Question

The Shallow Company has two bonds outstanding. Bond A was issued exactly 5 years ago at a coupon rate of 9%. Bond Z was issued exactly 1 year ago at a coupon rate of 8%. Both bonds were originally issued with semi-annual coupon payments, terms of 20 years, and face values of $1,000. The current yield to maturity (YTM) is 7.5% for both bonds. Which of the following statements is LEAST correct? The internal rate of return (IRR) on Bond Z is less than an investor's required return if they are only willing to pay $1000 for the bond. Bond 2 sells at a smaller price premium than Bond A. Bond A has higher price sensitivity to changes in interest rates than Bond z. The net present value (NPV) of Bond A is so if purchased for a price of $1133.72.

Answer 1

we need to find price of the bond first

Bond A
Years	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
Price	1133.72
Coupon payment(9% semiannual)		45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45
Par value																															1000
Total cashflows	-1133.72	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	45	1045
IRR	7.50%
NPV	$0.00

The cashflows of bond A for 15 years(30 semi annual terms) are plotted in excel. From this we can see that when the price of the bond is set at 1133.72, the NPV =0 which means bonds YTM is 7.5% at this price.

Hence option D is correct.

similarly plotting for bond z will show that other options are not correct