Question

Suppose a 10-year, $1,000 bond with a 10% coupon rate and semiannual coupons is trading for a price of $ 913.23. a. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)? b. If the bond's yield to maturity changes to 9% APR, what will the bond's price be?

Answer 1

a

Calculator
Inputs:
PV	(913.230)
PMT	50.0
FV	1,000.00
N	20
Output:
I/Y = IRR	5.74%
Yield to maturity	11.48%

Answer is:

11.48%

b

Particulars	Cash flow	Discount factor	Discounted cash flow
present value Interest payments-Annuity (4.5%,20 periods)	$                         50.00	13.00794	$                650.40
Present value of bond face amount -Present value (4.5%,20 periods)	$                    1,000.00	0.41464	$                414.64
Bond price			$             1,065.04
Face value			$             1,000.00
Premium/(Discount)			$                  65.04
Interest amount:
Face value	1,000
Coupon/stated Rate of interest	10.000%
Frequency of payment(once in)	6 months
Interest amount	1000*0.1*6/12=		$                  50.00
Present value calculation:
yield to maturity/Effective rate	9.00%
Effective interest per period(i)	0.09*6/12=		4.500%
Number of periods:
Particulars	Amount
Number of interest payments in a year	2
Years to maturiy	10.0
Number of periods	20

Answer is:

1,065.04

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