Question

Company Y issues $1 million face value bond that matures in 3 years. The bond has a coupon rate of 5%. The required rate of return is 8% (compounded semiannually). Calculate the following. a)The price of the bond today.

b)The price elasticity of the bond, assuming that the required rate of return increases to 9%. Is the elasticity higher or lower when the bond has a lower coupon rate?

c)The modified duration of the bond. Use it to estimate the change in the bond price when the required rate of return increases by 1%.

Answer 1

					Face Value (USD)	1,000,000	1,000,000
					Maturity (Years)	3	3
					Coupon Rate	5%	5%
					Required Rate of return (Semiannually)	8%	9%
					Payout per year	2.00	2.00
					The price of the bond today.	$921,367.95	"-PV(Required Rate of Return / Payour per year,Maturity*Payout per year,Coupon Rate* Face Value/Payout per year, Face Value)"
					b)The price elasticity of the bond, assuming that the required rate of return increases to 9%. Is the elasticity higher or lower when the bond has a lower coupon rate?
					At %	8%	9%	13%	Change in required rate
					Price of Bond	$921,368	$896,843	-3%	Change in price
					Price elasticity of the bond			-21.29%	Change in price / Chanage in required rate
					Price elasticity of the bond			-21.80%	At 3% coupon
					Price elasticity of the bond			-21.29%	At 5% coupon
					Price elasticity of the bond			-20.63%	At 8% coupon
					From the above it is clear that the price elasticity is higher with lower coupon rates.
					c)The modified duration of the bond. Use it to estimate the change in the bond price when the required rate of return increases by 1%.
					period	1	2	3	4	5	6
					Cupon	25,000	25,000	25,000	25,000	25,000	25,000
					Face value						1,000,000
					Cash flow	25,000	25,000	25,000	25,000	25,000	1,025,000
					Sum of the time adjusted cashflow	22,936	42,084	57,914	70,843	81,241	3,667,044
					3,942,062	The Macaulay duration is calculated by multiplying the time period by the periodic coupon payment and discounting it by yield and total is later divided by price of the bond
					Current bond price	921,368
					Macaulay Duration	4.28
					Modified duration	Macaulay Duration /(1 + YTM/2)
					Modified duration	4.09	Macaulay Duration/(1+9%/2)