Jane, is looking to start up her own business of building construction, and estimates she will need $500 000 as initial cost of setting up the business. Jane has only $200 000 in savings and must borrow the other $300 000. If the interest rate is 10%, what is the opportunity cost of starting up the business?

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BlackTom AI · Accepted Answer

The question asks for the opportunity cost of Jane starting up the business, given she must use $200,000 of her own savings and borrow $300,000. 
Option a. $50,000 per annum: This would imply a very large foregone return, but the standard opportunity cost for using her own funds is the return she could have earned on those funds if she kept them invested elsewhere. With a 10% rate, $200,000 x 10% = $20,000 per year, not $50,000. This misrepresents both the amount of capital involved and the return rate.
Option b. $500,000 per annum: This is far too large and suggests conflating the total project size with the opportunity cost. Opportunity cost is about the return on the alternative use of her own funds, not the total upfront capital required for the project.
Option c. $30,000 per annum: This would correspond to 15% of $200,000 or some other misapplied rate or amount. The problem gives a 10% rate, so this value does not align with the stated opportunity cost calculation for her own savings.
Option d. $20,000 per annum: This matches the standard calculation for opportunity cost of using her own funds. At 10% annual return, keeping $200,000 invested elsewhere would yield $20,000 per year in foregone interest. Therefore, the opportunity cost of using her own savings to start the business is $20,000 per year, assuming the alternative is earning interest on the savings at 10%.
In summary, the key idea is that opportunity cost focuses on the next best alternative use of the resources you already control. Here, Jane’s own savings amount to $200,000, and the 10% return on that amount represents the annual foregone benefit if she funds the venture with her savings instead of investing it. The borrowed $300,000 does not produce an opportunity cost for her personal decision, since it is not her own foregone return. Thus, option d reflects the correct concept and calculation, while the other options misstate either the base amount or the rate, or both.

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