Question

Question 3: A bond with a face value of $1000 and maturity of exactly 5 years pays 10% annual coupon. This bond is currently selling at an annual yield-to-maturity (YTM) of 11.5%. Answer the following questions for this bond. Calculate the current price of the bond. (5 points) Calculate modified duration of the bond using the timeline method. (10 points) Using just the modified duration, what is the new price of the bond when YTM is 12%? (5 points)

solve using excel show all steps

Answer 1

Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
N	CF	Df = 1/(1+11.5%)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1	100.0000	0.8969	89.6861	100.0000	89.6861
2	100.0000	0.8044	80.4360	200.0000	160.8719
3	100.0000	0.7214	72.1399	300.0000	216.4196
4	100.0000	0.6470	64.6994	400.0000	258.7978
5	1100.0000	0.5803	638.2905	5500.0000	3191.4523
		Total = P = Current Price =	945.2518	Total = Weighted Price = WP =	3917.2277

Current price = P = 945.2518

Macaulay Duration or Duration = WP/P =

4.1441

Modified duration = Macaulay Duration /(1+Yield) = 3.7167

.

New bond price = Current price x (1+(-Modified Duration x Change in yield))

New bond price = 945.2518 x (1+(-3.7167 x 0.50%))

New bond price = ~$927.69