Question

Consider a bond (with par value = $1,000) paying a coupon rate of 8% per year semiannually when the market interest rate is only 5% per half-year. The bond has three years until maturity.

a. Find the bond's price today and six months from now after the next coupon is paid. (Round your answers to 2 decimal places.)

Current price

Price after 6 months

b. What is the total (six-month) rate of return on the bond? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Answer 1

Par value of Bond	$             1,000.00
Semi annual coupon @8% pa=	$                   40.00
No of coupons due (semi annual)	6
Market interest rate semi annual	5%
PV annuity factor @5% for 6 periods=(1-1.05^-6)/5%=	5.07569
PV factor @5% for 6 period s=1/1.05^6=	0.74622

Let us find the curent Bond price from the PV of Future cash flows
Cash flow	Amt $	PVA /PV factor	PV of Cash flows=a*b
Semi annual coupon payments for 6 periods	$                 40.000	5.075692	203.03
Maturity value receivable after 6 semi annual periods	$             1,000.00	0.7462154	746.22
PV of Total Cash flows =			949.24
So Current Bond Price is $949.24	Ans a.

Ans a.
Let us find the Bond price after 6 months
No of coupons due (semi annual)	5
Market interest rate semi annual	5%
PV annuity factor @5% for 5 periods=(1-1.05^-5)/5%=	4.32948
PV factor @5% for 5 period s=1/1.05^5=	0.78353

Let us find the curent Bond price from the PV of Future cash flows
Cash flow	Amt $	PVA /PV factor	PV of Cash flows=a*b
Semi annual coupon payments for 5 periods	$                 40.000	4.329477	173.18
Maturity value receivable after 5 semi annual periods	$             1,000.00	0.7835262	783.53
PV of Total Cash flows =			956.71
So Current Bond Price is $956.71	Ans a.

Ans b.
Current Bond Price =	949.24
Bond Price after 6 months	956.71
Capital appreciation in 6 months	7.46
Add : Dividend received in 6 months =	40.00
Total Capital appreciation+Dividend =	47.46
Return in 6 months=47.76/949.24=	5.00%