Question

Sentinel Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $259,000 and will yield the following expected cash flows. Management requires investments to have a payback period of 3 years, and it requires a 9% return on investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the table provided.)

Period	Cash Flow
1		$	48,500
2			52,300
3			76,100
4			95,600
5			125,300

Required:
1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

1.

Year	Cash Inflow (outflow)	Cumulative Net Cash Inflow (Outflow)
0	$(259,00)
1
2
3
4
5
Payback Period=

2.

Year	Cash Inflow (outflow)	Table Factor	Present Value of Cash Flows	Cumulative Present Value of Cash Flows
0	$(259,000)
1
2
3
4
5
Break Even time=

3.

Net Present Value

Answer 1

Solution

Sentinel Company

1. Determination of the payback period for the investment:

Payback period (non-uniform cash flows)

First add the cash flows, till the cumulate cash flows match the initial investment.

The period at which the cumulative cash flows equals the initial investment is the payback period.

Initial investment =$259,000

Cumulative cash flows = $48,500 + $52,300 + $76,100 = $176,900

The company expects to recover $176,900 of the initial investment of $259,000. After 3 years, the company needs to recover $82,100 more of the investment.

In year 4, the company would recover the remaining $82,100 while the corresponding cash flow is $95,600.

Since, the question assumes uniform cash flows throughout the year, we can divide $82,100 by $95,600 to get = 0.86, or (0.86 x 12 =10.3months)

The payback period for the investment = 3 years 10 months

1. Break-even time for the investment:

Year	Cash Flows	Present Value of $1 at 9%	Present Value of cash flows	Cumulative Present value of cash flows
0	($259,000)	1.000	($259,000)	($259,000)
1	$48,500	0.9174	44,475	($214,525)
2	$52,300	0.8417	$44,021	($170,504)
3	$76,100	0.7722	$58,764	($111,740)
4	$95,600	0.7084	$67,723	($44,017)
5	$125,300	0.6499	$81,432	$37,415

From the above table, the break-even point lies between year 4 and year 5.

44,017/81,432 = 0.54 months

Hence the break-even time of the investment = 4years 5 months

The net present value of the investment at 9% for 5 years = $37,415