Laurel, Inc., and Hardy Corp. both have 7 percent coupon bonds outstanding, with
ID: 2815065 • Letter: L
Question
Laurel, Inc., and Hardy Corp. both have 7 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has four years to maturity, whereas the Hardy Corp. bond has 15 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Laurel Percentage change in price of Hardy If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Laurel Percentage change in price of HardyExplanation / Answer
Requirement 1:
Percentage change in price of Laurel
-6.60 %
Percentage change in price of Hardy
-16.29 %
Requirement 2:
Percentage change in price of Laurel
7.17 %
Percentage change in price of Hardy
20.93 %
Explanation:
As the price of bonds is same as per value, coupon rate must be equal to yield rate I.e. 7 % p.a.
If the interest increases by 2 %, the price of bond will change as:
Formula for Bond Price = C x [1-{1/ (1+r) n}/r ] + M/(1+r)n
M = Face Value = $ 1,000
C= Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually
= ($ 1,000 x 7 %)/2 = $ 70/2 = $ 35
r = Rate of interest = 7 % + 2 % = 9 % p.a. or 0.09/2 = 0.045 semiannually
n = No of periods to maturity = 4 years x 2 periods = 8 periods
New bond Price Laurel Inc. = $ 35 x [1-{1/ (1+0.045)8}/0.045] + $ 1,000/ (1+0.045)8
= $ 35 x [1-{1/ (1.045)8}/0.045] + $ 1,000/ (1.045)8
= $ 35 x [1-(1/ 1.422101)/0.045] + $ 1,000/ 1.422101
= $ 35 x [(1- 0.703185)/ 0.045] + $ 703.1851
= $ 35 x (0.296815/0.045) + $ 703.1851
= $ 35 x 6.595886 + $ 703.1851
= $ 230.856 + $ 703.1851
= $ 934.0411 or $ 934.04
Change in bond price = (new price – original price)/ original price
= ($ 934.0411 - $ 1,000)/$ 1,000
= $ -65.9589/$ 1,000 = -0.0659589 or - 6.60 %
For Hardy Corp. bond n = 15 years x 2 periods = 30 periods
New bond Price Hardy Corp. = $ 35 x [1-{1/ (1+0.045)30}/0.045] + $ 1,000/ (1+0.045)30
= $ 35 x [1-{1/ (1.045)30}/0.045] + $ 1,000/ (1.045)30
= $ 35 x [1-(1/ 3.745318)/0.045] + $ 1,000/ 3.745318
= $ 35 x [(1- 0.267)/ 0.045] + $ 267
= $ 35 x (0.733/0.045) + $ 267
= $ 35 x 16.28889 + $ 267
= $ 570.1111 + $ 267
= $ 837.1111 or $ 837.11
Change in bond price = (new price – original price)/ original price
= ($ 837.1111 - $ 1,000)/$ 1,000
= $ -162.8889/$ 1,000 = -0.1628889 or -16.29 %
If the interest decreases by 2 %, the price of bond will change as:
r = 7 % - 2 % = 5 % p.a. or 0.05/2 = 0.025 semiannually
New bond Price Laurel Inc. = $ 35 x [1-{1/ (1+0.025)8}/0.025] + $ 1,000/ (1+0.025)8
= $ 35 x [1-{1/ (1.025)8}/0.025] + $ 1,000/ (1.025)8
= $ 35 x [1-(1/ 1.2184029)/0.025] + $ 1,000/ 1.2184029
= $ 35 x [(1- 0.8207466)/ 0.025] + $ 820.74657
= $ 35 x (0.1792534/0.025) + $ 820.74657
= $ 35 x 7.1701372 + $ 820.74657
= $ 250.9548 + $ 820.74657
= $ 1,071.7014 or $ 1,071.70
14 Change in bond price = (new price – original price)/ original price
= ($ 1,071.7014- $ 1,000)/$ 1,000
= $ 71.7014/$ 1,000 = 0.0717014 or 7.17 %
New bond Price Hardy Corp. = $ 35 x [1-{1/ (1+0.025)30}/0.045] + $ 1,000/ (1+0.025)30
= $ 35 x [1-{1/ (1.025)30}/0.025] + $ 1,000/ (1.025)30
= $ 35 x [1-(1/ 0.4767427)/0.025] + $ 1,000/ 2.0975676
= $ 35 x [(1- 0.267)/ 0.025] + $ 476.7427
= $ 35 x (0.5232573/0.025) + $ 476.7427
= $ 35 x 20.930293 + $ 476.7427
= $ 732.56024 + $ 476.7427
= $ 1,209.3029 or $ 1,209.30
Change in bond price = (new price – original price)/ original price
= ($1,209.3029 - $ 1,000)/$ 1,000
= $ 209.3029/$ 1,000 = 0.2093029 or 20.93 %
Percentage change in price of Laurel
-6.60 %
Percentage change in price of Hardy
-16.29 %
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