$2.$ Athena Investment Co$.$ is considering the purchase of an office property. After a careful review of the market and leases that are in place, Athena believes that next year$$s cash flow will be $$100,000.$ It also believes cash flow will rise by $$7,000$ each year for the foreseeable future. It plans to own the property for at least ten years. Based on a review of sales of properties that are now $10$ years older than the subject property, Athena has determined that cap rates are in the range of $\mathrm{.}10.$ Athena believes that it should earn an IRR of at least $12\%.$

a$.$ What is the estimated value of the property, assuming a $\mathrm{.}10$ terminal cap rate?

b$.$ What is the current, or $$going in$,$ cap rate for this property?

c$.$ What accounts for the difference between the cap rate in b and the terminal cap rate of $\mathrm{.}10?$