Question

1. A 3% coupon, $1,000 face amount, 5-year bond is convertible into 25 shares of company stock. The current stock price is $30. At maturity, the stock price is $50. Assuming the bond is bought at issuance for $1,000, i.e. par, and interest is paid semi-annually, the total annual return for the investor will be:
   1. 3.00%
   2. 3.62%
   3. 7.24%
   4. 5.40%

Answer 1

	Frequency in a year	2
	YTM
	Coupon rate	3.00%
	Face value	$       1,000
	Coupon payment	$       15.00	=1000*3%/2
	Years to maturity	5
	No. of periods	10
	Maturity conversion	25 shares
	Maturity share price	50
	Total maturity amount	$       1,250	25*50
		3.00%						4.00%
Year	Cash Flow	PV factor = 1/ (1+r)^t	PV					PV factor = 1/ (1+r)^t	PV
0	$               (1,000.00)	1.000	$(1,000.00)					1.000	$(1,000.00)
1	$                      15.00	0.971	$       14.56					0.962	$       14.42
2	$                      15.00	0.943	$       14.14					0.925	$       13.87
3	$                      15.00	0.915	$       13.73					0.889	$       13.33
4	$                      15.00	0.888	$       13.33					0.855	$       12.82
5	$                      15.00	0.863	$       12.94					0.822	$       12.33
6	$                      15.00	0.837	$       12.56					0.790	$       11.85
7	$                      15.00	0.813	$       12.20					0.760	$       11.40
8	$                      15.00	0.789	$       11.84					0.731	$       10.96
9	$                      15.00	0.766	$       11.50					0.703	$       10.54
10	$                      15.00	0.744	$       11.16					0.676	$       10.13
10	$                 1,250.00	0.744	$     930.12					0.676	$     844.46
		Total	$       58.07					Total	$     (33.88)
NPV @ 0.03	58.07
NPV @ 0.04	(33.88)
Difference in both	91.95
Investor return	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=3%+ (4%-3%)*(58.070/(58.070+33.881)
Investor return=	3.62%