Question

Hello,

Can you please answer this question with showing work.

A four-year bond has an 8% coupon rate and a face value of $1,000. If the current price of the bond is $870.51, calculate the yield to maturity of the bond (assume annual interest payments). Also, indicate whether the bond is a discount bond or a premium bond or a par bond.

Thanks

Answer 1

you have invested 870.51 in year 0 and coupon will be paid every year on face value of bond which would be 1000*8/100 = 80 per year and at the end of year 4 you will get 1000 par value.

so 870.51 = 80*PVIFA(x,4) + 1000*PVIF(x,4)

you can calculate through excel like as below -

year	Coupon rate
0	-870.51
1	80
2	80
3	80
4	1080

now use function IRR(sum of all-870,80,80,80,,1080) you will get yield to maturity = 12.29%

or we can solve it by interpolation also -

year	Coupon rate	Dis. @10%	PV @ 10%	Dis. @13%	PV @ 13%
0	-870.51	1	-870.51	1	-870.51
1	80	0.909091	72.72727	0.884956	70.79646
2	80	0.826446	66.1157	0.783147	62.65173
3	80	0.751315	60.10518	0.69305	55.44401
4	1080	0.683013	737.6545	0.613319	662.3842
			66.09269		-19.2336

now the IRR will be between 10% to 13% so

at (66.09+19.23) = 85.32 value comes on 3%

so on 66.09 --------------------3/85.32*66.09

= 2.32%

so IRR = 10+2.32 = 12.32%(with approximation error)

Please comment in case of any clarification required.