Question

Suppose a​ ten-year, $1,000 bond with an 8.4% coupon rate and semiannual coupons is trading for $1,034.63.

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 9.1% APR, what will be the​ bond's price?

Answer 1

Bond's ytm = [C + (F-P)/n ] / (F + P)/2

Where C = Coupons = 1000 * 8.4% / 2 = 42

F= Face value = 1000

P= Price = 1034.63

n = years to maturity = 10 * 2 = 20

ytm =[ 42 + ( 1000 -1034.63) / 20] / [( 1000 + 1034.63)/2]

= [ 42 - 34.63 / 20] / (2034.63 /2)

= ( 42 - 1.7315) / 1017.315

= 3.96 %

Bonds ytm = 3.96 *2 = 7.92%

Year	Cashflows	Discounting Factor @9.1%	Present Value
0.5	42	0.956480153	40.17
1.0	42	0.914854283	38.42
1.5	42	0.875039965	36.75
2.0	42	0.836958359	35.15
2.5	42	0.800534060	33.62
3.0	42	0.765694940	32.16
3.5	42	0.732372013	30.76
4.0	42	0.700499295	29.42
4.5	42	0.670013673	28.14
5.0	42	0.640854781	26.92
5.5	42	0.612964879	25.74
6.0	42	0.586288741	24.62
6.5	42	0.560773545	23.55
7.0	42	0.536368766	22.53
7.5	42	0.513026079	21.55
8.0	42	0.490699263	20.61
8.5	42	0.469344106	19.71
9.0	42	0.448918322	18.85
9.5	42	0.429381466	18.03
10.0	1042	0.410694850	427.94
Price of Bond			954.67

If the​ bond's yield to maturity changes to 9.1% APR, the​ bond's price is $954.67