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There are two sides to your question.
One, if you are right and have the right justification, the risk lies with your boss and it will show later on. However, if you are wrong and your decision was not correctly aligned with the requirements, then you most probably will cost the company tons of money and or you may be fired for not basing your decision on facts.
Find where your ideas align
Presenting your ideas in a story format
Back it up with how it will benefit the comany
Show my Hard work and smart work which is related to benefit of company and explain my positive opinions.
Thank you for addressing your question to me. I have faced such emotions from both sides of the desk. However in my opinion, there are two major concerns that the senior management has ;
1. The decisions must be in alignment with the company vision and long term goals.
2. Commercially beneficial.
I give you a recent incident with one of the company. They have been seeking funding from financial institutions to clear of their debts and fund their new project. The staff have not been getting salaries in time and vendors had been pressurizing for delay. The company needed funds desperately. Their Manager Finance who had put up a proposal with various institutions almost all the prime banks did not show interest due to recession and fall in sales and profitability of their running projects but he gets a response from only one NBFC. They were ready to fund at a acceptable rate of interest. This funding could bail the company out of their crisis. Incidentally this NBFC had poor record of releasing collateral at the borrower exit stage. The boss refused to accept the offer letter from NBFC.
The finance manager had similar emotions as mentioned in your question. The boss did not want to associated with company with stained image, this would have scared other and future investors. So in the long term interest of the company he declined this offer and advised the manager to look for other financiers.Although this vertical was on the verge of collapse. AS they say you are recognized by the company you move in.
Therefore my experience is that what you think is right may not be right in terms of company philosophy and long term business interest although you may provide much needed short term gain and comfort to the company. Please keep up your efforts and should your suggestion meets the mindset of the boss and above mentioned two objectives that he is accountable for, he will be much pleased to agree with you.
Show of evidence if there are any
Be polite but persistent
Keep him interested in the debate by bringing up related matters
Wait for him to realize
The biggest and common mistake is when people are afraid to protect their opinion in front of the boss even if they know that boss's opinion is wrong, and they simply agree with him. When you know that yours opinion has the right solutions for sme issue, the way to convinced your boss that yours decision is the right one, you should not tell him directly that his opinion is wrong, but you need to conversate your decision and his decision,to make scenario analyze according to your opinion and another scenario according to his opinion, in that way you can estimate the outputs of each decision and that will provide all the arguments why you think that yours opinion is right, In that way, in suptile way you can push your opinion( because you deeply trust it) and it will look like it was achieved by mutual agreement
Politely say, you are a person of facts and numbers, do you have a minute to talk?
Explain with the help of example, give him some options with advantages and disadvantages. Emphasise on one which you want to convince him. Now he can make choice.
Provide proof or concrete evidence.
