Question

Bond X is noncallable and has 20 years to maturity, a 7% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Formula sheet

A1	B	C	D	E	F	G	H	I	J	K
2
3		Calculation of Value of Bond after 5 Years:
4		Par value (F)	1000
5		Annual Coupon Rate	0.07
6		Yield to maturity after 5 year	0.105
7		Time to maturity	15	Years
8
9		Interest is paid once a year i.e. annual.
10		Annual coupon (C)	=D4*D5
11		Annual Period (n)	=D7
12		YTM (i)	=D6
13		Value of the bond can be calculated by finding the present value of cash flows of bonds.
14		Cash Flow of Bonds can be written as follows:
15		Period	0	1	2	3	4	…	=D11
16		Cash Flow of Bonds		=$D$10	=$D$10	=$D$10	=$D$10	=$D$10	=$D$10+D4
17
18		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
19		Where, C is coupon, F is par value of bond, i is market rate and n is total number of periods.
20
21		Current Value of Bond	=C*(P/A,10.5%,15)+F*(P/F,10.5%,15)
22			=D10*PV(D12,D11,-1,0)+D4*(1/((1+D12)^D11))	=D10*PV(D12,D11,-1,0)+D4*(1/((1+D12)^D11))
24
25		Hence value of the bond after 5 years is	=D22
26
27		Price of the bond can also be calculated by finding the present value of cash flows of the bond using PV formula of excel as follows:
28		RATE	=D12
29		NPER	=D11
30		PMT	=D10
31		FV	=D4
32		Price of the Bond	=-PV(D27,D28,D29,D30)	=-PV(D27,D28,D29,D30)
33
34		Hence value of the bond after 5 years is	=D24
34
35		Calculation of amount to be paid today:
36
37		Amount paid today will the present value of the value of bond after 5 years discounted at required rate of return.
38
39		Value of bond after 5 years from today	=D33
40		Required rate of return	0.09
41		Period	5	Years
42
43		Amount to be paid today	=Present value of the bond price at year 5
44			=$741.22*(P/F,9%,5)
45			=D39*(1/((1+D40)^D41))	=D39*(1/((1+D40)^D41))
46
47		Hence amount to be paid today for the bond is	=D45
48