BAC1644
Tut Ch 8
Oct 2011/2012
1.
To calculate the payback period, we need to find the time that the project has recovered its initial
investment. After three years, the project has created:
$32,000 + 97,000 + 102,000 = $231,000
in cash flows. The project still needs to create another:
$472,500 – 231,000 = $241,500
in cash flows. During the fourth year, the cash flows from the project will be $301,000. So, the
payback period will be 3years, plus what we still need to make divided by what we will make during
the fourth year. The payback period is:
Payback = 3 + ($241,500 / $301,000)
Payback = 3.80years
2.
To calculate the payback period, we need to find the time that the project has recovered its initial
investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial
cost is $4,800, the payback period is:
Payback = 4 years
There is a shortcut to calculate payback period when the future cash flows are an annuity. Just divide
the initial cost by the annual cash flow. For the $4,800 cost, the payback period is:
Payback = $4,800 / $1,200
Payback = 4 years
For an initial cost of $5,800, the payback period is:
Payback = $5,800 / $1,200
Payback = 4.83 years
The payback period for an initial cost of $10,800 is a little trickier. Notice that the total cash inflows
after eight years will be:
Total cash inflows = 8($1,200)
Total cash inflows = $9,600
If the initial cost is $10,800, the project never pays back. Notice that if you use the shortcut for annuity
cash flows, you get:
Payback = $10,800 / $1,200
Payback = 9 years
This answer does not make sense since the cash flows stop after eight years, so again, we must
conclude the payback period is never