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4) Suppose there is a 3-year bond with a $1000 face value, 30% annual coupon payments and a 20% annual yield to maturity a) Without any calculation, briefly explain whether this bond will be selling a premium or a discount Calculate the price of this bond Calculate the duration of this bond Suppose the interest rates in the economy rise by 5 percentage points immediately after someone bought this bond. Show a calculation using duration for what should happen to the price of this bond immediately Suppose now one year passes and the interest rates in the economy are still 5 percentage points higher. If the person that owns this bond sells it for fair value, what would be their one year rate of return? Show a calculation. b) c) d) e)
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nswer tHere, Coupon kati alCu c duwati en oy boud 24 3.bl2lo. 652l1 dy 16-6จ 526 & 3 la-36 , 11 29 23 , 61 , 12.04h % 2ぶ 102Aio1210.65 Ra tuun Cto2 1210.bio6Sus 256 2300o oo 3 30 900 520、83 361 WLLu Coupon --faCL value Coup en sate 2.0% , n.. 31 (c) oluta ton btnol be touwInputs Rate Convention: 1 EAR, 0 APR Annual Coupon Rate (CR) Yield to Maturity (Annualized) (y) Number of Pavments/ Year (NOP Number of Periods to Maturity Face Value (F 0 30.00% 20.00% 3 $1,000 Outputs Discount Rate Period (RATE) Coupon Payment (PMT) 20.0% $300 Calculate Bond Duration using the Cash Flows Period Time (Y ears Cash Flows Present Value of Cash Flow Weight Weight * Time Maculay Duration Modified Duration 0 3 3.0 3 3.0 0.0 2.0 Total $300.00$300.00 $300.00 $1,000.00 $1,900.00 $250.00 $208.33 $173.61 $578.70 $1,210.65 20.6501% 17.2084% 14.3403% 47.8011% 100.0% $2.41 0.207 0.344 0.430 1.434 2.41 2.01BOND DURATION Basics 3 Inputs 4 Rate Convention 1 EAR, 0 APR 5 Annual Coupon Rate (CR) 6 Yield to Maturity (Annualized) (y) 7 Number of Payments Year ( 8 Number of Periods to Maturity (T) 9 Face Value (FV) 10 11 Outputs 12 Discount Rate /Period (RATE 13 Coupon Payment (PMT) 1000 15 Calculate Bond Duration using the Cash Flows 16 Period 17 Time (Years 18 Cash Flows 19 Present Value of Cash Flow 20 Weight 21 Weight Time 22 Maculay Duration 23 Moditied Duration -B16/NOP -C16/NOP PMT =C18/((1 + RATE)C16) -C19/SGS19 C20 C17 -D16/NOP -E16/NOP PMT モ18/K1 + RATE)E16) モ19/SG$19 -F16/NOP 1000 :F18/((1+RATEYF16)|=SUM(C19:F19) -F19/SGS19 :F20F17 Total PMT =D18/((1+RATErD16) -D19/SG$19 D20 D17 -SUM C18 F18) G19/SG$19 SUM(C21 F21) 20E 1 7 -SUM C21:F21) -B22(1+RATEaculy duration 2-4 n) Coupon faC Value Coupon ati 1000 x 30 -800 Subati ingtrtau la noe

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