a question about terminal growth rate, discount rate and property evaluation
You are considering purchasing a property with a 5 year holding period. The sum of your discounted cash flows for this 5 year holding period is $500,000. The anticipated cash flow in year 5 is $150,000 and the anticipated cash flow in year 6 is $175,000. Your terminal growth rate is 2% and your discount rate is 7%. How much should you be willing to pay for this property (to the nearest cent).
Can anyone help me with this question??? Thank you
If this is a homework or study question it is very poorly written... but I'll take a stab at it.
I'm gonna go ahead and assume that the "sum of discounted cash flows" is really the sum of the annual NOI and that the annual NOI is 100,000 each year. See the attached excel spreadsheet for the math.
https://drive.google.com/file/d/0By4ERkd08v6sN2JQQzdLejdHM2c/view?usp=s…
See link below..
https://docs.google.com/spreadsheets/d/1K6c6EiiopjdiJaY7f_S8dfAQijD0pjz…
I've taken a different approach to Trunk Yeti but arrived at an (almost identical value)
you need to free up your permissions as the link does not allow entry.
Apologies - try now... https://docs.google.com/spreadsheets/d/1K6c6EiiopjdiJaY7f_S8dfAQijD0pjz…
I interpreted it slightly different as well, but arrived at a similar value. If the sum of the discounted cash flows are $500,000 then this includes the $150,000 year 5 cash flow, and they are already discounted. Just calculated terminal value and discounted to present. $2,495,452 + $500,000 (in already discounted CF) = $2,995,452
Trunk Yeti, I believe you have too many periods for the property given the 5 year holding period. Anyway, I agree that the question isn't very clear.
Shouldn't the value of the property be the present value of all future cash flows, not just the ones within the holding period?
While that is true; remember that we capture that cash flow beyond the investment horizon in the terminal value. The value of the property to you will be the present value of the future benefit streams that you expect to receive while holding the asset.
yes, that was actually correct answer. Thank you!
were you able to get an answer?
The $500,000 in cash flows are already discounted, so you don't need to do anything with these. The year five cash flow of $150,000 is really just extra information and you don't need. The year 6 cash flow of $175,000 is your terminal year cash flow; here we simply capitalize the the cash flow using the formula [CF / (r-g)] = $175,000 / (.07-.02) = $3,500,000
This is then discounted to PV using FV / (1+r)^n = $3,500,000 / (1+.07)^5 = $2,495,451.63
Add the cash flows up $500,000 + $2,495,451.63 = $2,995,451.63
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