Question

Graph (show the cash flows) of the following bond:

a. A $20,000 par value bond with a coupon of 4.0% paid semi-annually, maturing in 6 years.

b. Find the current price of the Bond if you use 4.0% as the discount rate.

c. Is this bond priced at a discount or a premium?

Macaulay Duration:

a. Calculate the price of a bond with a Face Value of $1,000, with an ANNUAL coupon of 10% (not paid semi-annually, but once a year), with 3-years left to maturity, if current interest rates were 7.0%.

b. Calculate the Macaulay Duration of this bond and explain what your answer means.

c. Calculate the Modified Duration and explain what your answer means.

Answer 1

Cash flow of the bond

Year	0.5	1.00	1.50	2.00	2.50	3.00	3.50	4.00	4.50	5.00	5.50	6.00
Cash flow	400	400	400	400	400	400	400	400	400	400	400	20,400

F = Face value = $ 20,000

C = Coupon = 2% (4%/2 = 2% semi annual coupon)

Rate = Yield = 4%/2 = 2%

Number of coupon payments = N = 6 x 2 = 12

PV or Price of Bond = (C x F x ((1-((1+R)^-N)) / R) + (F/(1+R)^N)

Price of the bond = (2%*20000*((1-((1+2%)^-12))/2%)+(20000/(1+2%)^12))

Price of the bond = $ 20,000.00

Hence, bond is selling at par (neither on discount nor on premium)

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Macaulay Duration:

	Yield =	7%
Period	Cash flow	Discounting factor Df = 1/(1+Yield)^Period	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
1	100	0.934579439	93.46	100	93.46
2	100	0.873438728	87.34	200	174.69
3	1100	0.816297877	897.93	3300	2693.78
		Total	1078.73	Total	2961.93
		Price of the Bond	1078.73	Weighted Price	2961.93

Duration or Macaulay Duration = Weighted price of the bond / Price of the bond = 2961.93/1078.73 = ~ 2.75 Years

Macaulay duration states that number of years required to get present value of future payments

Modified Duration = Macaulay Duration / (1+Yield)

Modified Duration = 2.75/1.07

Modified Duration = ~ 2.57 Years

Modified duration measures the change in value or price sensitivity in response to yield.