Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

The net present value (NPV) of an investment opportunity is the difference between the present value of cash inflows and outflows. In this case, there would be a $10,000 outflow at time 0 and a $12,000 inflow one year later. The NPV can therefore be calculated as follows: PV(cash flows) = -$10,000 + ($12,000 / 1.1^1) = -$818. If we assume that the cost of capital is 10%, then the NPV is negative and it may not be worth taking on this investment opportunity.

The internal rate of return (IRR) is another measure that can be used to determine whether or not to undertake an investment opportunity. It measures the rate at which invested money grows over time in order to reach its final value (in this case, it would represent the “break-even” point for investing $10K). The IRR for this opportunity can be calculated using trial and error methods or numerical methods such as Newton’s Method: IRR = 12%. This means that if you invest $10K today at 10% interest per annum then after one year you will have earned back your initial sum plus enough extra to cover inflation/costs/etc., leaving you with no gains but also no losses from undertaking this particular investment opportunity.

Since we know both the NPV and IRR values for our given situation, we can use them to determine how much deviation in our estimated cost of capital would still leave us with a desirable outcome (whether positive or neutral). To do so, calculate what would happen if the cost of capital was set just slightly higher than 10%. For example: at 11% APR, suppose our PV calculation changes to -$474 resulting in a positive NPV; alternatively, suppose setting it lower like 9% APR results in a negative NPV (-$1128). This indicates that any change up to approximately 1 percent from our original estimate should leave us with either a positive or neutral result depending on whether it shifts upwards or downwards respectively – thus indicating that even if our original estimation was off by about 1%, we could still consider taking on this particular investment opportunity without fear of making any losses from doing so.