Question

You have been hired to value a new 20-year callable, convertible bond, with a $1,000 par value. The bond has a coupon rate of 5 percent, payable annually. The conversion price is $92, and the stock currently sells for $34.10. The stock price is expected to grow at 10 percent per year. The bond is callable at $1,300, but, based on prior experience, it won’t be called unless the conversion value is $1,400. The required return on this bond is 7 percent.

What value would you assign to this bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Value of the bond
Year	Cash Flow	Present value factor (7%)	Present Value ($)
01-20	$1000*5%	50	10.594	529.7
20	$1000+$50	1050	0.2584	271.32
Value of the bond	801.02

For further understanding :-
Year	value of the share at beginning of the year (a)	Growth in value of equity @10% per annum (b)	value of a share @ end of the year(a+b)=c	(c)* 11 shares(no of shares - see workings)
1	34.1	3.41	37.51	413
2	37.51	3.75	41.26	454
3	41.26	4.13	45.39	499
4	45.39	4.54	49.93	549
5	49.93	4.99	54.92	604
6	54.92	5.49	60.41	665
7	60.41	6.04	66.45	731
8	66.45	6.65	73.10	804
9	73.10	7.31	80.41	884
10	80.41	8.04	88.45	973
11	88.45	8.84	97.29	1070
12	97.29	9.73	107.02	1177
13	107.02	10.70	117.72	1295
14	117.72	11.77	129.49	1424
15	129.49	12.95	142.44	1567
16	142.44	14.24	156.69	1724
17	156.69	15.67	172.36	1896
18	172.36	17.24	189.59	2086
19	189.59	18.96	208.55	2294
20	208.55	20.86	229.41	2523
	Workings:-
	Note:- As conversion ratio is not given, it is calculated on basis of given information.
	Conversion Price =	Par Value of Bond
		Conversion ratio
	92	=  1000
		Conversion ratio
	Conversion ratio	= 1000 / 92
		= 11 shares (rounded off)
Conclusion:-
As they expect value of the bond to be $1400 in the 14th year, it can be callable.