Question

A 15-year, 14% semiannual coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,075. The bond sells for $1,050. (Assume that the bond has just been issued.)

1 What is the bond's yield to maturity? Round your answer to two decimal places

2What is the bond's current yield? Round your answer to two decimal places

3 What is the bond's capital gain or loss yield? Loss should be indicated with minus sign. Round your answer to two decimal places

4 What is the bond's yield to call? Round your answer to two decimal places.

Answer 1

1) Yeild to Maturity for a bond is the return which would be earned (interest plus capital gain) if he/she holds bond upto maturity.

First Will find out approximate rate which can be rate of Yeild to Maturity By using below Formula

(C+ ((F-P)/2))/((F+P)/2)

Here C stands For Coupon Interest Payment it may be annually or short duration like semi annually quarterly or so

F = Face Value of Bond

P= Price which Investor Paid for Bond

N= no of Years to Maturity ( so here 30 times period in case of Semi Annually

= 70+((1000-1050)/30)/(1000+1050)/2 = 6.67% So YTM would be near by to 6.67% Semi Annually so Annual Rate would be 13.33% now let us check through reverse calulation by doing trial & Error Method

P= C*((1-(1/(1+i)ⁿ))/i) + (M/(1+i)ⁿ

P = Current Price of Bond

C= Coupon Payment

i=YTM Rate

M= Face Value

N=No of Coupon Payment

so P= 70*((1-(1/(1+0.66)³⁰))/.066) + (1000/(1+0.66)³⁰

P= 70*((1-(1/(1.066)³⁰))/.066) + (1000/(1.066)³⁰

P= 70*((1-(1/(6.80324))/.066) + (1000/6.80324)

P= 70*(((6.80324-1)/6.80324)/.066)) + (1000/6.80324)

P= 70*((0.85301))/.066) + (1000/6.80324)

P= 70*(12.9244) + (1000/6.80324)

P = 904.708+146.9853

P=1051.69 If We Consider 0.6666 then answer would be near to P =1050 so YTM =6.6666*2 =13.3332%

2) Bonds Current Yeild means Return divided by current price of bond

(1000*14%)/1050 =140/1050 =13.33%

3)Current yeild = ((P₁ -P₀)/P₀)*100

P1= Current Price of Bond $1050 Po = Original Price of bond Par Value so ((1050-1000)/1000)*100

(50/1000)*100

=5%

4)Yeild to call is the yield of a bond if you hold such security until the call date, but this yield would be effective only if the security is called prior to maturity. The calculation of yield to call is based on the coupon rate, the Duration of call and the market price.