Class 1 SBWL Finance Summer Term 2023

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Simon Fraser University *

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BUS315

Subject

Finance

Date

Feb 20, 2024

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3

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Exercise 1.1: RF = 5% F = 40*(1+5%) = 42 P = (42-35)/(43-35) = 0.875 1-P = 0.125 V = (0.875*2.5+0.125*0.75)/(1.05)^2 = 2.07 Exercise 1.2: A) A straight coupon bond “vanilla bond” is a bond with no additional features like convertibility, put options. A straight bond will pay out coupon payments at fixed intervals (like monthly, annually, semi-annually, etc.), pay back the principle at the maturity date, and have a fixed maturity date. B) Face value = 100, coupon rate = 3% pa, and 1 year maturity. a. What is the fair price of this bond if the risk-free rate is 2.75% p.a. 100*3%=3 100+3=103 103/(1+2.75%)^1=100.24 b. What is the fair price of this bond if the risk-free rate is 5% p.a. 100*3%=3 100+3=103 103/(1+5%)^1=98.10 c. Repeat your calculations above for a bond with face value 100, a coupon rate of 3% paid annually but with a maturity of 5 years. Comment on your results. If RF=2.75% pa 100*3%=3 … after 5 years equals 115.93 (done in Excel) 115.93/(1+2.75%)^5=101.22 If RF=5% pa 100*3%=3 … after 5 years equals 115.93 (done in Excel) 115.93/(1+5%)^5=90.83 Because the maturity is in 5 years instead of 1, the fair values are further away from the face value as we go further in time. This is because of discounting to the power of 5 years vs 1 year. C) Cash flows: T0: -100; T1: +103 D = 20 * 4 shares = 80; U = 30 * 4 shares = 120; Therefore, it is optimal to convert the bond only in the “U” scenario. Fair issuance price: 100*3%=3 100+3=103 RF = 2.75%; Sd = 20; Su = 30; Vd = 103; Vu = 120 due to conversion F = 22*(1+2.75%) = 22.605 P = (22.605-20)/(30-20) = 0.2605 1-P = 0.7395 V = (0.2605*120+0.7395*103)/1.0275 V = 104.55
Exercise 1.3: RF = 4% per period F = 100*(1+4%)^2 = 108.16 P = (108.16-50)/(300-50) = 0.2326 1-P = 0.7674 V = (0.2326*105+0.7674*50)/1.04 V = 60.38 Exercise 1.4: A) It should call the bond in Period 1. B) 105/(1+0.04)^1 = 100.96 Exercise 1.5: Arbitrage is basically taking advantage of a price difference between markets to make a profit. For example, if widgets in Market A are sold for $5 and widgets in Market B are sold for $10, you can buy widgets in Market A for $5 and resell them in Market B for $10 to make yourself a profit of $5 (before transport and other costs). In real life, a good example arbitrage is the existence of the “Kimchi Premium”. The premium exists because the price of Bitcoin in South Korea is much higher than it is in other western/developed countries. Therefore, you can buy “cheap” bitcoin in your home country and then resell it on South Korean crypto exchanges for a profit. Exercise 1.6: A) $85.94 ($68.75*1.25) UU $68.75 ($55*1.25) U $55 $55 ($68.75*0.8) O UD (or DU) $44 ($55*0.8) D $35.20 ($44*0.8) DD
B) RF = 2.5% pa F = 55*(1+2.5%)^2 F = 57.78 P = (57.78-44)/(68.75-44) = 0.5569 1-P = 0.4431 V = (68.75*0.5569+44*0.4431)/(1+2.5%)^2 V = $54.9958 C) You would buy the forward contract at the price the bank quoted. Then you would expect to sell the contract at your calculated price to make the profit. For example, if the bank quoted $45 as the price, you would by for $45 and sell for the above calculated $54.9958 to make a profit of about $10 ($54.9958-$45=$9.9958).
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