Question

Suppose an investor can purchase a 6-year 9% coupon bond with a par value of $100 that pays interest semi-annually. The yield to maturity for this bond is 10% on a bond-equivalent yield basis. What is the coupon interest, capital gain/loss and reinvestment income associated with this bond over its 6-year life? Assume that the reinvestment rate is equal to the yield to maturity.

Answer 1

Given

Coupon Rate = 9% per anum paid semi annually

Tenure of the Bond = 6 Years

Frequency of the coupon = Semi Annual

Yield to Maturity = 10%

Face Value of the bond = 100 dollars

(1) CALCULATION OF COUPON INTEREST

Coupon Interest = Principal Amount * Coupon Rate = 100*9% = 9 dollars per anum

But it is given that coupon is paid semi annually so Coupon for Half year = 9/2 = 4.5 dollars.

(2) CALCULATION OF CAPITAL GAIN OR LOSS

In order to find whether it is capital gain ir loss, first we have to find the purchase price of the bond which can be found by using following formula

Price of the bond = C1/(1+YTM)^1 + C2/(1+YTM)^2 + C3/(1+YTM)^3 + ............ +Cn/(1+YTM)^n + MV/(1+YTM)^n

C = Coupon on the bond = 4.5

YTM = Yield to Matuirty= 10% per anum = 5% Half Yearly

n = Number of periods = 10*2 = 20 (Since it is Semi Annual)

MV = Maturity Value = 100

Number of Periods	Coupons(A)	YTM@5%(B)	Present value of Coupons (A*B)
1	4.5	0.952381	4.285714286
2	4.5	0.907029	4.081632653
3	4.5	0.863838	3.887269193
4	4.5	0.822702	3.702161137
5	4.5	0.783526	3.525867749
6	4.5	0.746215	3.357969285
7	4.5	0.710681	3.198065986
8	4.5	0.676839	3.045777129
9	4.5	0.644609	2.900740123
10	4.5	0.613913	2.762609641
11	4.5	0.584679	2.631056801
12	4.5	0.556837	2.505768382
13	4.5	0.530321	2.386446078
14	4.5	0.505068	2.272805788
15	4.5	0.481017	2.164576941
16	4.5	0.458112	2.061501849
17	4.5	0.436297	1.963335094
18	4.5	0.415521	1.869842947
19	4.5	0.395734	1.780802807
20	104.5	0.376889	39.38495096
Price of the Bond Now	93.76889483

Capital Gain = Maturity Value - Purchase Price = 100-93.7689 = 6.2311 Dollars

(3) CALCULATION OF REINVESTMENT INCOME

Number of Periods	Coupons and Principal(A)	Number of Periods Coupon is reinvested	Yield at 5% (B)	Future Value of Coupons(A*B)
1	4.5	19	2.526950195	11.37127588
2	4.5	18	2.406619234	10.82978655
3	4.5	17	2.292018318	10.31408243
4	4.5	16	2.182874588	9.822935648
5	4.5	15	2.078928179	9.355176807
6	4.5	14	1.979931599	8.909692197
7	4.5	13	1.885649142	8.48542114
8	4.5	12	1.795856326	8.081353467
9	4.5	11	1.710339358	7.696527112
10	4.5	10	1.628894627	7.33002582
11	4.5	9	1.551328216	6.980976972
12	4.5	8	1.477455444	6.648549497
13	4.5	7	1.407100423	6.331951902
14	4.5	6	1.340095641	6.030430383
15	4.5	5	1.276281563	5.743267031
16	4.5	4	1.21550625	5.469778125
17	4.5	3	1.157625	5.2093125
18	4.5	2	1.1025	4.96125
19	4.5	1	1.05	4.725
20	104.5	0	1	104.5
Reinvestment Income at the end of 20 th year	248.7967935