I have done some further thinking regarding the unsolicited offer and looked at a few other properties in the same area (Mid Levels). The conclusions are as follows:
1. the yield on purchase price is attractive (it is higher than the cost of funds);
2. the yield on the offer price is still attractive (at or just slightly below the cost of funds);
3. properties in that area which show better yields are few and far between and usually have major problems with them (e.g. very old buildings or low floors right next to a noisy road). Finding a replacement value proposition in the same price range will not be easy. Most likely we would end up buying something more expensive (which in the longer term we may want to do anyway);
4. the location (close to the escalator) means that it should always be easy to rent;
5. we have no need of cash at the moment;
6. the price offered is right on the bank valuation. Looking at recent sales I think the property is worth more than this. However, the recent comparative sales are for very low floors and there are only two of them meaning that it is hard to be too confident about the market value;
7. my previous thoughts on the difficulty in adding value to the property remain. In the longer term we may wish to sell and reinvest in a better quality property in the same area, but as we are currently looking for another investment property anyway, there is no need to sell this flat now.
I have concluded that the offer is not attractive. I have nominated a price which is slightly above my assessment of the current value. If someone wants to pay the nominated price, that is fine with me. If not, I will keep the property.