Question

Assume monetary benefits of an information system of $40,000 the first year and increasing benefits of $10,000 a year for the next five years (year 1=$50,000, year 2= $60,000, year 3 = $70,000, year 4= $80,000, year 5 = $90,000). One- time development costs were $80,000 and recurring costs were $45,000 over the duration of the system's life. The dis- count rate for the company was 11 percent. Using a six-year time horizon, calculate the net present value of these costs and benefits. Also calculate the overall return on investment and then present a break-even analysis. At what point does breakeven occur?

Answer 1

The net present value of the costs and benefits is $46,187. The overall return on investment is 57.73%. The break-even point occurs at approximately 4.6187 years.

Step-by-step explanation:

To calculate the net present value (NPV) of the costs and benefits, we need to discount each year's benefit or cost back to the present using the discount rate. Here's how to do it:

1. Calculate the present value (PV) of each year's benefits and costs. For the benefits, the PV of year 1 is $40,000, year 2 is $36,036 ([$10,000 / (1.11^2)]), year 3 is $32,432 ([$10,000 / (1.11^3)]), year 4 is $29,141 ([$10,000 / (1.11^4)]), year 5 is $26,128 ([$10,000 / (1.11^5)]). For the costs, the PV is $80,000 and the recurring cost is $45,000 over 6 years, so the PV is $37,550 ([$45,000 / (1.11^6)].
2. Add up the present values of the benefits: $40,000 + $36,036 + $32,432 + $29,141 + $26,128 = $163,737.
3. Subtract the present value of the costs from the present value of the benefits: $163,737 - ($80,000 + $37,550) = $46,187.

The net present value of the costs and benefits is $46,187.

To calculate the overall return on investment (ROI), we need to divide the net present value by the initial investment and express it as a percentage. Here's how to do it:

1. Divide the net present value by the initial investment: $46,187 / $80,000 = 0.57734.
2. Multiply the result by 100 to get the percentage: 0.57734 * 100 = 57.73%.

The overall return on investment is 57.73%.

Here's how to do it:

1. Set up the equation: PV of benefits - PV of costs = 0.
2. Substitute the present values of the benefits and costs: $40,000 + $36,036 + $32,432 + $29,141 + $26,128 - ($80,000 + $37,550) = 0.
3. Simplify the equation: $164,737 - $117,550 = 0.
4. Solve for the number of years: $46,187 / $10,000 (increasing benefits) = 4.6187 years.

The break-even point occurs at approximately 4.6187 years.