2. Bond valuation Calculate the price of a bond with 20 years remaining until it

Question

2. Bond valuation

Calculate the price of a bond with 20 years remaining until it is due. The coupon rate is 7%, par value is $1000. The required return on debt is 6% (equivalent risk)

Now assume a year has passed. Calculate the price of the bond now with 19 years remaining until it is due. The required return on debt has fallen to 4% (equivalent risk)

What is the capital gain (both $ and %) from holding the bond for a year (in A) and selling it at the price you calculated in (B)?

What is the coupon yield over the period?

What was the total return from holding for a year?

Now assume the required return on debt remained at 6%. Repeat B-E assuming that the required return on debt remained at 6%.

Explanation / Answer

B0 = I *[(1+i)n - 1] / [(1+i)n * i]
+ M/ (1+i)n

B0= bond's value at time zero

I= annual interest payments =70

i= discount rate=6%

n= number of years to maturity=20

M= par value (payment at maturity)=1000

So Bond’s value B0 = 70*[(1.06)20-1]/[(1.06)20*0.06] +1000/(1.06)20

=70*(2.207/0.1924)+311.81

=802.96+311.81

=1114.77

Current Bond price is $1114.77

After 1 year. n=19, i=4%

So Bond price= 70*[(1.04)19-1]/[(1.04)19*0.04]+1000/(1.04)19

=70*(1.107/0.0843)+474.60

=919.22+474.60

=1393.82

So Bond price after 1 year will be 1393.82

Capital Gain in One year is $ (1393.82-1114.77)= $ 279.05

Capital Gain %=25.03% (on price $1114.77)

Coupon yield in one year =$70 =7%

Total return from holding a year = Capital Gain + Coupon interest

=$279.05+$70

=$349.05

If after one year the required rate remain 6% , the n Bond price after one year will be

B0=70*[(1.06)19-1]/[(1.06)19*0.06] +1000/(1.06)19

= 70*(2.026/0.181)+330.47

=783.53+330.47

=1114.00

So the price reduced to $1114

Capital Loss is -$0.77

=-0.06%

Coupon yield is $70

Total Return from holding a year= -0.77+70=$69.23

B0 = I *[(1+i)n - 1] / [(1+i)n * i]
+ M/ (1+i)n

B0= bond's value at time zero

I= annual interest payments =70

i= discount rate=6%

n= number of years to maturity=20

M= par value (payment at maturity)=1000

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