Question

WTA bonds have a 5.80% coupon rate and paid annually. The face value is $1,000 and the current market price is $975. The bonds mature in 16 years. What is the yield to maturity?

Answer 1

Market price= ∑ coupon/(1+ytm)t+ face value/(1+ytm)n

Or we can apply the formula

Market price = (Coupon*PVFA) + (face value*PVF)

coupon= face valu*coupon rate

= 1000*0.58

coupon=58

Assume YTM as 10

PVFA for 16 years, 10% = 7.8237

PVF for 16 years, 10% = 0.2176

Market price at 10% YTM = (58*7.8237) + (1000*0.2176)

=453.77+217.6

Market price at 10% YTM = 671.37

Assume YTM as 5

PVFA for 16 years, 5% = 10.8378

PVF for 16 years, 10% = 0.4581

Market price at 10% YTM = (58*10.8378) + (1000*0.4581)

=628.59 +458.1

Market price at 10% YTM = 1086.69

YTM =

Lowest rate + [(value at lowest rate – market price)/(value at lowest rate – value at highest rate)] * difference in rate

= 5+[(1086.69-975)/(1086.69-671.37)]*10-5

= 5+(111.69)/(415.32)]*5

= 5+ 1.3445

YTM = 6.3445

Note- PVFA= present value factors for annuity

           PVF= present value factor