Question

1) Colorado Mattress Company is considering the purchase of land and the construction of a new plant. The land, which would be bought immediately (at t = 0), has a cost of $200,000 and the building, which would be erected at the end of the first year (t = 1), would cost $800,000. It is estimated that the firm's after-tax cash flow will be increased by $150,000 starting at the end of the second year, and that this incremental flow would increase at a 10 percent rate annually over the next 10 years. What is the approximate payback period? Please use xx.xx format for your answer.

Answer 1

Cost of land = $200,000

Cost of building in year 1 = $800,000

Therefore, total cost = 200,000 + 800,000 = 1,000,000

After tax cash inflow will start from year 2

Cash inflow in year 2 = $150,000

Cash inflow is increasing by 10% every year

So, cash inflow in year 3 = 150000*(1+0.1) = $165,000

cash inflow in year 4 = 165000*(1+0.1) = $181,500

cash inflow in year 5 = 181500*(1+0.1) = $199,650

cash inflow in year 6 = 199650*(1+0.1) = $219,615

Now, adding all cash inflows = 150000 + 165000 + 181500 + 199650 + 219615 = $915,765

cash inflow in year 7 = 219615*(1+0.1) = $241,576.5

Adding all cash inflows = 150000 + 165000 + 181500 + 199650 + 219615 + 241576.5 = $1,157,341.5

So payback is in between year 6 and year 7

Remaining payback after year 6 = 1000000 - 915765 = $84,235

If total cash inflow of $241,576.5 is flowing in year 7, then 84235 cash will come in 84235/241576.5 = 0.38 year

In total payback period is 5 + 0.38 = 5.38 years

In this case, total payback will come in 6.38 years, as cash inflow is starting in year 2