End-of-year-one net operating cash flow is $89,000 and additional net sale proceeds at that same date are $1,000,000. No other cash flows apply. At a 10% annual discount rate, what present value results?
Correct Answer
C) $990,000
(89000+1000000)÷1.10 = 990000. Common errors: adding the cash flows without discounting gives $1,089,000; discounting the sale proceeds for two years gives $907,355; leaving out the year-one operating cash flow gives $909,091.
Why This Is the Correct Answer
Option C is correct because both amounts arrive at the end of year one, so PV = ($89,000 + $1,000,000) ÷ 1.10 = $990,000. Cash flows on the same date share the same discount factor.
Why the Other Options Are Wrong
Option A: $907,355
Option A, $907,355, comes from discounting the sale proceeds for two years: $89,000 ÷ 1.10 + $1,000,000 ÷ 1.10² = $907,355. The proceeds arrive at the end of year one, so PV = $1,089,000 ÷ 1.10 = $990,000.
Option B: $909,091
Option B, $909,091, results from leaving out the year-one operating cash flow: $1,000,000 ÷ 1.10 = $909,091. Including the $89,000 gives ($89,000 + $1,000,000) ÷ 1.10 = $990,000.
Option D: $1,089,000
Option D, $1,089,000, is the undiscounted total: $89,000 + $1,000,000 = $1,089,000. Discounting one year at 10% gives $1,089,000 ÷ 1.10 = $990,000.
Same date, same discount
Group cash flows by the date they arrive; each amount on that date is divided by the same factor.
How to use: Use this when a DCF problem has income and reversion arriving together.
Exam Tip
Map each cash flow to its year before discounting; the reversion is often received at the same time as the final year's income.
Common Mistakes to Avoid
- -Discounting the reversion one period too many
- -Omitting the final year's operating cash flow
- -Forgetting to discount at all
Concept Deep Dive
Analysis
This question tests discounting cash flows that occur at the same date. Both the $89,000 operating cash flow and the $1,000,000 sale proceeds arrive at the end of year one, so they are combined and discounted for one period at 10%.
Background Knowledge
Discounted cash flow analysis discounts each periodic cash flow and the net sale proceeds at an appropriate discount rate according to when they occur. Amounts received on the same date share the same discount factor. The present value of a dollar is 1 ÷ (1 + i)^n.
Real-World Application
An appraiser models a one-year hold for a rented fourplex, with year-one NOI and resale proceeds both received at year end. The appraiser adds them and discounts the total one period at the market yield rate.
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