Question

XYZ Company's convertible bond has 14 years to maturity, face value of $1,000 and a coupon rate of 5% paid annually.
The bond can be converted into 20 shares of common stock. Currently, similar 14 years to maturity bonds are yielding 9%.
XYZ does not distribute dividends.
a) Today, XYZ common stock closed at $70 per share. What is the lowest price that
this convertible bond could be trading at?
b) How would your answer change if today's stock price is $40 per share?
Give a numerical answer, not just a direction of change.
c) How would your answer change if today's stock price is $30 per share?
Give a numerical answer, not just a direction of change.
d) What will you do if the corporation calls the convertible bond? Assume the current stock price is $60,
and the call price is $1010.

Answer 1

Soln : a) We are considering here that instead of the bond value received, the bonds will be converted to common stock at given price of $70 per share. Accordingly the calculations are done.

Year	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Coupon	50	50	50	50	50	50	50	50	50	50	50	50	50	50
Value of share in terms of today price														1400
Discount rate @9%	0.92	0.84	0.77	0.71	0.65	0.60	0.55	0.50	0.46	0.42	0.39	0.36	0.33	0.30
PV	45.87	42.08	38.61	35.42	32.50	29.81	27.35	25.09	23.02	21.12	19.38	17.78	16.31	433.91
NPV	808.25

Value of the bond today = $808.25

(b) In case if the price is 40 per share, if it is converted will gve = 20*40 = $800< face valeu of bond , hence not to be converted.

Year	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Coupon	50	50	50	50	50	50	50	50	50	50	50	50	50	50
Value of share in terms of today price														1000
Discount rate @9%	0.92	0.84	0.77	0.71	0.65	0.60	0.55	0.50	0.46	0.42	0.39	0.36	0.33	0.30
PV	45.87	42.08	38.61	35.42	32.50	29.81	27.35	25.09	23.02	21.12	19.38	17.78	16.31	314.21
NPV	688.55

Value of convertible bond = $688.55

(c) Again if the stock price will get change to $30, the value of convertible bond remain same . As it convertible option not being converted.

Value of convertible bond = $688.55

(d) In case if the stck price = $60, then it is beneficial to convert it in common stock and hence the value of convertible bond = $748.40

Year	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Coupon	50	50	50	50	50	50	50	50	50	50	50	50	50	50
Value of share in terms of today price														1200
Discount rate @9%	0.92	0.84	0.77	0.71	0.65	0.60	0.55	0.50	0.46	0.42	0.39	0.36	0.33	0.30
PV	45.87	42.08	38.61	35.42	32.50	29.81	27.35	25.09	23.02	21.12	19.38	17.78	16.31	374.06
NPV	748.40

It is less than call price given by company , hence, we sell the bond to corporation.