Choose an investment option only knowing the costs, cost of capital and lifetime

A question in my course hasn't given us much to go on. I'm not sure if there is a specific model I could use to determine which project is the better one.

1st option costs 350.000, has a life expectancy of 7 years and the benefits it will provide have been evenly distributed. 2nd option has a cost of 450.000, a life expectancy of 11 years and the benefits have been similarly calculated.The company will borrow the amount at an annual rate of 3%. Which project should it select?

• Presumably either project would meet your requirements and they are mutually exclusive (for example two machines that do the same task, but the more expensive one lasts longer than the other). In your textbook's subject index, look up 'Comparing Projects with Unequal Lives' and read that section. Dec 3, 2020 at 17:13
• Two (equivalent) models are popular for this problem: the Equivalent Annual Annuity method and the Replacement Chains Method. Dec 3, 2020 at 17:50
• @noob2 I think you're right about the Equivalent Annual Annuity method, my issue is calculating the PV of costs, the only information given is the initial payment of 350K and 450K and an annual borrowing rate of 3%. Should I just divide the initial payment by the annuity factor and use that as the equivalent annual cost? sorry for all the questions and thanks for your help! :D Dec 3, 2020 at 19:16
• Yes, an upfront payment of 350,000 is equivalent in PV to an annuity of X dollars each year for 7 years. You have to find X. And similarly a payment of 450,000 today is equivalent in PV to paying Y per year for 11 years. Then you compare X and Y, which is cheaper? (Note that if interest rates were zero you could just divide 350,000 by 7 and 450,000 by 11, but here the interest rate is 3% not 0%). Dec 3, 2020 at 19:53