Question

Consider a convertible bond with the information given below; assuming the bond is non-callable and non-puttable.

Maturity = 10 years

Coupon rate = 8%

Conversion ration = 40

Par value = $1,000

Convertible bond’s current market price = 920

Current market price per share of the underlying stock = $20

Annual dividend per share = $0.50

Comparable bonds without the conversion option are trading to yield 12%

Required 1. a. Market conversion premium per share (1point)

b. Market conversion premium ratio (1point)

c. Downside risk of the convertible bond (give a numerical measure, not just a statement (1point)

d. Premium payback period (1 point)

2. Suppose, in one month from now, the price of the underlying stock goes up from $20 to $30 per share.

a. What will be the approximate difference in the realized rates of return from investing directly in the underlying stock versus investing in the convertible bond? (2 points)

b. Why did the difference calculated in part a. above occur? (1 point)

3. Suppose, in one month from now, the price of the underlying stock declines from $20 to $10 per share.

a) What will be the approximate realized rate of return from investing in the underlying stock? (1 point)

b) What will be the approximate realized rate of return from investing in the convertible bond? (3 points)

c) Why did the difference in the realized rates of return calculated in parts a. and b. above occur? (1 point)

Answer 1

Answer,

A. Market Conversion premium per share.

=Market Conversion Price - Market Conversion Value.

Market Conversion Price =Market price of convertible bond / Conversion ratio

ie, = 920/40 =23

Premium per share = 23-20 =3

B. Market Conversion premium Ratio

= Market price - Conversion Value

Conversion Value.

= 920 - (40* 20)/ (40* 20)

920 - 800 = 120/800 =15%

C. Downside risk of Convertible bond

=Market Price of convertible bond - Straight value of bond /Straight value of bond.

Here, Straight value of bond =PVIF of 10 years interest @ 12 %

Interest = 8% of 1000= 80

PVIF value of 10 years @12 % = 5.650 *80 =452 + (1000* .PVIF of 10 th Year .322 )

=452 + 322 =774

Downside risk =920 - 774/ 774 =146 / 774=18.86 %

D.Premium Pay Back Period =Conversion Premium per Share / Favorable Income Differencial Per share.

Favourable Income Differencial per share = Coupon Interest from debenture - conversion Ratio* Dividend per share/

Conversion ratio

so, Faviorable income differncial per share = 80 - 40*.50 / 40

= 80-20/40 =60/40=1.5.

Premium payback = 3 ( Ans of Q no A )/ 1.5 =1.5years