The Value of the Bond - Assignment Example

Question 1 a. PV = 5000 i= 7.3% n = 7 FV = PV x (1 + i) n = 5000 x (1.073) 7 = $8187.82 b. at the end of 7 years the amount is $8187.82 Now interest rate = 5.5%; time – 6 years FV = = PV x (1 + i) n = 8187.82 x (1.055) 6 = $11289.72 at the end of 13 years Now the interest rate is 8.2% for 3 years FV = = PV x (1 + i) n = 11289.72 x (1.082) 3 = $14300 Now the interest rate is 4.6% for 2 years FV = = PV x (1 + i) n = 14300 x (1.046) 2 = $15646.9 Now the interest rate is 7.6% for 3 years FV = = PV x (1 + i) n = 15646.9 x (1.076) 3 = $19492.39 The money accumulates to $19492.39 at the end of 21 years c. Since another 1200 was depositied at the end of 7 years so money at the end of 7 years is $20187.2 Now interest rate = 5.5%; time – 6 years FV = = PV x (1 + i) n = 20187.2 x (1.055) 6 = $27834.98 at the end of 13 years Now the interest rate is 8.2% for 3 years FV = = PV x (1 + i) n = 27834.98 x (1.082) 3 = $35259.21 Now the interest rate is 4.6% for 2 years FV = = PV x (1 + i) n = 35259.21 x (1.046) 2 = $38577.67 Now the interest rate is 7.6% for 3 years FV = = PV x (1 + i) n = 38577.67 x (1.076) 3 = $48058.79 The money accumulates to $48058.79 at the end of 21 years Question 2 a. House Value = 450,000 Down Payment = 143,000 Loan Value = 307000 Interest Rate = 6.6% Loan Period = 25 years The value of the loan at the end of year 15 looks as = $183426.01 The value has been calculated on a compounded basis where interest I paid and loan repaid on a monthly basis Question 3 a. Expected Return on Security A = (p1 * r1) + (p2 * r2) + (p3 * r3) + (p4 * r4) = (0.1 * 31) + (0.3 * 13) + (0.4 * 12) + (0.2 * -9) = 10% Standard Deviation = (p1 (r1 – E(R))2) + (p2 (r2 – E(R))2) + (p3 (r3 – E(R))2) + (p4 (r4 – E(R))2) = (0.1 (31 – 10)2) + (0.3 (13 – 10)2) + (0.4 (12 – 10)2) + (0.2 (-9 – 10)2) = 44.1 + 2.7 + 1.6 + 72.2 = 120.6 squarred % = 10.98 b. Expected Return on Security A = (p1 * r1) + (p2 * r2) + (p3 * r3) + (p4 * r4) = (0.1 * 15) + (0.3 * 18) + (0.4 * 10) + (0.2 * 3) = 11.5% Variance = (p1 (r1 – E(R))2) + (p2 (r2 – E(R))2) + (p3 (r3 – E(R))2) + (p4 (r4 – E(R))2) = (0.1 (15 – 11.5)2) + (0.3 (18 – 11.5)2) + (0.4 (10 – 11.5)2) + (0.2 (3 – 11.5)2) = 1.225 + 12.675 + 0.9 + 14.45 = 29.25 squarred % = 5.41 c. Covariance = (.31-.10) (.15-.115) + (.13-.10) (.18-.115) + (.12-.10) (.10-.115) + (-.09-.10) (.03-.115) / 4-1 = (.21) (.035) + (.03) (.065) + (.02) (-.015) + (-.19) (-.085) / 3 = 0.2445 / 3 = 0.00815 d. Coefficient Correlation = Cov (A, B) / SaSb = 0.00815 / .1098 * .541 = 0.137 Question 4 a. C = 7.2%/2 * 1000 = 36 n= 50 i= 4% Value of Bond = C/I * (1-1/(1+i)n) + F / (1+i)n = 36 / 0.04 * (1 – 1/1.0450) + 1000 / 1.0450 = 774 + 140.84 = 914.84 b. If the market rate becomes 5.8% then Value of Bond = C/I * (1-1/(1+i)n) + F / (1+i)n = 36 / 0.029 * (1 – 1/1.02950) + 1000 / 1.02950 = 934.44 + 239.8 = 1183.25 If the market rate becomes 10.2% then Value of Bond = C/I * (1-1/(1+i)n) + F / (1+i)n = 36 / 0.056 * (1 – 1/1.05650) + 1000 / 1.05650 = 597.86 + 65.62 = 663.48 c. Value of zero coupon bond = 1000 / (1.04)50 = $140.84 d. The value of the bond gets altered due to the market rate as it helps to determine whether the bond sells at a premium value or at a discount rate. It is clearly evident that when the market rate is below the bond rate then the bond sells at a premium as the return the investors gets is higher and when the market rate is more than the bond rate than the bond sells at a discount as there are other lucrative investment avenues in the market which the investors can look forward to. This results in determining whether the investor will look towards investing in the bond or not. Also, in situations when the bond rate matches the market rate then it results in no gain and loss situation. Thus the bond prices get affected by the prevailing bond and market rates on the instrument traded. Question 5 a. FV of share = PV (1+ i)n = 2.35 (1+ 0.22)5 = 6.351 is the future value after 5 years Present value for the same at the discount rate of 15% is PV = FV / (1+i)n = 6.351 / (1.15)5 = 3.16 b. D = 6.351; g = 6%; R = 15% Value of the share = D (1+g) / R – G = 6.351 (1.03) / .15 - .06 = 72.68 c. D= 2.35; R = 15%; 81-3 = 22%; g4+ = 6% P0 = D1 / (1+R) + D2 / (1+R)2 +….. + Pt / (1+R)t Pt = Dt+1 / R – g4+ Pt = 2.35 * (2.35)3 * 1.06 / 0.15 - -.6 = 359.19 P0 = 2.35 * 2.351 / 1.15 + 2.35 * 2.352 / 1.152 + 2.35 * 2.353 / 1.153 + 359.19 / 1.153 = 4.8022 + 9.8131 + 20.0529 + 236.1733 = 270.8415 Read More