What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887

Computation of Yield to Maturity using Rate Function in Excel:

=rate(nper,pmt,-pv,fv)

When Bond Price is $887:

Here,

Rate = Yield to Maturity = ?

Nper = 10 Years 

PMT = $1,000*9% = $90

PV = $887

FV = $1,000

Substituting the values in formula:

=rate(10,90,-887,1000)

Rate or Yield to Maturity = 10.91%

When Bond Price is $1,134.20:

Here,

Rate = Yield to Maturity = ?

Nper = 10 Years 

PMT = $1,000*9% = $90

PV = $1,134.20

FV = $1,000

Substituting the values in formula:

=rate(10,90,-1134.20,1000)

Rate or Yield to Maturity = 7.08%

Generally, the coupon prices are fixed, bond price and the interest rates are inversely proportional.

if the current market price of the bond is at the premium, the YTM of the bond is less compared to the bond which is at a discounted price.

Computation of Current Yield:

Current Yield = Annual Coupon / Price of Bond 

= $90/$887 

= 10.15%

Computation of Capital Gains yield:

Capital Gains yield = (Face Value-Purchase Price)/Purchase Price

= ($1,000-$887)/$887

=  12.74%

Computation of Total Return:

Total Return = Current Yield + Capital Gains Yield 

= 10.15% + 12.74%

= 22.89%