Answer:
3.241 years
Explanation:
In the payback, we analyze in how many years the invested amount is recovered. The computation is shown below:
In year 0 = $750,000
In year 1 = $250,000
In year 2 = $300,000
In year 3 = $300,000
In year 4 = $300,000
In year 5 = $100,000
And, the discounted rate of return is 10%
The discount factor should be computed by
= 1 ÷ (1 + rate) ^ years
where,
rate is 9%
Year = 0,1,2,3,4 and so on
Discount Factor:
For Year 1 = 1 ÷ 1.10^1 = 0.9091
For Year 2 = 1 ÷ 1.10^2 = 0.8264
For Year 3 = 1 ÷ 1.10^3 = 0.7513
For Year 4 = 1 ÷ 1.10^4 = 0.6830
For Year 5 = 1 ÷ 1.10^5 = 0.6209
So after applying the discounting rate, the cash flows would be
In year 0 = $750,000
In year 1 = $250,000 × 0.909 = $227,250
In year 2 = $300,000 × 0.8264 = $247,920
In year 3 = $300,000 × 0.7513 = $225,390
In year 4 = $300,000 × 0.6830 = $204,900
In year 5 = $100,000 × 0.6209 = $62,090
If we sum the first 3 year cash inflows than it would be $700,560
Now we deduct the $700,560 from the $750,000 , so the amount would be $49,440 as if we added the fourth year cash inflow so the total amount exceed to the initial investment. So, we deduct it
And, the next year cash inflow is $204,900
So, the payback period equal to
= 3 years + $49,440 ÷ $204,900
= 3.241 years
In 3.241 years, the invested amount is recovered.
