Question

What is yield to maturity of $1000 face-value 8% coupon bond with a selling price of $1010 that has 1 year left to maturity? Assuming no inflation, under what conditions will this coupon bond have a negative yield (think about its selling price)? What about any coupon bond with any maturity?

Answer 1

1.
FV = 1000
PV = 1010
Nper = 1
PMT = 1000 * 8% = 80

Yield to maturity can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(1,80,-1010,1000)
= 6.93%

Yield to maturity = 6.93%

2.
The coupon bond may have a negative yield when the investors paid more than the face value.
For example, If the face value = $1000, Years to maturity = 1, Selling price = $1200, coupon rate = 8%, then yield to maturity:
=RATE(nper,pmt,pv,fv)
=RATE(1,80,-1200,1000)
= -10%

3.

If the bond has less years to maturity and the selling price is greater than the face value then the bond yield will be negative.

If the bond has less years to maturity:

face value = $1000
Years to maturity = 1
Selling price = $1200
coupon rate = 8%
Yield to maturity can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(1,80,-1200,1000)
= -10%

Here the bond has negative yield.

If the bond has more years to maturity:

face value = $1000
Years to maturity = 10
Selling price = $1200
coupon rate = 8%
Yield to maturity can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(10,80,-1200,1000)
= 5.36%

Here the bond has positive yield.