London NV has two different types of perpetual bonds outstanding. The callable bond has the call premium of three annual coupons and it is callable after three years. The company is determined to offer the callable bond with the lowest price possible. First year, the one-year interest rate is 10 per cent. Second year, the one-year interest rate is 20 per cent. Third year, the one-year interest rate is 15 per cent. The year after, there is a 70 per cent probability that interest rates will increase to 20 per cent, there is a 20 per cent probability that they will fall to 10 per cent, and there is 10 per cent probability that they will stay the same.

The non-callable bond has a coupon rate of 20 per cent, payable annually.

As an investor, if you aim the cheapest bond in the market, which one of these two outstanding bonds of London NV shall you choose? Show full working.