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Concept of Present Value

- Business investments extend over long periods of time, so we must recognize the time value of money.
- Investments that promise returns earlier in time are preferable to those that promise returns later in time.

An Organization as a Collection of Projects and Programs

Projects

and

Programs

F

E

Overall

performance

in this period

is the combined

results of

projects A - F.

D

C

B

A

Time

Concept of Present Value

Fn = P(1 + r)n

If Pdollars are invested today . . .

At interest rate of r. . .

Fornperiods . . .

You would have Fndollars.

Concept of Present Value

If $100 is invested today at 10% interest, how much will the investment be worth in five years?

Concept of Present Value

If $100 is invested today at 10% interest, how much will the investment be worth in five years?

F5 = $100 × (1 + .10)5

F5 = $161.05

Concept of Present Value

The present value of any sum to be received in the future can be computed by using the interest formula and solving for P . . .

Fn

P =

(1 + r)n

or

1

P = Fn ×

(1 + r)n

Concept of Present Value

You do not know the amount of the initial investment, but know you will need $161.05 at the end of five years. You can earn 10% on your investment. What amount must you invest today?

(1 + .10)5

Concept of Present ValueYou do not know the amount of the initial investment, but know you will need $161.05 at the end of five years. You can earn 10% on your investment. What amount must you invest today?

P = $161.05 ×

P = $161.05 × .6209 = $100

Concept of Present Value

Suppose you want to accumulate $18,000 to buy a new car in four years, and you can earn interest at the rate of 8% per year on an investment. How much do you need to invest now?

(1 + .08)4

Concept of Present ValueSuppose you want to accumulate $18,000 to buy a new car in four years, and you can earn interest at the rate of 8% per year on an investment. How much do you need to invest now?

P = $18,000 ×

P = $18,000 × .735 = $13,230

$100

$100

$100

$100

$100

1

2

3

4

5

6

Present Value of a Cash-Flow SeriesAn investment that involves a series of identical cash flows at the end of each year is called an annuity.

Present Value of a Cash-Flow Series

An investment that involves a series of identical cash flows at the end of each year is called an annuity.

Laken Company purchased a tract of land

on which a $60,000 payment will be due

each year for the next five years. What is

the present value of this stream of cash

payments when the discount rate is 12%?

Present Value of a Cash-Flow Series

Present Value of a Cash-Flow Series

The present value of our 5

$60,000 payments is $216,300.

Present Value of a Cash-Flow Series

We could solve the problem like this . . .

$60,000 × 3.605 = $216,300

Present Value of a Cash-Flow Series

We could solve the problem like this . . .

$60,000 × 3.605 = $216,300

Look in Appendix for the Present Value

of an Annuity of $1 Table IV

Discounted-Cash-Flow Analysis

Plant expansion

Equipment selection

Equipment replacement

Cost reduction

Lease or buy

Net-Present-Value Method

- Prepare a table showing cash flows for each year,
- Calculate the present value of each cash flow using a discount rate,
- Compute net present value,
- If the net present value (NPV) is positive, accept the investment proposal. Otherwise, reject it.

Net-Present-Value Method

Mattson Co. has been offered a five year contract to provide component parts for a large manufacturer.

Net-Present-Value Method

- At the end of five years the working capital will be released and may be used elsewhere by Mattson.
- Mattson uses a discount rate of 10%.

Should the contract be accepted?

Net-Present-Value Method

Annual net cash inflows from operations

Net-Present-Value Method

Mattson should accept the contract because the present value of the cash inflows exceeds the present value of the cash outflows by $85,955. The project has apositivenet present value.

Internal-Rate-of-Return Method

- The internal rate of return is the true economic return earned by the asset over its life.
- The internal rate of return is computed by finding the discount rate that will cause the net present value of a project to be zero.

Internal-Rate-of-Return Method

- Black Co. can purchase a new machine at a cost of $104,320 that will save $20,000 per year in cash operating costs.
- The machine has a 10-year life.

Internal-Rate-of-Return Method

Future cash flows are the same every year in this example, so we can calculate the internal rate of return as follows:

Investment required

Net annual cash flows

= Present value factor

$104, 320

$20,000

=5.216

Internal-Rate-of-Return Method

The present value factor (5.216) is located on the Table IV in the Appendix. Scan the 10-period row and locate the value 5.216. Look at the top of the column and you find a rate of14% which is the internal rate of return.

$104, 320

$20,000

= 5.216

Internal-Rate-of-Return Method

Here’s the proof . . .

Comparing the NPV and IRR Methods

Net Present Value

- The cost of capital is used as the actual discount rate.
- Any project with a negative net present value is rejected.

Internal Rate of Return

The cost of capital is compared to the internal rate of return on a project.

To be acceptable, a project’s rate of return must be greater than the cost of capital.

Net Present Value

The cost of capital is used as the actual discount rate.

Any project with a negative net present value is rejected.

Comparing the NPV and IRR MethodsComparing the NPV and IRR Methods

The net present value method has the following advantages over the internal rate of return method . . .

- Easier to use.
- Easier to adjust for risk.
- Provides more usable information.

Assumptions Underlying Discounted-Cash-Flow Analysis

Assumes a

perfect

capital

market.

All cash flows are

treated as though

they occur at year end.

Cash inflows are

immediately

reinvested at

the required

rate of return.

Cash flows are

treated as if

they are known

with certainty.

Choosing the Hurdle Rate

- The discount rate generally is associated with the company’scost of capital.
- The cost of capital involves a blending of the costs of all sources of investment funds, both debt and equity.

Form 1120

Depreciable AssetsBoth the NPV and IRR methods focus on cash flows, and periodic depreciation charges are not cash flows . . .

Depreciation

is tax

deductible

and . . .

Reduces

cash

outflows for

taxes.

Comparing Two Investment Projects

To compare competing investment projects we can use the following net present value approaches:

- Total-Cost Approach.
- Incremental-Cost Approach.

Total-Cost Approach

- Black Co. is trying to decide whether to remodel an old car wash or remove it entirely and install a new one.
- The company uses a discount rate of 10%.

Total-Cost Approach

- The new washer costs $300,000 and will produce revenues for 10 years.
- The brushes have to be replaced at the end of 6 years at a cost of $50,000.
- The old washer has a current salvage value of $40,000.
- The estimated salvage value of the new washer will be $7,000 at the end of 10 years.
- Remodeling the old washer costs $175,000 and the brushes must be replaced at the end of 6 years at a cost of $80,000 .

Should Black replace the washer?

Total-Cost Approach

If Black Co. installs the new washer,

the investment will yield a

positive net present value of $83,202.

Total-Cost Approach

If Black Co. remodels the existing

washer, it will produce a

positive net present value of $56,405.

Total-Cost Approach

Both projects yield a positive net present value.

However, investing in the new washer will produce a higher net present value than remodeling the old washer.

Incremental-Cost Approach

Under the incremental-cost approach, only those cash flows that differ between the two alternatives are considered.

Let’s look at an analysis of the

Black Co. decision using

the incremental-cost approach.

Incremental-Cost Approach

$300,000 new - $175,000 remodel = $125,000

Incremental-Cost Approach

$80,000 remodel - $50,000 new = $30,000

Incremental-Cost Approach

$60,000 new - $45,000 remodel = $15,000

Incremental-Cost Approach

We get the same answer under either the

total-cost and incremental-cost approach.

Managerial Accountant’s Role

Managerial accountants are often asked to predict cash flows related to operating cost savings, additional working capital requirements, and incremental costs and revenues.

When cash flow projections are very uncertain, the accountant may . . .

- increase the hurdle rate,
- use sensitivity analysis.

Sensitivity Analysis

What annual cost-savings amount would result in a zero NPV for the project?

We have an investment that cost $50,470, and

produces a $14,000 annual cost savings for the

next 5 years. We use a hurdle rate of 10%

for all investment projects.

Sensitivity Analysis

What annual cost-savings amount would result in a zero NPV for the project?

Acquisition cost

Annuity discount factor

= annual cost savings

$50,470

3.791*

= $13,313

*n = 5, r = 10%

Sensitivity Analysis

What annual cost-savings amount would result in a zero NPV for the project?

Projected cash savings of $14,000 could fall as low as

$13,313, and the project would still be acceptable.

$50,470

3.791*

= $13,313

*n = 5, r = 10%

Capital Budget Administration

Most organizations have an elaborate approval process for proposed investment projects. The larger the cost of a proposal, the higher in the organization is the authority for final approval.

Postaudit of Investment Projects

A postaudit is a follow-up after the project has been approved to see whether or not expected results are actually realized.

Performance Evaluation:A Behavioral Issue

Discounted cash

flows methods of

investment

decision making

(NPV and IRR)Focus on cash

flows

Accrual

accounting

methods of

evaluating

periodic

performanceFocus on

accounting

revenues and

expenses

Conflict

Justification of Investments in Advanced Manufacturing Systems

Hurdle

rates are

too high

Time

horizons

are too

short

Bias

towards

incremental

projects

Benefits

difficult to

quantify

Greater

cash flow

uncertainty

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