Question

A A consol (perpetuity) with a yearly payment of $20, calculate the rate of return for the year if its yield to maturity at the beginning of the year is 29 and at the end of the year the interest rate unexpectedly rises to 4%. B. A 2% coupon bond, with a $1,000 face value, selling at par with 2 years to maturity, calculate the rate of return for the year if its yield to maturity at the beginning of the year is 2% and at the end of the year the interest rate unexpectedly rises to 4%. Briefly explain why there is a difference between the results of the rate of return of the consol and the coupon Bond.

Answer 1

Yearly payment $20 sate of letum e? yuld to maturity at leeguining a 2% at the end of the year e 4% Current yeild & Annual & ruleust paid to - market puce Present value iba D is the payment r is discount eate 208 TEF 7.08 (150ogo go 1 + eo x 0.04 : 2000.04(1+r) zor rz 0.04 +0.048 0.96 re 0.04 - Pa 0.0416 82 4.16% when 20 20 x 0.02 It opp 82 0.02 +0.020 . 0.98 r.3 0.02. 0.0204 ? Scannadaniel CamScanner

Camlin Page Date - 0.04 . The cate of retum ie the disconting will de 2.04% when yield to maturity is a to and will increase to 4.16% vohen it is 470 LIEF 2% coupon lond face value a na $1000 2 years maturity interest rate 2% at the beginning - 4% at the end of the Rate of retum & |- |1t )_+_F r/n and year (1+r/n)-nxt, - ne nof years a 2 OR 1- (1 + YTM) e утм (1+ утм) c x YIM = yilla to maturity ca coupon payment p.:? Par value n No of years (0.02x1900) x ! - [1+0.02) + - 0.04 1000 (1+0.04) Scanned with CamScanner

-0.02 x 1000 * Camin Page Date 0.02 202_ X +0.02 1021100 0.0 2 1 .02. - 19.6208 -0,04x 1196.41X L140.04 + 980.392 11 96. 4 4 9.999 2480.398 + 39.996 oo 0.04* 1000 7496_x_0.96 .04. 36.39 45.25 tot 961.5 t 961.5 999.89 Total 2 1999.88 0.ll 384_ 1__5.69. of Rate of retum & s.r% The difference in sate of retum in consol & 8 % coupon bonds is due to its maturity. Longa the matussity, Mates the investment Sunda lower the rate of return cs, Scanned with CamScanner