Question

Shannon Co. is considering a project that has the following cash flow and cost of capital (r) data. What is the project's discounted payback?r = 10.00%Year 0 1 2 3 4Cash flows −$950 $525 $485 $445 $405a. 1.61 yearsb. 1.79 yearsc. 1.99 yearsd. 2.22 yearse. 2.44 years

Answer 1

Answer:

d. 2.22 years

Explanation:

The formula to compute the payback period is shown below:

= Initial investment ÷ Net cash flow

In this question, the discount rate is given i.e 10%

The discount factor should be computed by

= 1 ÷ (1 + rate) ^ years

where,  

rate is 10%  

Year = 0,1,2,3,4

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

Yearly cash inflows:

Year 1 = Year 1 cash inflow × Present Factor of Year 1

= $525 × 0.9091

= $477.27

Year 2 = Year 2 cash inflow × Present Factor of Year 2

= $485 × 0.8264

= $400.80

Year 3 = Year 3 cash inflow × Present Factor of Year 3

= $445 × 0.7513

= $334.33

Year 4 = Year 4 cash inflow × Present Factor of Year 4

= $405 × 0.6830

= $276.62

If we sum the first 2 year cash inflows than it would be $878.03

Now we deduct the $878.03 from the $950 , so the amount would be $71.97 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 $334.33

So, the payback period equal to

= (2 years + $71.97) ÷ ($334.33)

=  2.22 yeas

In 2.22 yeas, the invested amount is recovered.