Question

Today (T=0), an investor purchased a 20 year bond with a 5.00% coupon and a face value of $100,000 for $106,550. In six months (T=0.5) interest rates have decreased by 0.50% and the investor decides to sell the bond immediately after receiving the first coupon payment. What is the investor’s total gain (loss) on the bond? HINT: Total Gain (Loss) = Price Change in Bond + Coupon

Answer 1

First, calculate the interest rates today at (T=0) using excel or financial calculator.

NPER     = 40 (Number of payment periods 20 years x 2)

PMT       = $2,500 (coupon payments = $100,000 x 5% x ½)

PV          = ($106,550) (Payment today at T=0)

FV           = $100,000 (Face value to be received at maturity)

Thus,

Rate       = 2.25% (Result)

The rate of 2.25% corresponds to 6 months. Thus, the annual rate is 2.25% x 2 = 4.50%.

Now, in six months at T=0.5, interest rates decrease by 0.50%. Therefore, new rate will be 4.50% - 0.50% = 4%.

Using the new rate, price of bond after 6 months at T=0.5 can be calculated using excel or financial calculator as below:

RATE      = 0.02 (rate per period = 0.04/2)

NPER     = 39 (Number of payment periods remaining)

PMT       = $2,500 (coupon payments)

FV           = $100,000 (Face value to be received at maturity)

Thus,

PV          = ($113,451) (Result, Rounded to nearest dollar)

Thus, the price of the bond increase by $113,451 - $106,550 = $6,901

Total gain on the bond = Increase in price of the bond + 1 coupon payment received

= $6,901 + $2,500

= $9,401

Thus, investor’s total gain on the bond is $9,401.