Question

Your firm is considering an investment that will cost​ $750,000 today. The investment will produce cash flows of​ $250,000 in year​ 1, $300,000 in years 2 through​ 4, and​ $100,000 in year 5. What is the​ investment's discounted payback period if the required rate of return is​ 10%?

Answer 1

3.241 years

Step-by-step 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.