Question

A certain 7?% annual coupon rate convertible bond? (maturing in 20? years) is convertible at the? holder's option into 23 shares of common stock. The bond is currently trading at ?$820. The stock? (which pays 92?¢ a share in annual? dividends) is currently priced in the market at $35.87a share.

a.??What is the? bond's conversion? price?

b.??What is its conversion? ratio?

c.??What is the conversion value of this? issue? What is its conversion? parity?

d.??What is the conversion? premium, in dollars and as a? percentage?

e.??What is the? bond's payback? period?

f.?If comparably? rated, nonconvertible bonds sell to yield 9 % what is the investment value of the? convertible?

a. The? bond's conversion price is -$---------?? (Round to the nearest? cent.)

b.?The conversion ratio is --------------- shares. ?(Round to the nearest? integer.)

c.?The conversion value of this issue is ---------------?$ (Round to the nearest? cent.)

      The conversion parity of this issue is ----------------?$.?(Round to the nearest? cent.)

d.?The conversion premium in dollars is ?$---------- (Round to the nearest? cent.)

      The conversion premium as a percentage is ------------?%. ?(Round to two decimal? places.)

e.?The? bond's payback period is -------------years. (Round to one decimal? place.)

f.?The investment value of the convertible is ---------------?$? (Round to the nearest? cent.)

Answer 1

a) Conversion Price = $820.00

b) Conversion Ratio = 23

c) Conversion Value = 23 x 35.87 = $825.01

Conversion Parity = Bond Price / Ratio = 820 / 23 = $35.65

d) Conversion Premium = 820 - 825.01 = -5.01

As a percentage = -5.01 / 820 = -0.61%

e) Payback Period = Premium / (1 + Premium) / (Current Yield - Dividend Yield)

= -5.01 / (1 - 5.01) / (70/820 - 0.92/35.87) = 20.9 years

f) Investment Value is the value of the bond without convertible option, which can be calculated using PV function

I/Y = 9%, PMT = 70, FV = 1000, N = 20 => Compute PV = $817.43