Question

A bond very recently purchased for $9, 000 has a face value of $10, 000 and a bond interest

rate of 10% per year payable semiannually. The bond is due (matures) in 3 years. The

company that issued the bond is contemplating a liquidity problem in 3 years and has just

advised all bondholders that if they will keep their bonds for an additional 2 years past the

original due date, the bond interest rate for the additional two years will be 16% payable

semiannually. (a) What nominal rate of return per year would the bondholder receive if he

held the bond for the additional two years? (b) What is the market value for the bond if

the required market rate of return on such bonds is 10%? Ignore the impacts of taxation.

Answer 1

[a]	The nominal rate of return is the IRR of the cash flows. IRR is that discount rate
	for which the PV of cash ouflows is equal to the PV of cash inflows of NPV = 0.
	Half year	Cash flow	PVIF at 7%	PV at 7%	PVIF at 8%	PV at 8%
	0	-9000	1	-9000.00	1	-9000.00
	1	500	0.93458	467.29	0.92593	462.96
	2	500	0.87344	436.72	0.85734	428.67
	3	500	0.81630	408.15	0.79383	396.92
	4	500	0.76290	381.45	0.73503	367.51
	5	500	0.71299	356.49	0.68058	340.29
	6	500	0.66634	333.17	0.63017	315.08
	7	800	0.62275	498.20	0.58349	466.79
	8	800	0.58201	465.61	0.54027	432.22
	9	800	0.54393	435.15	0.50025	400.20
	10	10800	0.50835	5490.17	0.46319	5002.49
				272.40		-386.86
	The IRR (semi-annual) lies between 7% and 8%.
	The exact value = 7+272.40/(272.40+386.86) = 7.413191%
	NOMINal RATE OF RETURN PER YEAR = 7.413191*2 = 14.83%
[b]	Market value for the bond is the PV of the expected cash inflows discounted
	at 5% (semi-annual interest rate)
	Half year	Cash flow	PVIF at 5%	PV at 5%
	1	500	0.95238	476.19
	2	500	0.90703	453.51
	3	500	0.86384	431.92
	4	500	0.82270	411.35
	5	500	0.78353	391.76
	6	500	0.74622	373.11
	7	800	0.71068	568.55
	8	800	0.67684	541.47
	9	800	0.64461	515.69
	10	10800	0.61391	6630.26
				10793.81
	MARKET VALUE FOR THE BOND = $10,793.81