Question

A 15-year, $1,000 par bond with a 6.5% semi-annual coupon currently trades at a price of $1,215. If the yield to maturity of the bond remains constant, what will be its price in six years?

• A. $1,268.00

• B. $1,145.73

• C. $1,080.16

• D. $846.71

• E. $1,103.49

Answer 1

Information given:

Time - 15 years

Coupon rate - 6.5%

Price - $1215

Par value - $1000

Yield to maturity formula:

Where,

C - Coupon rate

F - par value

P - Price

n - Years to maturity

YTM =

= 65 - 215/15 / 2215/2

= 65 - 14.33 / 1107.5

= 0.0457 or 4.57%

In six years, there are 9 years remaining:

Price = Current price of par value + present value of coupon rate

Price = 1000/ (1+4.57/100)^9 + ( 32.5/ (1+4.57/100)^0.5 + ..... + 32.5/ (1+4.57/100)^9 )

Solving using excel:

Face Value	1000
Rate	4.57%
Coupon payment	32.5
Year	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6	6.5	7	7.5	8	8.5	9
Discount rate	0.977905	0.956297	0.935167	0.914504	0.894298	0.874538	0.855215	0.836318	0.817839	0.799769	0.782098	0.764817	0.747918	0.731392	0.715232	0.699428	0.683974	0.668861
PV of coupons	31.7819	31.07966	30.39294	29.72139	29.06468	28.42248	27.79448	27.18034	26.57978	25.99249	25.41817	24.85654	24.30732	23.77024	23.24503	22.73142	22.22915	690.5992
Sum	1145.167

This price in 6 years is approx. 1145.167$ [The slight difference is ue to the method used to find the YTM value, it is an approximation method]

Thus, answer - B. 1145.73$

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