Question

A bond with a face value of $1,000 has 8 years until maturity, carries a coupon rate of 7.0%, and sells for $1,085. a. What is the current yield on the bond? (Enter your answer as a percent rounded to 2 decimal places.) b. What is the yield to maturity if interest is paid once a year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.) c. What is the yield to maturity if interest is paid semiannually? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.)

Answer 1

a

Current yield = annual interest / price of bond * 100

Given details:

Annual interest = 1000 * 7% = 70

Price of bond = 1085

Current yield = 70/1085 *100= 6.45%

b

Yiled to maturity is nothing but IRR of the bond where initial investment is the bond price and future cash flows are interest payments and principle repayment at bond period end.

At around 5.65% the present value of cash interest payments and principal repayment total matches with the given bond price of $1085

Particulars	Cash flow	Discount factor	Discounted cash flow
Interest payments-Annuity (5.65%,8 periods)	70.0	6.2967	440.77
Principle payments -Present value (5.65%,8 periods)	1,000	0.6442	644.23
Bond price			1,085.01

c

when interest is paid semi-annually, selection of annuity factor and present value factor differs as interest is compounded semi-annually.

Interest payment will be = 1000* 7%* 6/12 = 35

total interest payments = 8 years * 2 times a year = 16

At around 5.6639%

	Particulars	Cash flow	Discount factor	Discounted cash flow
	Interest payments-Annuity (2.83195%,16 periods)	35.0	12.7240	445.34
	Principle payments -Present value (2.83195%,16 periods)	1,000	0.6397	639.66
A	Bond price			1,085.00
	Face value			1,000
	Premium/(Discount)			85.00
	Interest amount:
	Face value	1,000
	Coupon/stated Rate of interest	7.00%
	Frequency of payment(once in)	6 months
B	Interest amount	1000*0.07*6/12=		35
	Present value calculation:
	yield to maturity/Effective rate	5.6639%
	Effective interest per period(i)	0.056639*6/12=		2.832%
	Number of periods:
Ref	Particulars	Amount
a	Number of interest payments in a year	2
b	Years to maturiy	8
c=a*b	Number of periods	16

#Please comment if further explanation is required. Your rating is appreciated#

of yield to maturity bond price matches $1085