Question

A ten year $1,000 bond has a 10% coupon rate convertible semiannually. It is callable at any time after a two-year lockout period. An investor wishes to buy the bond to yield at least 8% convertible semiannually. What is the price which will yield at least 8% convertible semiannually?? Please show work and steps without excel or financial calculator

Answer 1

If bond is callable at any time after a two-year lockout period and an investor wishes to buy the bond to yield at least 8% convertible semiannually. Therefore assume that yield-to-call is 8% per year

The formula to calculate the price of bond with the help of yield-to-call is as follows

P = C * {(1 – 1/ (1 + YTC) ^ t) / (YTC)} + (CP / (1 + YTC) ^t)

Where,

P = the current market price of bond =?

Par value or face value of the bond = $1000

C = the semi-annual coupon payment 10%/2 of par value = $1000*10%/2 = $50

CP = the call price = $1,000 (assumed it as the maturity value if the bond is callable)

t = the number of payment until the call date = 2 *2 years = 4

YTC = the yield to call =8% per annum or 8%/2 = 4% semi-annual

Therefore,

P = $50 *{(1- 1/ (1+ 4%) ^4)/ (4%)} + ($1,000/ (1+4%) ^4)

= $181.49 + $854.80

= $1036.30

If bond is callable then Price of bond is $1036.30

[And we have following formula for calculation of bond’s price with the help of yield to maturity (YTM) for the case when it is not called (normal bond price calculation)

Bond price P = C* [1- 1/ (1+YTM) ^n] /i + M / (1+YTM) ^n

Where,

P0 = the current market price of bond =?

C = the semi-annual coupon payment 10%/2 of par value = $1000*10%/2 = $50

n = number of payments = 2 * 10 years = 20

YTM = interest rate, or yield to maturity = 8% per annum or 8%/2 = 4% semi-annual

M = value at maturity, or par value = $ 1000

Now we have,

P = $50 * [1 – 1 / (1+4%) ^20] /4% + 1000 / (1+4%) ^20

= $679.52 + $456.39

= $1135.90

If bond is not callable then Price of bond is $1135.90]