Question

Consider a 3 year bond with a face value is $1,000 and a 10% coupon rate

a) If the current interest rate is 2%, what should be the price of the bond?

b) If you could purchase the bond for $1,100, is the yield you are getting higher or lower than 2%? How can you tell?

c) Assume you purchase the bond for $1,100 and hold if for one year. You collect one coupon payment and then sell the bond for $980. What is your rate of return?

Answer 1

a) The price of the bond will be equal to the present value of the discounted cash flow generated by the bond at 2% rate of interest.

After first year $100 as coupon amount will be received and after second year another $100 will be received as a coupon amount and after 3rd year the face value plus the coupon amount will be received which is equal to ( 1000 + 100) = $1100.

Price of bond = 100/(1+.02) + 100/(1+.02)^2 + 1100/(1.02)^3

Price of bond = 98.03 + 96.11 + 1036.55

Price of bond =$1230.69 or approx $1,231.

b) Since the price we calculated in above part is inversely related to the yield or the discounting rate which is 2% or 0.02. Which means higher price will generate lower yield and lower price price will generate higher yield. So if the price is $1,100 as opposed to what we calculated as $1,231 then yield must be higher at this price since the price has decreased which means yield has to be higher than before which was at 2%.

So the yield will be higher.

C) Now we know the price of the bond and we need to calculate the yield.

Since the bond is sold just after 1 year after receiving the coupon payment of $100 and sold it for $980. So total amount received after 1 year is equal to $980 + $100 = $1,080

Price of bond = discounted cash flow.

1,100 = 1,080/(1+i)

Now we need to solve for i here.

1 + i = 1080/1100

1 + i = 0.9818

i = 1 - 0.9818

i = 0.0182

Or i = 0.0182×100 = 1.82%

So the rate of return in this case is 1.82%

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