Question

Compute the duration for Bond C and rank the bonds on the basis of their price volatility. The current rate of interest is 8 percent, so the prices of Bonds A and B are $1,000 and $1,268, respectively.

            Bond                   Coupon                   Term                           Duration

            A                           8%                       10 years                     7.25

            B                          12%                      10 years                       6.74

            C                           8%                       5 years                        ?

Confirm your ranking by calculating the percentage change in the price of each bond when interest rates rise from 8 to 12 percent. (Bond A’s and B’s prices become $774 and $1,000, respectively).

Answer 1

Calculation of the duration for Bond C:

Year (t)	Cash Flow from coupon payments (8% of $1000)	Cash Flow from maturity amount	Total Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 8% of yield to maturity	PV *t
1	$80.0		$80.0	$74.07	$74.07
2	$80.0		$80.0	$68.59	$137.17
3	$80.0		$80.0	$63.51	$190.52
4	$80.0		$80.0	$58.80	$235.21
5	$80.0	$1,000.0	$1,080.0	$735.03	$3,675.15
sum				$1,000.00	$4,312.13
				Bond's Price↑
			Duration = sum of (PV*t)/sum of PVs =	$4,312.13/$1,000	4.31	Years

Ranking of the bonds on the basis of their price volatility: Bonds with higher duration are more volatile

Bond                   Coupon                   Term                           Duration                 Ranking (High to low)

A                           8%                       10 years                     7.25                                        1

B                          12%                      10 years                       6.74                                       2

C                           8%                       5 years                        4.31                                        3

The percentage change in the price of each bond when interest rates rise from 8 to 12 percent:

Bond                 Coupon                  Term                     Duration         Ranking (High to low) % Change in Price

A                          8%                       10 years                     7.25                            1                            22.60%

B                         12%                      10 years                      6.74                           2                           21.16%

C                          8%                       5 years                        4.31                             3                          14.42%