Question

A 20-year maturity bond pays interest of $90 once per year and has a face value of $1,000. Its yield to maturity is 10%. Over the upcoming year, you expect interest rates to decline and that the yield to maturity on this bond will only be 8% a year from now. Using horizon analysis, the return you expect to earn by holding this bond over the upcoming year is _________.

Answer 1

Answer:

Return = 29.64%

Explanation:

As per the data given in the question,

Time = 20 years

Interest = $90

Face value = $1,000

Rate = 10%

Current price of the bond = interest [1 - (1-rate)^(-time)] ÷ rate + Face value × (1+r)^(-time)

= 90 [1 - (1-0.10)^(-20)] ÷ 0.10 + $1,000 × (1+0.10)^(-20)

= 90 × 8.5136 + $1,000 × 0.14864

= $914.864

Price of the bond after 1 year = 90[1-(1-0.08)^(-19)] ÷ 0.08 + $1,000 × (1+0.08)^(-19)

= 90 × 9.6036 + $1,000 × 0.23171

= $1,096.04

Return = Ending price + Coupon - Beginning price ) ÷ Beginning price

= ($1,096.04 + 90 - $914.864) ÷ $914.864

= 0.2964  

= 29.64 %

Answer 2

The Return = 29.64%

• The calculation is as follows:

Current price of the bond = interest [1 - (1-rate)^(-time)] ÷ rate + Face value × (1+r)^(-time)

= 90 [1 - (1-0.10)^(-20)] ÷ 0.10 + $1,000 × (1+0.10)^(-20)

= 90 × 8.5136 + $1,000 × 0.14864

= $914.864

Now

Price of the bond after 1 year = 90[1-(1-0.08)^(-19)] ÷ 0.08 + $1,000 × (1+0.08)^(-19)

= 90 × 9.6036 + $1,000 × 0.23171

= $1,096.04

So,

Return = Ending price + Coupon - Beginning price ) ÷ Beginning price

= ($1,096.04 + 90 - $914.864) ÷ $914.864

= 0.2964  

= 29.64 %

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