Question

The below bond is traded at yield 5.2 % and has seven (7) years to maturity. The face value is $1000 and coupons are paid semi-annually.

Bond	Coupon Rate
A	6.00%

(a) Calculate the price of the bond. (3 marks)

(b) Calculate the duration of the bond. (5 marks)

(c) Due to unforeseen circumstances, the last payment will be postponed to two years later. All other payments have no change. Calculate the new price and duration of the bond at the same yield. (12 marks)

Please write down the formulas and show the workings accurately.

Thank you

Answer 1

Answer - In below mentioned images, the price of a bond has calculated with duration

In part (C) the last payment has been extended to 2 years, so in that 2 years an investor will receive coupon payment. With the increase in time, the duration will also increases.

Ans Parka) Price of a Bond YTM (Yield To Maturity ) = 5.2%. Time period - 7 years Face value (Future Value) = $1000 Coupon Rate = 6.1 on (460) {re 1600x 6 = 607 Price . CFI (1+r) + CFg (1+0) ..... - & Cf ₂ (toys Con (178) where CF = Cash flow r = nate of interest CYTM) t = time period 60 +60 +60 +60 +60 14*)' (1452) (47572) (503)(1493) + 60 +1060 (160ot6o) . 216 11+52) where in 7 year an investon will receive inlerelt tfale rawe ) Price = $ 1045.95 Ans

Part B Duration of Bond D- (F (t) + CF (to) ...... (In (to) (Hr)* +(1+r)? СЕ CF (1+r) (tr (1+y) D= 60 (1) 60 (3 Go (3 ) 60(4) (1+5.2 ( 52 100 145.21 w 60 (1+5.2 60 GO 1752 (1+5.213 7 60 60 1452 1060 Crt512 145. 27 3 : 5.65019 years

Part of payment is postponed by 2 years then +60 + + 60 (1+r) (to je Go +60 1+2) 3 (178) 4 + 1060 (148)5 +60 (Ho) +60 +60 (Ita) (1878 (1409 = $ 1056.35 * duration (Hot T (14) CFG (9) (1429 (178 CFg (142) 2 (tra - 60 (1) 60(2) 1060 (9) (+ ) 60 60 (1+) (1152 1060 Do 69 year