5 Basic Investment Analysis

The Theory

When a manager is trying to decide whether to make an investment that will provide returns over a number of years, they must consider the time value of money when they decide whether the project will provide an adequate return, because money received today is worth more than money received in the future.

Net present value analysis is a widely used technique for analyzing potential long-term investments. To conduct a net present value analysis, discount the future cash flows of the project to their present value using the firm’s required rate of return as the discount rate, and subtract the initial investment in the project, which is already at present value. A positive net present value indicates that the project would earn more than the required rate of return, so accepting the project would therefore be financially beneficial, while a negative net present value indicates that the project would earn less than the required rate of return, so rejecting the project would therefore be financially beneficial.

When performing net present value analysis, consider only cash flows, including cash flows from taxes. Thus, all annual cash flows should be included on an after-tax basis, and the tax effects from non-cash items such as depreciation, gains, or losses should be included as well.

Another technique for analyzing potential long-term investments is to find a project’s internal rate of return. This is the annual rate of return a project actually earns, factoring in the time value of money. If a project is discounted using the internal rate of return as the discount rate, its net present value will be zero. An internal rate of return higher than the required rate of return indicates that accepting the project would be financially beneficial, while an internal rate of return lower than the required rate of return indicates that rejecting the project would be financially beneficial.

Often managers will also consider the payback period of a project when making decisions about long-term investments. The payback period is the amount of time required to earn back the initial investment in a project, without considering the time value of money.

The Method

For any of the long-term investment analysis techniques, you will need to calculate the net initial investment, the annual cash flows, and possibly the terminal cash flows of the project:

Terminal cash flows are any expected cash flows at the end of the project, resulting from sales or disposal of assets or recovery of working capital. It can be helpful to place cash flows on a timeline to better understand when they occur.

Net Present Value

First, calculate the net initial investment, annual cash flows, and terminal cash flows.

Next, discount the annual cash flows and terminal cash flows to present value:

• If annual cash flows are the same each year, you can multiply the annual amount by the present value factor from the annuity table
• If annual cash flows are different each year, you can multiply the amount each year by the present value factor from the single amount table
• Terminal cash flows should be multiplied by the present value factor from the single value table

Next, add the present values of the annual cash flows and terminal cash flows and subtract the net initial investment to find the net present value of the project.

Finally, indicate whether accepting the project would be financially beneficial by determining whether the net present value is positive.

Internal Rate of Return

The internal rate of return is difficult to calculate by hand if cash flows differ from year to year, in which case it is best to use a spreadsheet function or financial calculator. If annual cash flows are the same every year, you can find the range in which the internal rate of return falls by solving for the present value factor. Because the net present value of a project discounted at its internal rate of return is zero, if cash flows are even:

First, calculate the net initial investment and annual cash flows.

Next, solve for the present value factor (annuity) by dividing the net initial investment by annual cash flows.

Next, find the range for the internal rate of return by looking in the row corresponding to the number of years in the life of the project on the annuity table. Find the point where the calculated present value factor would fit—where the factor in one column is larger than the calculated factor, and the factor in the next column is smaller. The internal rate of return will fall between the rates corresponding to those two columns.

Finally, indicate whether accepting the project would be financially beneficial by determining whether the internal rate of return is higher than the required rate of return.

Payback Period

First, calculate the net initial investment and annual cash flows.

Next, calculate the payback period:

If cash flows are the same every year, divide the net initial investment by annual cash flows.

If cash flows differ from year to year:

• First, calculate the cumulative cash flows each year.
• Next, find the first year in which cumulative cash flows are larger than the net initial investment, and subtract the proportion of cash flows occurring during that year since payoff:

Payback period = Years − (Cumulative cash flows − Net initial investment) ÷ Cash flows during the year

Note: If cash flows are the same every year but the last, you can try dividing the net initial investment by the annual cash flows. If the payback period is less than the years in the life minus one, you can use the figure you calculated. If not, you will need to use the procedure for cash flows that differ from year to year.

Illustrative Examples

Net Present Value

Zarbine Company is considering replacing a piece of machinery with a book value of $100,000. The new machine will cost $800,000, and will have a useful life of five years, after which its salvage value will be $250,000. The machine would save the company $200,000 a year in operating costs. The current machinery could be sold now for $20,000. Zarbine has a tax rate of 30% and a required rate of return of 12%.

Find the net present value of the machine replacement.^[1]

First, calculate the net initial investment, the annual cash flows, and the terminal cash flows of the project:

• Net initial investment:
  • Cost of new machine: $800,000
  • Sales value of old machine: $20,000
  • Tax savings from loss on sale of old machine: ($100,000 – $20,000) × 30% = $24,000
  • Total: $800,000 – $20,000 – $24,000 = $756,000
• Annual cash flows:
  • Annual cash flows: $200,000
  • Tax on cash flows: $200,000 × 30% = $60,000
  • Tax savings from depreciation
    • Straight-line depreciation: ($800,000 – $250,000) / 5 = $110,000
    • Tax savings: $110,000 × 30% = $33,000
  • Total: $200,000 – $60,000 + $33,000 = $173,000
• Terminal cash flows: $250,000

Next, discount the annual cash flows and terminal cash flows to present value:

• Present value factors for 5 years, 12%: Single amount 0.5674, Annuity 3.6048
• Annual cash flows: $173,000 × 3.6048 = $623,630.40
• Terminal cash flows: $250,000 × 0.5674 = $141,850

Next, add the present values of the annual cash flows and terminal cash flows, and subtract the net initial investment to find net present value:

• Net present value = $623,630.40 + $141,850 – $756,000 = $9,480.40

Finally, indicate whether accepting the project would be financially beneficial.

• The net present value is positive, so accepting the project would be financially beneficial.

Payback Period (Uneven Cash Flows)

Find the payback period of the investment described above.

First, calculate the cumulative cash flows each year:

• Cash flows during Years 1–4 will be $173,000
• Cash flow during Year 5 will be $173,000 + terminal cash flow $250,000 = $423,000

Finally, find the first year in which cumulative cash flows are larger than the net initial investment, and subtract the proportion of cash flows occurring during that year since payoff:

• The first year in which cumulative cash flows are greater than the net initial investment of $800,000 is Year 5.
• Payback period = 5 − ($1,115,000 − $756,000) / $423,000 = 5 − 0.85 = 4.15 years

Internal Rate of Return

Ozzley Company plans to invest in a new product line. Up-front costs for equipment will total $3,000,000. Ozzley plans to sell old equipment with a book value of $500,000 to make way for the new product line’s equipment. The old equipment will sell for $700,000. Ozzley projects that the new product will bring in additional revenues of $1,200,000 per year and will increase costs by $750,000 per year. Ozzley estimates that the product’s life will be ten years, at which point the product will become obsolete and the equipment used to manufacture it will be worthless. Ozzley has a required rate of return of 14% and a tax rate of 15%.

Find the internal rate of return of the new product.

First, calculate the net initial investment and annual cash flows:

• Net initial investment:
  • Up-front costs: $3,000,000
  • Sales value of old machine: $700,000
  • Tax cost from gain on sale of old machine: ($700,000 – $500,000) × 15% = $30,000
  • Total: $3,000,000 – $700,000 + $30,000 = $2,330,000
• Annual cash flows:
  • Annual cash flows: $1,200,000 − $750,000 = $450,000
  • Tax on cash flows: $450,000 × 15% = $67,500
  • Tax savings from depreciation
    • Straight-line depreciation: ($3,000,000 – $0) / 10 = $300,000
    • Tax savings: $300,000 × 15% = $45,000
  • Total: $450,000 – $67,500 + $45,000 = $427,500

Next, solve for the present value factor by dividing the net initial investment by annual cash flows:

• $2,330,000 ÷ $427,500 = 5.4503

Next, find the range for the internal rate of return by looking in the row corresponding to the number of years in the life of the project on the annuity table.

• 5.4503 falls between 5.6502 (12%) and 5.4262 (13%). The internal rate of return falls between 12% and 13%.

Finally, indicate whether accepting the project would be financially beneficial.

• The internal rate of return is less than the required rate of return of 14%, so rejecting the project would be financially beneficial.

Payback Period (Even Cash Flows)

Find the payback period of the investment described above.

Divide the net initial investment by annual cash flows: $2,330,000 ÷ $427,500 = 5.45 years

Lecture Examples

Your firm is considering purchasing a new piece of equipment that would cost $400,000. It will last 10 years, after which it can be sold for $50,000. The new equipment will generate cost savings of $60,000 per year over the firm’s existing equipment, which has a book value of $20,000 and could be sold now for $40,000. Your firm has a tax rate of 25% and a required rate of return of 12%.

1. Find the net present value of the investment.
2. Based on the net present value, would accepting the project be financially beneficial?
3. Find the payback period of the investment.
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?