How to find IRR given discount rate and exit cap rate

I was asked in an interview. What is the IRR if discount rate is 6% and exit cap rate is 5%. Is it 11% (i.e. 6% is your risk free return + your return on exit)?

Also, what would be the best to answer the follow question: "how would you determine your discount rate?"

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This is a ridiculous question unless they gave you additional info. Was there any information on cash flows and hold period? If not you literally can't answer it and your interviewer is either an idiot, or they wanted you to ask follow up questions to fill in the gaps. IRR is a time-based metric, you need duration, cash flow and equity information.

For your second question, that's much more subjective. The simple answer is your discount rate should be no higher than your required unlevered IRR. The detailed answer is that you would take your risk free rate and add premiums for various forms of perceived risk (i.e. financial risk, market risk, political risk, etc etc.). Very few places get that involved in formulating a discount rate.

 

The IRR is the discount rate (unlevered). The exit cap is irrelevant. IRR is 6% because you are discounting the cash flow at 6%. 
 

Determining discount rate is twofold. 1) speak to brokers in your market. They will know where deals are trading from an IRR perspective. That’s your discount rate. (5 or 10 year unlevered IRR). From another perspective, you and your firm need to ask the question of: the market discount rate is 6%, do we feel this is an adequate return for the risk we are taking? If yes, buy the deal, if not, pass. Your goal, knowing the market discount rate, is to find deals that will exceed that and provide a higher relative IRR or meet your return thresholds. 

 

IRR is DR if purchase price is the same as the NPV derived from the 6% DR in the DCF.

DR is determined based on your cost of capital. On an unlevered basis, how much are you willing to accept as your return depending on your 5/7/10 year DCF. Usually ties to what other investors in the market doing, but not always - really depends on your capital structure. A more mathematical answer is that your DR is the cap rate plus annualized growth rate of CF - when you essentially boil down the DR formula.

 

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