4. A five-year bond has a 4% coupon and 1,000 face value. But here\'s the thing:
ID: 2810431 • Letter: 4
Question
4. A five-year bond has a 4% coupon and 1,000 face value. But here's the thing: - At the end of year 3, along with the coupon, it pays 200 of its principal -Then at the end of year 4 it pays the 4% on the remaining principal. And it pays an additional 200 of principal. Finally, at maturity it pays coupon on whatever principal was outstanding that year, plus remaining principal What is its price at a yield-to-maturity of4%? What is its percentage price change when the yield increases to 5%? Compare the price change of this bond to that of an ordinary frond whh en yeld increases 4% to 5%Explanation / Answer
1-
Year
cash inflow
present value of cash flow = cash inflow/(1+r)^n r = 4%
Year
cash inflow
present value of cash flow = cash inflow/(1+r)^n r = 5%
1
40
38.46154
1
40
38.0952381
2
40
36.98225
2
40
36.28117914
3
240
213.3591
3
240
207.3210236
4
240
205.153
4
240
197.448594
5
640
526.0333
5
640
501.4567465
price of bond at 4% YTM
sum of present value of cash inflow
1019.989
price of bond at 4% YTM
sum of present value of cash inflow
980.6027814
3-
% change in Bond price due to change In Yield from 4% to 5%
(980.60-1019.99)/1019.99
-3.86%
4-
Price of ordinary bond with 4% Interest and 4% YTM =It would be equal to par value as YTM and coupon rate is same
1000
Price of bond at 5% YTM
956.7052
% change in Bond price due to change In Yield from 4% to 5%
(956.71-1000)/1000
-4.33%
Year
cash inflow
present value of cash flow = cash inflow/(1+r)^n r = 5%
1
40
38.09524
2
40
36.28118
3
40
34.5535
4
40
32.9081
5
1040
814.8672
price of bond at 4% YTM
sum of present value of cash inflow
956.7052
1-
Year
cash inflow
present value of cash flow = cash inflow/(1+r)^n r = 4%
Year
cash inflow
present value of cash flow = cash inflow/(1+r)^n r = 5%
1
40
38.46154
1
40
38.0952381
2
40
36.98225
2
40
36.28117914
3
240
213.3591
3
240
207.3210236
4
240
205.153
4
240
197.448594
5
640
526.0333
5
640
501.4567465
price of bond at 4% YTM
sum of present value of cash inflow
1019.989
price of bond at 4% YTM
sum of present value of cash inflow
980.6027814
3-
% change in Bond price due to change In Yield from 4% to 5%
(980.60-1019.99)/1019.99
-3.86%
4-
Price of ordinary bond with 4% Interest and 4% YTM =It would be equal to par value as YTM and coupon rate is same
1000
Price of bond at 5% YTM
956.7052
% change in Bond price due to change In Yield from 4% to 5%
(956.71-1000)/1000
-4.33%
Year
cash inflow
present value of cash flow = cash inflow/(1+r)^n r = 5%
1
40
38.09524
2
40
36.28118
3
40
34.5535
4
40
32.9081
5
1040
814.8672
price of bond at 4% YTM
sum of present value of cash inflow
956.7052
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