BUSINESS AND FAITH INTEGRATION

Assume you plan to invest $1,000 today and will receive $600 each year for two years (assume the cash is received at the end of the year). What is the net present value if there is a 10% opportunity cost of capital?

C0 = $1,000

C1 = $600

C2 = $600

r = 0.10

Net Present Value: Example 2

Assume you invest $1,000 today and will receive $1,200 in two years (assume the cash is received at the end of the 2nd year). What is the net present value if there is a 10% opportunity cost of capital?

C0 = ? C0 = $1,000

C1 = ? C1 = $0

C2 = ? C2 = $1,200

r = ? r = 0.10

Net Present Value Rule

Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost. Therefore, managers should accept all projects with a positive net present value.

Using the NPV Rule to Choose among Projects

When choosing among mutually exclusive projects, calculate the NPV of each alternative and choose the highest positive-NPV project. Example: Consider two projects, assuming a 10% opportunity cost of capital.

Which project should be selected?

Challenges to the NPV Rule

1. The Investment Timing Decision

2. The Choice between Long and Short-Lived Equipment

3. When to Replace an Old Machine

Investment Timing

Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision.

Example: A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow. Assume an opportunity cost of capital of 10%.

Year Cost Sales Value NPV

0 50 70 20 20.0

1 55 80 25 22.7

2 60 88 28 23.1

3 64 95 31 23.3

4 68 102 34 23.2

5 70 105 35 21.7

Long vs. Short-Lived Equipment: Equivalent Annual Annuity

The Choice between Long- and Short-lived Equipment:

· Equivalent Annual Annuity - The cash flow per period with the same present value as the cost of buying and operating a machine.

· Annuity Factor - The present value of $1 paid every year for each of t years.

Note: Think of the equivalent annual annuity as the level annual charge that is necessary to recover the present value of investment outlays and operating costs.

Equivalent Annual Annuity: Example

Given the following costs of operating two machines and an 8% cost of capital, select the lower-cost machine using the equivalent annual annuity method.

Select Machine 1 because its EAA is less negative.

Payback Method

· Payback Period - Time until cash flows recover the initial investment of the project.

Payback Rule

Says a project should be accepted if its payback period is less than a specified cutoff period.

· Payback Rule - Specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this statement.

Payback Method: Example

Example:

The three projects below are available. The company accepts all projects with a 2 year or less payback period. Show how this will impact your decision.

Drawback of Payback Rule

1. Though Projects 1, 2 and 3 have payback periods less than 2 years, notice the differences in NPV.

2. The Payback Rule ignores the time value of money.

· Discounted Payback Rule – This is the number of periods before the present value of prospective cash flows equals or exceeds the initial investment.

Other Investment Criteria: IRR

· Internal Rate of Return (IRR) - Discount rate at which NPV = 0.

· Sometimes termed the discounted cash flow (DCF) rate of return.

Internal Rate of Return: Example*

* Calculating the IRR can be a laborious task. Fortunately, financial calculators and spreadsheets can perform this function easily

Internal Rate of Return Rule

Managers increase shareholders’ wealth by accepting all projects which offer a rate of return that is higher than the opportunity cost of capital.

NVP and Internal Rate of Return

Note: The Internal rate of return rule will give the same answer (accept or reject) as the NPV rule as long as the NPV of a project declines smoothly as the discount rate increases.

IRR vs. NPC

Pitfall 1 – Lending or Borrowing?

IRR vs. NPV

Pitfall 2 – Mutually Exclusive Projects

IRR vs. NPV

Pitfall 3 – Multiple Rates of Return

This problem can be corrected using MIRR (modified internal rate of return). See Chapter 8 appendix for details.

Other Investment Criteria: Profitability Index