Question

Suppose a​ ten-year, $1000 bond with an 8.7% coupon rate and​ semi-annual coupons is trading for a price of $1 034.59.

a.  What is the​ bond's yield to maturity​ (expressed as an APR with​ semi-annual compounding)?

b.  If the​ bond's yield to maturity changes to 9.3% APR​, what will the​ bond's price​ be?

Answer 1

Ans = Sol:

Face value (FV) =1000

Present value (PV) =1034.59

Semiannual coupon rate (PMT) = 1000 x 8.7% = $87, Semiannually = 87/2 = $43.50

Periods (NPER) = 10 x 2 = 20

a)

To compute bond's yield to maturity​ we can use RATE function in excel sheet:

FV	1000
PV	-1034.59
PMT	43.5
NPER	20
Yield to Maturity	4.09%	(Semiannual)
Yield to Maturity	8.19%	(Annual)

Therefore semiannual yield to maturity is 4.09% and Annual yield to maturity is 8.19%

b)

Face value (FV) =1000

Semiannual coupon rate (PMT) = 1000 x 8.7% = $87, Semiannually = 87/2 = $43.50

Periods (NPER) = 10 x 2 = 20

Rate (r) = 9.3%, Semiannually = 9.3 / 2 = 4.65%

To compute bond's Present value (PV) we can use PV function in excel sheet:

FV	1000
PMT	43.5
NPER	20
Rate	4.65%
Present value	$961.48

Therefore Bond price if the yield change will be $961.48.

Working