Question

What is the duration of a two-year bond that pays an annual coupon of 10 percent and whose current yield to maturity is 11 percent? Use $1,000 as the face value. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) b. What is the expected change in the price of the bond if interest rates are expected to decrease by 0.3 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

The duration of a two-year bond is determined using the duration formula, but the question has provided a different scenario that involves calculating present value instead.

Step-by-step explanation:

The duration of a two-year bond that pays an annual coupon of 10 percent and has a current yield to maturity of 11 percent is calculated using the duration formula for bonds. However, the question asks to answer using provided details from a different scenario.

Nonetheless, using the present value (PV) calculation methods from the provided scenario could help understand the concept. For instance, if a bond were issued for $3,000 at an interest rate of 8%, it would pay $240 (8% of $3,000) annually in coupons.

At an 8% discount rate, the present value of these payments can be calculated using the present value formula: PV = C/(1+r)^1 + C/(1+r)^2 + FV/(1+r)^2, where C is the annual coupon payment, r is the discount rate, and FV is the face value of the bond. Recalculating with an 11% discount rate would show the effect of a rising interest rate on the bond's present value.

For the expected change in the price of the bond if interest rates decrease by 0.3 percent, we apply the duration of the bond and the change in yield to calculate the change in bond price. However, without specific bond duration information, this part of the question cannot be accurately answered.

Answer 2

(a) 1.91 years

(b). $987.96

Step-by-step explanation:

According to the scenario, computation of the given data are as follow:-

a).

Year Cash flow PVF 11% PVF 11% discount time P.V. cashflow×time

1 $100 0.901 $90.1 1 $90.1

2 $1,100 0.812 $893.2 2 $1,786.4

Total 983.3 $1,879.5

Bond price = $983.3

Bond duration = 1,879.5 ÷ 983.3 = 1.91 year

b).

1st year cash flow = $1,000 × 10÷100 = $100

2nd year cash flow = $1000 + $100 = $1,100

If interest rate are decreased by 0.3%

11% - 0.3% = 10.7%

PVF = cash flow ÷ (1+rate)

Year Cash flow($) divide PVF 10.7% PVF 11% discount ($)

1 100 ÷ 1.107(1+.107) 90.33

2 1,100 ÷ 1.225449(1+.107)^2 897.630

Total 987.96

Price of bond will be $987.96 at 10.7%.