Question

25. Today (T=0), an investor purchased a 20 year bond with a 5.00% coupon and a face value of $100,000 for $106,550. In six months (T=0.5) interest rates have decreased by 0.50% and the investor decides to sell the bond immediately after receiving the first coupon payment. What is the investor’s total gain (loss) on the bond? HINT: Total Gain (Loss) = Price Change in Bond + Coupon

1. ($6,548)

2. ($6,048)

3. $7,130

4. $7,602

5. $7,630

Answer 1

A1	B	C	D	E	F	G	H	I	J	K
2
3		Calculation of yield to maturity:
4		Face value	$100,000
5		Coupon rate	5%
6		Current Price	$106,550
7		Maturity	20	years
8		Semi-Annual Coupon	$2,500
9		Semi-annual Period	40
10
11		Cash flow to investor will be as follows:
12		Semi-Annual Period	0	1	2	3	4	…	40
13		Cash flow	($106,550.00)	$2,500	$2,500	$2,500	$2,500	$2,500	$102,500
14
15		Yield to maturity is the rate at which if future NPV to Investor will be zero.
16
17		Rate(nper,pmt,PV, [fv],type) function of excel can be used to find the yield to maturity as follows:
18		nper	40
19		pmt	$2,500
20		PV	($106,550.00)
21		FV	$100,000
22
23		Semi annual Yield to maturity	2.25%	=RATE(D18,D19,D20,D21)
24		Yield to maturity	=2* Semi-annual Yield to maturity
25			4.50%	=D33*2
26
27		Hence current interest rate is	4.50%
28
29
30
31		Calculation of Price of the Bond after 1st Payment:
32		Par value (F)	$100,000
33		Semiannual Coupon Rate	5%
34		Market demanded return (Yield to maturity)	4.00%	=D27-0.5%
35		Original term of Bond	20	Years
36		Number of coupons Paid	1
37		Interest is paid twice a year i.e. semiannual.
38		Semiannual coupon (C)	$2,500.00
39		Remaining Semiannual Period (n)	39
40		Semiannual YTM (i)	2.00%
41		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
42		Cash Flow of Bonds can be written as follows:
43		Semiannual Period	0	1	2	3	4	…	39
44		Cash Flow of Bonds		$2,500.00	$2,500.00	$2,500.00	$2,500.00	$2,500.00	$102,500.00
45
46		Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
47		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
48
49		Value of Bond after first coupon payment	=C*(P/A,i,n)+F*(P/F,i,n)
50			=2500*(P/A,2%,39)+100000*(P/F,2%,39)
51			$113,453.03	=D38*PV(D40,D39,-1,0)+D32*(1/((1+D40)^D39))
52		Hence Selling price of bond is	$113,453.03
53
54		Calculation of Total Gain:
55		Purchase Price of Bond	$106,550
56		Selling Price of Bond	$113,453.03
57		Coupon Received	$2,500.00
58
59		Total Gain	=(Selling Price - Purchase Price) + Coupon Received
60			$9,403.03	=(D56-D55)+D57
61
62		Hence total gain is	$9,403.03
63		None of the answers is matching.
64		Please check the options given again.
65