How do taxes influence responsible financial planning? Discuss some examples of how taxes may influence a financial plan.

I will discuss how taxes affect the financial planning of individuals, not businesses.

The whole idea of responsible financial planning is to maximize an individual's wealth, and in order to be able to do this you generally need to minimize your tax liabilities. It doesn't mean that you shouldn't pay your taxes, but rather that the taxes that you owe should be lower.

An example about how this works is when you you invest in stocks. All dividends are taxed as ordinary income, but if you hold a stock for more than one year and then sell it making a profit, you will be taxed at a much lower rate. That is why it is always a good idea to hold stocks long enough for long term capital gains rate to apply. E.g. if you are married and your ordinary taxable income is less than $80,000, you pay 0 taxes for long term capital gains. Even couples earning up to $496,600 will pay only 15%, while their marginal tax rate on ordinary income is 35%. Remember that every cent that you save on taxes, increases your wealth, and a 20% difference is a lot.  

Another example are IRA accounts. Contributions to traditional IRA accounts lower your taxable income, which is great. Any interest gained by the account will not be taxed until you retire. This allows your money to grow tax free. E.g. you have $100,000 to invest and you an earn 8% per year. If you do not pay any taxes, in 10 years you will have $100,000 x 1.08¹⁰ = $215,894.50. But if you pay a 24% tax rate on your gains, then you will only have $100,000 x [1 + (0.08 x 0.76)]¹⁰ = $180,441.

In order to reduce your taxes, you might sometimes need to postpone or accelerate some expenses or donations. E.g. you generally donate $3,000 to church, it is December and you  are getting ready to sign a check. But you then realize that your current tax bracket is 12%, but since you got a raise, next year you will pay 24%. It is a good idea to write the check on January 2, since you will save $3,000 x (24% - 12%) = $360 in future taxes.