Question

1) You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. What is the payback period in whole number years for this investment? In other words, in what year do you break even on this investment? Use i = 9% annual rate compounded annually, and use the discounted payback approach (not Simple Payback).

Answer 1

Initial investment = $50000

Annual cash inflows = $10000

Then,

Cash inflows recovered in year 1 = 10000/1.09 = $9174.31

Cash inflows recovered in year 2 = 10000/1.09^2= $8416.80

Cash inflows recovered in year 3 = 10000/1.09^3 = $7721.83

Cash inflows recovered in year 4 = 10000/1.09^4 = $7084.25

Cash inflows recovered in year 5 = 10000/1.09^5 = $6499.31

Cash inflows recovered in year 6 = 10000/1.09^6 = $5962.67

Cash inflows recovered in year 7 = 10000/1.09^7 = $5470.34

Now,

Cash inflows in 7 years = 9174.31+8416.80+7721.83+7084.25+6499.31+5962.67+5470.24

Cash inflows in 7 years = $50329.41

So, the payback period (in whole number year) = 7 years