Question

Once upon a time, the treasurer of “Mighty Corporation” (MCO) decided to issue a bond (hereafter: The bond) The bond would have a 20-year life and promised that the holder of the bond would receive:

• 20 annual payments of $80,
• Along with the 20^th payment, MCO promised to return the principal of $1,000. In other words, the final payments received at maturity would be ($1000+$80) = $1080.
• On the day it is issued, the Coupon Yield is 80/1000= 8%
• On the day it is issued, the Yield-to-Maturity (YTM) is 8%

The bond is bought by an insurance company. One-year passes, the bond has made its first coupon payment, and the interest rate/yield-to-maturity on the bond falls to 6%.

A) What is the Coupon Yield on the bond?

B) The bond now has 19 years left. Calculate the Macaulay duration of the bond.

Answer 1

A

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =19

Bond Price =∑ [(8*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^19

k=1

Bond Price = 1223.16

Using Calculator: press buttons "2ND"+"FV" then assign

PMT = Par value * coupon %=1000*8/(100)

I/Y =6

N =19

FV =1000

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(6/(100),19,-8*1000/(100),-1000,)

current yield = coupon rate*par value/current price

Current yield%=(8/100)*1000/1223.16

Current yield% = 6.54

B

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,223.16)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	80.00	1.06	75.47	75.47
2	80.00	1.12	71.20	142.40
3	80.00	1.19	67.17	201.51
4	80.00	1.26	63.37	253.47
5	80.00	1.34	59.78	298.90
6	80.00	1.42	56.40	338.38
7	80.00	1.50	53.20	372.43
8	80.00	1.59	50.19	401.54
9	80.00	1.69	47.35	426.17
10	80.00	1.79	44.67	446.72
11	80.00	1.90	42.14	463.57
12	80.00	2.01	39.76	477.09
13	80.00	2.13	37.51	487.59
14	80.00	2.26	35.38	495.38
15	80.00	2.40	33.38	500.72
16	80.00	2.54	31.49	503.87
17	80.00	2.69	29.71	505.06
18	80.00	2.85	28.03	504.50
19	1,080.00	3.03	356.95	6,782.13
			Total	13,676.89

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=13676.89/(1223.16*1)

=11.181602