Question

a. Suppose an investor can purchase a 5-year 8% coupon bond with a par value of $100 that pays interest semi-annually. The yield to maturity for this bond is 9% on a bond-equivalent basis. What is the total future dollars and the total dollar return that should be generated from this bond if it is to yield 9%? b. What is the coupon interest, capital gain/loss and reinvestment income associated with this bond? Assume that the reinvestment rate is equal to the yield to maturity.

Answer 1

Given

Coupon Rate = 8% per anum paid semi annually

Tenure of the Bond = 5 Years

Frequency of the coupon = Semi Annual

Yield to Maturity = 9%

Face Value of the bond = 100 dollars

(1) CALCULATION OF COUPON INTEREST

Coupon Interest = Principal Amount * Coupon Rate = 100*8% = 8 dollars per anum

But it is given that coupon is paid semi annually so Coupon for Half year = 8/2 = 4 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

YTM = Yield to Matuirty= 9% per anum = 4.5% Half Yearly

n = Number of periods = 5*2 = 10 (Since it is Semi Annual)

MV = Maturity Value = 100

Number of Periods	Coupons(A)	YTM@ 4.5%(B)	Present value of Coupons (A*B)
1	4	0.9569378	4.28571429
2	4	0.91572995	4.08163265
3	4	0.8762966	3.88726919
4	4	0.83856134	3.70216114
5	4	0.80245105	3.52586775
6	4	0.76789574	3.35796929
7	4	0.73482846	3.19806599
8	4	0.70318513	3.04577713
9	4	0.67290443	2.90074012
10	4	0.64392768	2.76260964
10	100	0.42241081	42.2410807
Price of the Bond	76.9888879

Capital Gain = Maturity Value - Purchase Price = 100-76.9889 = 23.0111 Dollars

(3) CALCULATION OF REINVESTMENT INCOME

Number of Periods	Coupons and Principal(A)	Number of Periods Coupon is reinvested	Yield at 4.5% (B)	Future Value of Coupons(A*B)
1	4	9	1.48609514	5.94438056
2	4	8	1.422100613	5.68840245
3	4	7	1.36086183	5.44344732
4	4	6	1.302260125	5.2090405
5	4	5	1.246181938	4.98472775
6	4	4	1.192518601	4.7700744
7	4	3	1.141166125	4.5646645
8	4	2	1.092025	4.3681
9	4	1	1.045	4.18
10	104	0	1	104
Reinvestment Income at the end of 10th month(Sum of A*B)	149.152837