Question

Bond and Stock Value and Evaluation. PLEASE SHOW ALL FORMULAS/EQUATIONS AND SHOW ALL OF YOUR WORK. Do not use Excel.

2. A bond with annual coupon rate of 5.10% and price of $1,090 just yesterday paid a coupon. A total of 23 coupons remain to be paid. Suppose you buy the bond at today's price, hold it and receive 8 coupons, and then sell the bond. If at the time you sell the bond its YTM has decreased a total of 50 basis points, find the selling price of the bond. (FYI; 0.01=1%=100 basis points; use semiannual compounding). Note that the number of coupons left is the same as "n" at the time of pricing.

Answer 1

Given,

Present value (PV) = $ 1090

Coupon rate = 5.10%

Face value (FV) = $ 1000

Coupon payment = $ 1000 x 5.10% = $ 51

Semi annual Coupon payment (C) = $ 51/2 = $ 25.50

Total coupon (n) = 23

Solution :-

Lets assume YTm is S So, Stmi annual YTmly) 3.S% a 25.S0 0.025 1000 +00523/ 33 +0.025) 1000 CL0RSR3 1020 .0R53 1000 .76 4610 68 l02011- 1.76461068 eae O. 76461068 + 276461068 X- 1.764610 68 441.9688 +S66.6912 1008.666 Lets assume YTm is 4 7 So, Semi-arnual Tm Y) R O. 02

FV + ltyn Jo00 Utoni3 35.50 O.03 12I5 1000 .03)93+ l000 + 1.57689926 1.57689926 O. S768 9926 1.S7689926 l0o0 2.S7689936 + 466.4512 t 634.1559 $ 1100. 6021 Therc dent hen YTm is 3.5y, PU Is 41008.666 (less than l090 and when PU Is $1100. Go71mere PYTM is 2 than l090). S YTm lies behwcen R ard a.S

Yielel cto matuaity - LytHy- y)xPu of Ly-PV pu of Ly-Pu of Hy whert Lower YTM Higher YTM Hy= PV Paesent Value Nove Yield to matuaity 10o.6071-1090 1lo0. 6071-1008.666 = 0.02 H0025-0.0 10, 6071 0.00s X 91.9411 0.02 + 0.oo0S768 O.0205168 Semi -annual V7h This is u.12 Poual YTm is (R.06% x2)

50 basis points YIM decacased by Can Say, 0.s0 we Se u.122 YTM 0. So 11 3.62 . Semi annual VTMlE 3.62% No. of Perods 33 Nows Bond Parice- C FV + ltv RS.S0 0.0181 1000 ltooia's Lt0.018)15 s. S0 0.0181 000 Cle01813'15

35.S0 0.0181 000 1.30874960 + 7.30874960 O. 30874960 1.30814960 25.So O.018 1000 + 1.30874960 t 764.08& 333.36 $1096.45 1J ( 1
Thus, Selling price of the bond is $ 1096.45