64 30 + 1.005 + 1.0052 = 8.42 k=30: Puto = 5.57 - 30+ k-40: Puto = 1.85 - 30+ S + 0 = 16.43 + 052 = 10.25 Portfolio's price = 2 x 4.3-2 x 8.42-2 x 10.25 +2 x 16.43 = 4.12 Profit = (80 - 2 x 39) - 4.12 = -2.12 SECTION 111 (3.5 POINTS) - 20 MINUTES Consider that you just created the following portfolio with European options over OldSystem's stock with an expiration date of 6 months (all options have 6 months left to maturity): 2 Long Put (k - 40); 2 Short Put (k - 30); 2 Short Put (k - 20); 2 Long Put (k - 10). OldSystem's current stock price is 30 and the firm will pay a dividend of 5 next quarter. The annual effective risk free rate is 2.01505%. 6A You also collected the following prices of European Call options over OldSystem's with 6 months to maturity: Strike (1) 10 19.42 17.38 15 20 13.64 20 5.57 6.02 33 40 1.85 a) (1.5 points) Draw the payoff scheme of this portfolio as a function of OldSystem's stock in 6 months (expiration date). Please note that you are required to present a table to justify your graph Solution: 10 20 30 40 b) (2 points) Compute your profit if you buy this portfolio today and in 6 months OldSystem's stock equals 39. Solution: Using the Put-Call parity: 7A Puto = Callo - S. + PV(DPS) + PV(k) o = (1.0201505)4 - 1 = 0.5% 43 1.005 S 1.005 20 k-10: Puto = 19.42 - 30+ k=20: Puto = 13.64 30 + 1.005 + 1.0052 = 8.42 k=30: Puto = 5.57 - 30+ k-40: Puto = 1.85 - 30+ S + 0 = 16.43 + 052 = 10.25 Portfolio's price = 2 x 4.3-2 x 8.42-2 x 10.25 +2 x 16.43 = 4.12 Profit = (80 - 2 x 39) - 4.12 = -2.12 SECTION 111 (3.5 POINTS) - 20 MINUTES Consider that you just created the following portfolio with European options over OldSystem's stock with an expiration date of 6 months (all options have 6 months left to maturity): 2 Long Put (k - 40); 2 Short Put (k - 30); 2 Short Put (k - 20); 2 Long Put (k - 10). OldSystem's current stock price is 30 and the firm will pay a dividend of 5 next quarter. The annual effective risk free rate is 2.01505%. 6A You also collected the following prices of European Call options over OldSystem's with 6 months to maturity: Strike (1) 10 19.42 17.38 15 20 13.64 20 5.57 6.02 33 40 1.85 a) (1.5 points) Draw the payoff scheme of this portfolio as a function of OldSystem's stock in 6 months (expiration date). Please note that you are required to present a table to justify your graph Solution