Question

RHA fund invested in 1,000 units of 7 percent, 15-year, RM1,000 bond issued by CMX

Bhd. The bond was issued on 1/11/2018 at par. The firm bought the bonds on 1/11/2021

when the bond was selling at 2% discount. The firm intends to sell back all the bond when

the interest rate is expected to be at 5% on 1/11/2026. Throughout the period of holding

the bond, the firm reinvest all the coupons received in an investment alternative that pays

8 percent interest for the 1st 3 years and 9 percent interest for the remaining years. You

are required to assist RHA fund to determine:

i) their total yield from this bond investment

ii) total capital gain from this investment

Answer 1

i) The income to be repaid on a coupon bond is most often the sum of two components: coupon payments and the amount of the discount, or coupon payments and the amount of the premium.

$Discount=1000\times0.02=20$

$Purchased coupon income=1000\times0.07\times8=560$

$P=\frac{70}{1.05}+\frac{70}{(1.05)^2}+\frac{70}{(1.05)^3}+\frac{70}{(1.05)^4}+\frac{70}{(1.05)^5}+\frac{70}{(1.05)^6}+\frac{70}{(1.05)^7}+\frac{70}{(1.05)^8}+\frac{1000}{(1.05)^8}=1129.26$

$1129.26-1000=129.26$

$total yield=20+560+129.26=709.26$

ii)

15-8=7

$S=560(1+0.08)(1+0.08)^2(1+0.08)^3(1+0.09)^4(1+0.09)^5(1+0.09)^6(1+0.09)^7=5917.16$

$total capital gain=709.26+(5917.16-560)=6066.46$