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

Answer:

(a) 1.91 years

(b). $987.96

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%.