Bond J has a coupon rate of 4 percent. Bond K has a coupon rate of 14 percent. Both bonds have 17 years to maturity, a par value of $1,000, and a YTM of 8 percent, and both make semiannual payments.
a. 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.)
b.If interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
| a. | Bond J | -18.61% | ||||||||
| Bond K | -14.72% | |||||||||
| Working: | ||||||||||
| # 1 | Existing price of Bond J | = | =-pv(rate,nper,pmt,fv) | Where, | ||||||
| = | $ 631.78 | rate | = | 8%*(6/12) | = | 0.04 | ||||
| nper | = | 17*(12/6) | = | 34 | ||||||
| pmt | = | 1000*4%*(6/12) | = | $ 20.00 | ||||||
| fv | = | $ 1,000.00 | ||||||||
| Existing price of Bond K | = | =-pv(rate,nper,pmt,fv) | Where, | |||||||
| = | $ 1,552.34 | rate | = | 8%*(6/12) | = | 0.04 | ||||
| nper | = | 17*(12/6) | = | 34 | ||||||
| pmt | = | 1000*14%*(6/12) | = | $ 70.00 | ||||||
| fv | = | $ 1,000.00 | ||||||||
| # 2 | Price after rise of interest rate by 2 percent: | |||||||||
| New price of Bond J | = | =-pv(rate,nper,pmt,fv) | Where, | |||||||
| = | $ 514.21 | rate | = | 10%*(6/12) | = | 0.05 | ||||
| nper | = | 17*(12/6) | = | 34 | ||||||
| pmt | = | 1000*4%*(6/12) | = | $ 20.00 | ||||||
| fv | = | $ 1,000.00 | ||||||||
| New price of Bond K | = | =-pv(rate,nper,pmt,fv) | Where, | |||||||
| = | $ 1,323.86 | rate | = | 10%*(6/12) | = | 0.05 | ||||
| nper | = | 17*(12/6) | = | 34 | ||||||
| pmt | = | 1000*14%*(6/12) | = | $ 70.00 | ||||||
| fv | = | $ 1,000.00 | ||||||||
| # 3 | Percentage change in the price of: | |||||||||
| Bond J | = | (b-a)/a | Where, | |||||||
| = | -18.61% | a | Existing price | = | $ 631.78 | |||||
| b | New Price | = | $ 514.21 | |||||||
| Bond K | = | (b-a)/a | Where, | |||||||
| = | -14.72% | a | Existing price | = | $ 1,552.34 | |||||
| b | New Price | = | $ 1,323.86 | |||||||
| b. | Bond J | 24.84% | ||||||||
| Bond K | 18.87% | |||||||||
| Working: | ||||||||||
| # 1 | Price after fall of interest rate by 2 percent: | |||||||||
| New price of Bond J | = | =-pv(rate,nper,pmt,fv) | Where, | |||||||
| = | $ 788.68 | rate | = | 6%*(6/12) | = | 0.03 | ||||
| nper | = | 17*(12/6) | = | 34 | ||||||
| pmt | = | 1000*4%*(6/12) | = | $ 20.00 | ||||||
| fv | = | $ 1,000.00 | ||||||||
| New price of Bond K | = | =-pv(rate,nper,pmt,fv) | Where, | |||||||
| = | $ 1,845.27 | rate | = | 6%*(6/12) | = | 0.03 | ||||
| nper | = | 17*(12/6) | = | 34 | ||||||
| pmt | = | 1000*14%*(6/12) | = | $ 70.00 | ||||||
| fv | = | $ 1,000.00 | ||||||||
| # 2 | Percentage change in the price of: | |||||||||
| Bond J | = | (b-a)/a | Where, | |||||||
| = | 24.84% | a | Existing price | = | $ 631.78 | |||||
| b | New Price | = | $ 788.68 | |||||||
| Bond K | = | (b-a)/a | Where, | |||||||
| = | 18.87% | a | Existing price | = | $ 1,552.34 | |||||
| b | New Price | = | $ 1,845.27 | |||||||
Bond J has a coupon rate of 4 percent. Bond K has a coupon rate of...