Question

show work please ?

You have a 10 year treasury bond with 6 percent coupon rate per annum using spot rates all yields are continuously compounded.). Maturity CF Zero Rate Semiannual Zero Rate Semiannual Forward Rate Discount Factor PV of Cash Flow 2.882 2.753 0.080 0.083 0.089 0.040 0.042 0.045 0.040 0.043 0.051 0.961 0.918 0.858 0.051 N 0.057 0.061 0.070 0.065 0.062 0.092 0.095 0.098 0.101 0.106 0.109 0.110 0.112 0.116 0.117 0.120 0.124 0.123 0.125 0.132 0.134 0.136 0.046 0.047 0.049 0.051 0.053 0.054 0.055 0.056 0.058 0.059 0.060 0.062 0.061 0.063 0.066 0.067 0.068 بیا بیا بیا بیا بیا بیا با مما لها لما لها 0.816 0.772 0.711 0.653 0.572 0.559 0.536 0.495 0.383 0.412 0.341 0.259 0.432 0.242 0.118 0.193 0.162 1.022 ما 95 10.0 0.355 0.578 16.722 - a. Compute the missing forward rates in the table. b. Compute the missing present values of cash flow. c. Compute the value of the bond. d. Compute the duration and convexity.

Answer 1

Refer attached excel file for detailed solutions.

Answer (a): Computation of Forward Rates:

F/S = ((1 + Discount Rate)/(1 + Coupon Rate))^n

Where, F is the Forward Rate

S is the Spot Rate, i.e Semi Annual Zero Rate

Discount Rate is the Rate at which cash flows are discounted

Coupon Rate is the interest rate of the Bond

n is the maturity of the specific cash flows

Answer (b): Present Value of Cash Flows:

Cash Flows * Discount rate

Answer (c): Present Value of bond:

Sum of all Present Value of Cash Ffows

Answer (d): Duration of the Bond

Duration of the bond refers to the product of the Proportion of the cash flows and the period in which the cash flows occur. Simply put, it is the average payback period of the bond.

Answer (a):

Solution.xlsx - Excel Tell me what you want to do. - Sign in 0 X & Share Data Review View Power Pivot SSY Jabe = Home Insert Page Layout Formulas % Cut Calibri - 10 -A A ES Copy - Paste Format Painter Format Painter B I U . A Clipboard Font =, = = = Wrap Text Σ AutoSum ' Α Number 9 = = = =Merge & Center, $ % , 4 .09 Conditional Format as Cell Formatting Table Styles Styles BJJFill Insert Delete Format Clear Cells ZT Sort & Find & Filter Select Editing Alignment Number G7 4 А X ✓ fc =E7*((1+L7)/(1.06))^C7 в стр Е F I J K Ο Ι Ρ Ι Ο I Zero Rate 20-et Answers Maturity Semi Annual Zero Rate Semi Annual Forward Rate Discount Factor PV of Cash Flows Answers (b) Discount Rate (a) 2.883 2.754 0.040 0.043 0.051 0.051 2.448 2.316 0.053 0.13 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.500 5.000 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 ? ? ? 0.080 0.083 0.089 0.092 0.095 0.098 0.101 0.106 .109 .110 0.112 0.116 0.117 0.120 0.124 0.123 0.125 0.132 0.134 0.136 0.040 0.042 0.045 0.046 0.047 0.049 0.051 0.053 0.054 0.055 0.056 0.058 0.059 0.060 0.062 0.061 0.063 0.066 0.067 0.068 0.057 0.061 0.070 0.065 0.062 ? 0.961 0.918 0.858 0.816 0.772 0.711 0.653 0.572 0.559 0.536 0.495 0.383 0.412 0.341 0.259 0.432 0.242 10.118 0.193 0.162 2.883 2.754 2.574 2.448 2.316 2.133 1.959 1.716 1.677 | 1.608 1.485 1.149 1.236 1.023 0.777 1.296 0.726 0.354 0.579 16.722 8.28% 8.93% 10.75% 10.70% 10.91% 12.04% 12.95% 14.99% 13.80% 13.28% 13.64% 17.35% 14.62% 16.61% 19.74% 11.06% 18.17% 26.80% 18.91% 19.96% | Μ | Ν Ι Proportion Proportion of Bond of Bond Value * Value Time Value 0.06 0.03 0.06 0.06 0.05 0.08 0.05 0.10 0.05 0.04 0.04 0.14 0.04 0.14 0.04 0.16 0.03 0.17 0.03 0.17 0.02 0.15 0.03 0.17 0.02 0.15 0.02 0.12 0.03 0.22 0.02 0.13 0.01 0.07 0.01 0.35 3.53 Duration of the Bond 5.968 Answer (D) 1.149 1.236 1.023 0.082 0.107 0.098 0.117 0.155 0.089 0.159 0.331 0.200 0.234 ? 0.354 0.579 16.722 0.12 ? 103 Present Value of Bond (Answer (c)) 47.415 Sheet1 € Ready @ J -- + 100% + 10:56 PM A 7 * 23/03/2020 19

Answer (b)

Solution.xlsx - Excel Tell me what you want to do.... - Sign in 0 X & Share Data Review View Power Pivot =, = = = Wrap Text Σ AutoSum ' Α Custom 9 SSY Jabe = File Home Insert Page Layout Formulas % Cut Calibri - 10 -A A ES Copy - Paste Format Painter Format Painter BI U Clipboard Font K5 - x fc =H5*15 A B C D B u Insert Delete Format ZT S E M erge & Center, $ % , 4 Fill Clear .09 Conditional Format as Cell Formatting Table Styles Styles Sort & Find & Filter Select Editing Alignment Number Cells F G I J K Ο Ι Ρ Ι I Ο Maturity Answers Zero Rate 20-et Semi Annual Zero Rate Semi Annual Forward Rate Answers (a) Discount Factor PV of Cash Flows Discount Rate (b) 2.883 2.754 0.040 0.043 0.051 0.051 2.448 2.316 0.053 0.13 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.500 5.000 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 ? ? 0.080 0.083 0.089 0.092 0.095 0.098 0.101 0.106 .109 .110 0.112 0.116 0.117 0.120 0.124 0.123 0.125 0.132 0.134 0.136 0.040 0.042 0.045 0.046 0.047 0.049 0.051 0.053 0.054 0.055 0.056 0.058 0.059 0.060 0.062 0.061 0.063 0.066 0.067 0.068 0.057 0.061 0.070 0.065 0.062 ? 0.961 0.918 0.858 0.816 0.772 0.711 0.653 0.572 0.559 0.536 0.495 0.383 0.412 0.341 0.259 0.432 0.242 10.118 0.193 0.162 2.883 2.754 2.574 2.448 2.316 2.133 1.959 1.716 1.677 1.608 1.485 1.149 1.236 1.023 0.777 1.296 0.726 0.354 0.579 16.722 8.28% 8.93% 10.75% 10.70% 10.91% 12.04% 12.95% 14.99% 13.80% 13.28% 13.64% 17.35% 14.62% 16.61% 19.74% 11.06% 18.17% 26.80% 18.91% 19.96% | Μ | Ν Ι Proportion Proportion of Bond of Bond Value * Value Time Value 0.06 0.03 0.06 0.06 0.05 0.08 0.05 0.10 0.05 0.04 0.04 0.14 0.04 0.14 0.04 0.16 0.03 0.17 0.03 0.17 0.02 0.15 0.03 0.17 0.02 0.15 0.02 0.12 0.03 0.22 0.02 0.13 0.01 0.07 0.01 0.35 3.53 Duration of the Bond 5.968 Answer (D) 1.149 1.236 1.023 0.082 0.107 0.098 0.117 0.155 0.089 0.159 0.331 0.200 0.234 ? 0.354 0.579 16.722 0.12 ? 103 Present Value of Bond (Answer (c)) 47.415 Sheet1 € Ready @ J -- + + 100% 10:57 PM ^ * 2 * 23/03/2020 9

Answer (c):

Solution.xlsx - Excel Tell me what you want to do.... - Sign in 0 X & Share Review View Power Pivot AutoSum = Wrap Text Custom SSY Jabe = File Home Insert Page Layout Formulas Data Cut Calibri - 10 -A A = = E Copy - Paste B I U D , A, E Format Painter Clipboard Font K23 : x v fic =SUM(K3:K22) 4 А в стр Е B u Insert Delete Format ZT Merge & Center, $ % 48.09 Fill Clear Conditional Format as Cell Formatting Table Styles Styles Sort & Find & Filter Select Editing Alignment Number Cells F I J K Ο Ι Ρ Ι I Ο Zero Rate 20-et Maturity Answers Semi Annual Zero Rate Semi Annual Forward Rate Answers (a) Discount Factor PV of Cash Flows Discount Rate (b) 2.883 2.754 0.040 0.043 0.051 0.051 2.448 2.316 0.053 0.13 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.500 5.000 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 0.080 0.083 0.089 0.092 0.095 0.098 0.101 0.106 .109 .110 0.112 0.116 0.117 0.120 0.124 0.123 0.125 0.132 0.134 0.136 0.040 0.042 0.045 0.046 0.047 0.049 0.051 0.053 0.054 0.055 0.056 0.058 0.059 0.060 0.062 0.061 0.063 0.066 0.067 0.068 0.057 0.061 0.070 0.065 0.062 ? 0.961 0.918 0.858 0.816 0.772 0.711 0.653 0.572 0.559 0.536 0.495 0.383 0.412 0.341 0.259 0.432 0.242 10.118 0.193 0.162 ? ? ? ? 1.149 1.236 1.023 2.883 2.754 2.574 2.448 2.316 2.133 1.959 1.716 1.677 | 1.608 1.485 1.149 1.236 1.023 0.777 1.296 0.726 0.354 0.579 16.722 8.28% 8.93% 10.75% 10.70% 10.91% 12.04% 12.95% 14.99% 13.80% 13.28% 13.64% 17.35% 14.62% 16.61% 19.74% 11.06% 18.17% 26.80% 18.91% 19.96% | Μ | Ν Ι Proportion Proportion of Bond of Bond Value * Value Time Value 0.06 0.03 0.06 0.06 0.05 0.08 0.05 0.10 0.05 0.04 0.04 0.14 0.04 0.14 0.04 0.16 0.03 0.17 0.03 0.17 0.02 0.15 0.03 0.17 0.02 0.15 0.02 0.12 0.03 0.22 0.02 0.13 0.01 0.07 0.01 0.35 3.53 Duration of the Bond 5.968 Answer (D) 0.082 0.107 0.098 0.117 0.155 0.089 0.159 0.331 0.200 0.234 ? 0.354 0.579 16.722 0.12 ? 103 Present Value of Bond (Answer (c)) 47.415 Sheet1 + Ready @ J -- + + 100% 10:57 PM ^ * 2 * 23/03/2020 9

Answer (d):

0 Solution.xlsx - Excel Tell me what you want to do.... - Sign in 0 x & Share Review View Power Pivot AutoSum = Wrap Text Custom B u SSY Jabe = File Home Insert Page Layout Formulas Data Cut Calibri - 10 -A A = = E Copy - Paste BI U D A , EE Format Painter Clipboard Font N23 : x fic =SUM(N3:22) 4 А в стр Е ZT E Merge & Center - $ % 48.08 Insert Delete Format Conditional Format as Formatting Table Styles Fill Clear Cell Styles Sort & Find & Filter Select Editing Alignment Number Cells F I J K o P Q A I Maturity 20-et Zero Rate Semi Annual Zero Rate Semi Annual Forward Rate Answers (a) Discount Factor PV of Cash Flows Answers (b) Discount Rate 2.883 2.754 0.040 0.043 0.051 0.051 2.448 2.316 0.053 0.13 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.500 5.000 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 ? ? 0.080 0.083 0.089 0.092 0.095 0.098 0.101 0.106 .109 .110 0.112 0.116 0.117 0.120 0.124 0.123 0.125 0.132 0.134 0.136 0.040 0.042 0.045 0.046 0.047 0.049 0.051 0.053 0.054 0.055 0.056 0.058 0.059 0.060 0.062 0.061 0.063 0.066 0.067 0.068 0.057 0.061 0.070 0.065 0.062 ? 0.961 0.918 0.858 0.816 0.772 0.711 0.653 0.572 0.559 0.536 0.495 0.383 0.412 0.341 0.259 0.432 0.242 10.118 0.193 0.162 2.883 2.754 2.574 2.448 2.316 2.133 1.959 1.716 1.677 1.608 1.485 1.149 1.236 1.023 0.777 1.296 0.726 0.354 0.579 16.722 8.28% 8.93% 10.75% 10.70% 10.91% 12.04% 12.95% 14.99% 13.80% 13.28% 13.64% 17.35% 14.62% 16.61% 19.74% 11.06% 18.17% 26.80% 18.91% 19.96% I N Proportion Proportion of Bond of Bond Value * Value Time Value 0.06 0.03 0.06 0.06 0.05 0.08 0.05 0.10 0.05 0.04 0.04 0.14 0.04 0.14 0.04 0.16 0.03 0.17 0.03 0.17 0.02 0.15 0.03 0.17 0.02 0.15 0.02 0.12 0.03 0.22 0.02 0.13 0.01 0.07 0.01 0.12 0.35 3.53 Duration of the Bond 5.968 Answer (D) 1.149 1.236 1.023 0.082 0.107 0.098 0.117 0.155 0.089 0.159 0.331 0.200 0.234 ? 0.354 0.579 16.722 ? 103 Present Value of Bond (Answer (c)) 47.415 Sheet1 + Ready @ J -- + + 100% 10:57 PM ^ * 2 * 23/03/2020 F