CM1 CT1 September Q2 Booklet 5 Q12

[Yushuo Liu]

The first question told me to calculate the gross rate of return per annum convertible half yearly from bond, but why i(2)=D/R?

 

[Lucy England]

In this case, the redemption amount (R) is £110 per £100 nominal and the current price (P) is also £110 per £100 nominal. We therefore have P = R = 110 which means there's no capital gain or loss on redemption. We can therefore use the capital gains test formula that applies in this case:
$$ i^{(2)} = \frac{D}{R} (1 - t_1) $$
Where \(D\) is the annual coupon rate and \(t_1\) is the rate of income tax (paid on coupons). Since we're asked for the gross rate of return here, we can ignore income tax for this part of the question, so our equation just becomes:
$$ i^{(2)} = \frac{D}{R} $$
Hope this helps!