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BNFO 621: Business and Entrepreneurship :ACCOUNTING

Roxanne M. Spindle

Associate Professor of Accounting

February 16 &18, 2016

McGraw-Hill/Irwin

Time Value of Money

A dollar today is worth more than a dollar a year from now. Therefore, investments that promise earlier returns are preferable to those that promise later returns.

The time value of money concept recognizes that a dollar today is worth more than a dollar a year from now. Therefore, projects that promise earlier returns are preferable to those that promise later returns.

McGraw-Hill/Irwin

Computation of Present Value

Present Value

Future Value

An investment can be viewed in two ways—its future value or its present value.

Let’s look at a situation where the future value is known and the present value is the unknown.

An investment can be viewed in two ways – its future value or its present value. In the example just completed, the present value was known and the future value was the unknown that we computed. Let’s look at the opposite situation – the future value is known and the present value is the unknown that we must compute.

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Present Value – An Example

If a bond will pay $100 in two years, what is the present value of the $100 if an investor can earn a return of 12% on investments?

(1 + r)n

P =

Assume a bond will pay one hundred dollars in two years. If an investor can earn twelve percent on their investments, what is the present value of the bond?

The equation needed to answer this question is as shown, where:

F is the balance at the end of the periods.

P is the amount invested now.

r is the rate of interest per period.

n is the number of periods.

McGraw-Hill/Irwin

Present Value – An Example

$100 × 0.797 = $79.70 present value

Present value factor of $1 for 2 periods at 12%.

We can also use the present value of one dollar table from Appendix fourteen C three to verify the accuracy of the seventy nine dollars and seventy two cents figure.

An excerpt of the appropriate table is as shown.

The appropriate present value factor is zero point seven nine seven and the present value is seventy nine dollars and seventy cents. The two cents difference is due to rounding.

Sheet1


	Rate
Periods	10%	12%	14%
1	0.909	0.893	0.877
2	0.826	0.797	0.769
3	0.751	0.712	0.675
4	0.683	0.636	0.592
5	0.621	0.567	0.519

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McGraw-Hill/Irwin

Quick Check 

How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?

a. $62.10

b. $56.70

c. $90.90

d. $51.90

How much would you have to put in the bank today to have one hundred dollars at the end of five years if the interest rate is ten percent?

McGraw-Hill/Irwin

How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%?

a. $62.10

b. $56.70

c. $90.90

d. $51.90

Quick Check 

$100  0.621 = $62.10

Sixty two dollars and ten cents. Review the solution provided.

McGraw-Hill/Irwin

Present Value of a Series of Cash Flows

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

$100

Although some investments involve a single sum to be received (or paid) at a single point in the future, other investments involve a series of identical cash flows known as an annuity.

McGraw-Hill/Irwin

Present Value of a Series of Cash Flows – An Example

Lacey Inc. 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%?

Assume Lacey Inc. purchased a tract of land on which a sixty thousand dollars payment will be due each of the next five years.

What is the present value of this stream of cash payments when the discount rate is twelve percent?

McGraw-Hill/Irwin

Present Value of a Series of Cash Flows – An Example

We could solve the problem like this . . .

$60,000 × 3.605 = $216,300

Appendix fourteen C four contains a present value of an annuity of one dollar table.

An excerpt from this table is as shown.

The appropriate present value factor is three point six zero five. The present value is two hundred sixteen thousand three hundred dollars.

Sheet1


Present Value of an Annuity of $1
Periods	10%	12%	14%
1	0.909	0.893	0.877
2	1.736	1.690	1.647
3	2.487	2.402	2.322
4	3.170	3.037	2.914
5	3.791	3.605	3.433

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McGraw-Hill/Irwin

Quick Check 

If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?

a. $34.33

b. $500.00

c. $343.30

d. $360.50

If the interest rate is fourteen percent, how much would you have to put in the bank today so as to be able to withdraw one hundred dollars at the end of each of the next five years?

McGraw-Hill/Irwin

If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years?

a. $34.33

b. $500.00

c. $343.30

d. $360.50

Quick Check 

$100  3.433 = $343.30

Three hundred forty three dollars and thirty cents. Review the solution provided.

McGraw-Hill/Irwin

Typical Capital Budgeting Decisions

Plant expansion

Equipment selection

Equipment replacement

Lease or buy

Cost reduction

Capital budgeting analysis can be used for any decision that involves an outlay now in order to obtain some future return. Typical capital budgeting decisions include:

Cost reduction decisions. Should new equipment be purchased to reduce costs?

Expansion decisions. Should a new plant or warehouse be purchased to increase capacity and sales?

Equipment selection decisions. Which of several available machines should be purchased?

Lease or buy decisions. Should new equipment be leased or purchased?

Equipment replacement decisions. Should old equipment be replaced now or later?

McGraw-Hill/Irwin

Typical Capital Budgeting Decisions

Capital budgeting tends to fall into two broad categories . . .

Screening decisions. Does a proposed project meet some present standard of acceptance?

Preference decisions. Selecting from among several competing courses of action.

There are two main types of capital budgeting decisions:

Screening decisions relate to whether a proposed project passes a preset hurdle. For example, a company may have a policy of accepting projects only if they promise a return of 20% on the investment.

Preference decisions relate to selecting among several competing courses of action. For example, a company may be considering several different machines to replace an existing machine on the assembly line.

In this chapter, we initially discuss ways of making screening decisions. Preference decisions are discussed toward the end of the chapter.

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Time Value of Money

The capital budgeting techniques that best recognize the time value of money are those that involve discounted cash flows.

The capital budgeting techniques that best recognize the time value of money are those that involve discounted cash flows (the concepts of discounting cash flows and using present value tables are explained in greater detail in Appendix Fourteen A).

McGraw-Hill/Irwin

The Net Present Value Method

To determine net present value we . . .

Calculate the present value of cash inflows,

Calculate the present value of cash outflows,

Subtract the present value of the outflows from the present value of the inflows.

The net present value method compares the present value of a project’s cash inflows with the present value of its cash outflows. The difference between these two streams of cash flows is called the net present value.

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General decision rule . . .

The Net Present Value Method

The net present value is interpreted as follows:

If the net present value is positive, then the project is acceptable.

If the net present value is zero, then the project is acceptable.

If the net present value is negative, then the project is not acceptable.

Sheet1


	If the Net Present Value is . . .		Then the Project is . . .
	Positive . . .		Acceptable, since it promises a return greater than the required rate of return.
	Zero . . .		Acceptable, since it promises a return equal to the required rate of return.
	Negative . . .		Not acceptable, since it promises a return less than the required rate of return.

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The Net Present Value Method

Net present value analysis emphasizes cash flows and not accounting net income.

The reason is that accounting net income is based on accruals that ignore the timing of cash flows into and out of an organization.

Net present value analysis (as well as the internal rate of return, which will be discussed shortly) emphasizes cash flows and not accounting net income. The reason is that accounting net income is based on accruals that ignore the timing of cash flows into and out of an organization.

McGraw-Hill/Irwin

Typical Cash Outflows

Repairs and

maintenance

Incremental

operating

costs

Initial

investment

Working

capital

Examples of typical cash outflows that are included in net present value calculations are as shown. Notice the term working capital which is defined as current assets less current liabilities.

The initial investment in working capital is a cash outflow at the beginning of the project for items such as inventories. It is recaptured at the end of the project when working capital is no longer required. Thus, working capital is recognized as a cash outflow at the beginning of the project and a cash inflow at the end of the project.

McGraw-Hill/Irwin

Typical Cash Inflows

Reduction

of costs

Salvage

value

Incremental

revenues

Release of

working

capital

Examples of typical cash inflows that are included in net present value calculations are as shown.

McGraw-Hill/Irwin

Recovery of the Original Investment

Depreciation is not deducted in computing the present value of a project because . . .

It is not a current cash outflow.

Discounted cash flow methods automatically provide for return of the original investment.

The net present value method excludes depreciation for two reasons:

First, depreciation is not a current cash outflow.

Second, discounted cash flow methods automatically provide for a return of the original investment, thereby making a deduction for depreciation unnecessary.

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Recovery of the Original Investment

Carver Hospital is considering the purchase of an attachment for its X-ray machine.

No investments are to be made unless they have an annual return of at least 10%.
Will we be allowed to invest in the attachment?

Assume the facts as shown with respect to Carver Hospital. Will we be allowed to invest in the attachment?

Sheet1


		Cost	$ 3,170
		Life	4 years
		Salvage value	zero
		Increase in annual cash inflows	1,000

Sheet2

Sheet3

McGraw-Hill/Irwin

Present value

of an annuity

of $1 table

Recovery of the Original Investment

The net present value of the investment is zero.

Sheet1


Item	Year(s)	Amount of Cash Flow	10% Factor	Present Value of Cash Flows
Initial investment (outflow)	Now	(3,170)	1.000	(3,170)
Annual cash inflows	1-4	$ 1,000	3.170	$ 3,170
Net present value				$ -0-

Sheet2

Sheet3

Sheet1


Present Value of $1
Periods	10%	12%	14%
1	0.909	0.893	0.877
2	1.736	1.690	1.647
3	2.487	2.402	2.322
4	3.170	3.037	2.914
5	3.791	3.605	3.433

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Choosing a Discount Rate

The firm’s cost of capital is usually regarded as the minimum required rate of return.
The cost of capital is the average rate of return the company must pay to its long-term creditors and stockholders for the use of their funds.

A company’s cost of capital, which is defined as the average rate of return a company must pay to its long-term creditors and shareholders for the use of their funds, is usually regarded as the minimum required rate of return. When the cost of capital is used as the discount rate, it serves as a screening device in net present value analysis.

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Two Simplifying Assumptions

Two simplifying assumptions are usually made in net present value analysis:

All cash flows other than the initial investment occur at the end of periods.

All cash flows generated by an investment project are immediately reinvested at a rate of return equal to the discount rate.

Two simplifying assumptions are usually made in net present value analysis:

The first assumption is that all cash flows other than the initial investment occur at the end of periods.

The second assumption is that all cash flows generated by an investment project are immediately reinvested at a rate of return equal to the discount rate.

McGraw-Hill/Irwin

The Cash Flows from Income taxes

Companies give part of net income to the state and federal governments in form of income taxes.
Reduces size of cash inflows
Most expenditures reduce taxable income, so can be measured net of tax.
Reduces size of cash outflows
Capital expenditures reduce taxes over time and have to be treated differently from the others.

McGraw-Hill/Irwin

Simplifying Assumptions For After-Tax

Taxable income equals net income as computed for financial reports.

The tax rate is a flat percentage of taxable income.

First, let’s identify some simplifying assumptions.

Taxable income equals net income as computed for financial reports.

The tax rate is a flat percentage of taxable income.

McGraw-Hill/Irwin

Concept of After-tax Cost

An expenditure net of its tax effect is known as after-tax cost.

Here is the equation for determining the after-tax cost of any tax-deductible cash expense:

An expenditure net of its tax effect is known as after-tax cost.

The equation for determining the after-tax cost of any tax-deductible cash expense is as shown.

Sheet1


			After-tax cost (net cash outflow)	=	(1-Tax rate) ´ Tax-deductible cash expense

Sheet2

Sheet3

McGraw-Hill/Irwin

After-tax Cost – An Example

Assume a company with a 30% tax rate is contemplating investing in a training program that will cost $60,000 per year.

We can use this equation to determine that the after-tax cost of the training program is $42,000.

Assume a company with a thirty percent tax rate is contemplating investing in a training program that will cost sixty thousand dollars per year.

The aforementioned equation can be used to determine that the after-tax cost of the training program is forty two thousand dollars.

Sheet1


After-tax cost (net cash outflow)	=	(1-Tax rate) ´ Tax-deductible cash expense
$42,000	=	(1 - .30) ´ $60,000

Sheet2

Sheet3

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After-tax Cost – An Example

The answer can also be determined by calculating the taxable income and income tax for two alternatives—without the training program and with the training program.

The after-tax cost of the training program is the same—$42,000.

The answer can also be determined by calculating the taxable income and income tax for two alternatives – without the training program and with the training program.

Notice that the after-tax cost of the training program would be the same – forty two thousand dollars.

McGraw-Hill/Irwin

After-tax Cost – An Example

The amount of net cash inflow realized from a taxable cash receipt after income tax effects have been considered is known as the after-tax benefit.

The equation for determining the after-tax benefit of any taxable cash receipt is as shown.

Sheet1


			After-tax benefit (net cash inflow)	=	(1-Tax rate) ´ Taxable cash receipt

Sheet2

Sheet3

McGraw-Hill/Irwin

Depreciation Tax Shield

While depreciation is not a cash flow, it does affect the taxes that must be paid and therefore has an indirect effect on a company’s cash flows.

When depreciation deductions shield revenues from taxation, they are generally referred to as a depreciation tax shield.

The equation for calculating the tax savings from a depreciation tax shield is as shown.

Remember that when as asset is purchased, a cash outflow occurs. Depreciation is just the allocation of that purchase price over some estimated life.

Sheet1


			Tax savings from the depreciation tax shield	=	Tax rate ´ Depreciation deduction

Sheet2

Sheet3

McGraw-Hill/Irwin

Depreciation Tax Shield – An Example

Assume a company has annual cash sales and cash operating expenses of $500,000 and $310,000, respectively; a depreciable asset, with no salvage value, on which the annual straight-line depreciation expense is $90,000; and a 30% tax rate.

Assume that a company has:

Annual cash sales and cash operating expenses of five hundred thousand dollars and three hundred ten thousand dollars, respectively;

A depreciable asset, with no salvage value, on which the annual straight-line depreciation expense is ninety thousand dollars; and

a thirty percent tax rate.

Sheet1


			Tax savings from the depreciation tax shield	=	Tax rate ´ Depreciation deduction

Sheet2

Sheet3

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Depreciation Tax Shield – An Example

The depreciation tax shield is $27,000.

The aforementioned equation can be used to calculate the depreciation tax shield of twenty seven thousand dollars.

Sheet1


Tax savings from the depreciation tax shield	=	Tax rate ´ Depreciation deduction
$27,000	=	.30 ´ $90,000

Sheet2

Sheet3

McGraw-Hill/Irwin

Depreciation Tax Shield – An Example

The answer can also be determined by calculating the taxable income and income tax for two alternatives—without the depreciation deduction and with the depreciation deduction.

The depreciation tax shield is the same—$27,000.

The answer can also be determined by calculating the taxable income and income tax for two alternatives – without the depreciation deduction and with the depreciation deduction.

Notice that the depreciation tax shield would be the same – twenty seven thousand dollars.

McGraw-Hill/Irwin

Holland Company – An Example

Holland Company owns the mineral rights to land that has a deposit of ore. The company is deciding whether to purchase equipment and open a mine on the property. The mine would be depleted and closed in 10 years and the equipment would be sold for its salvage value.

More information is provided on the next slide.

Holland Company owns the mineral rights to land that has a deposit of ore. The company is deciding whether to purchase equipment and open a mine on the property. The mine would be depleted and closed in ten years and the equipment would be sold for its salvage value.

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Holland Company – An Example

Should Holland open a mine on the property?

Pertinent financial information is as shown.

Holland’s after-tax cost of capital is twelve percent and its tax rate is thirty percent.

Should Holland open a mine on the property?

Sheet1


		Cost of equipment	$ 300,000
		Working capital needed	$ 75,000
		Estimated annual cash receipts from ore sales	$ 250,000
		Estimated annual cash expenses for mining ore	$ 170,000
		Cost of road repairs needed in 6 years	$ 40,000
		Salvage value of the equipment in 10 years	$ 100,000
		After-tax cost of capital	12%
		Tax rate	30%

Sheet2

Sheet3

McGraw-Hill/Irwin

Holland Company – An Example

Step One: Compute the net annual cash receipts from operating the mine.

The first step is to compute the net annual cash receipts of eighty thousand dollars from operating the mine.

Sheet1


After-tax cost (net cash outflow)	=	(1-Tax rate) ´ Tax-deductible cash expense
			Cash receipts from ore sales	$ 250,000
			Less cash expenses for mining ore	170,000
			Net cash receipts	$ 80,000

Sheet2

Sheet3

McGraw-Hill/Irwin

Holland Company – An Example

Step Two: Identify all relevant cash flows as shown.

The second step is to identify all relevant cash flows as shown.

Notice, that Holland uses straight-line depreciation, assuming no salvage value, to compute depreciation deductions for tax purposes.

Sheet1


After-tax cost (net cash outflow)	=	(1-Tax rate) ´ Tax-deductible cash expense
			Cash receipts from ore sales	$ 250,000
			Less cash expenses for mining ore	170,000
			Net cash receipts	$ 80,000
					Holland Company
						(1)	(2)
					Items and Computations	Year	Amount
					Cost of new equipment	Now	$ (300,000)
					Working capital needed	Now	$ (75,000)
					Net annual cash receipts	1-10	$ 80,000
					Road repairs	6	$ (40,000)
					Annual depreciation deductions	1-10	$ 30,000
					Salvage value of equipment	10	$ 100,000
					Release of working capital	10	$ 75,000
					Net present value

Sheet2

Sheet3

McGraw-Hill/Irwin

Holland Company – An Example

Step Three: Translate the relevant cash flows to after-tax cash flows as shown.

The third step is to translate the relevant cash flows to after-tax cash flows as shown.

Sheet1


After-tax cost (net cash outflow)	=	(1-Tax rate) ´ Tax-deductible cash expense
			Cash receipts from ore sales	$ 250,000
			Less cash expenses for mining ore	170,000
			Net cash receipts	$ 80,000
					Holland Company
						(1)	(2)	(3)	(4)
					Items and Computations	Year	Amount	Tax Effect (1) ´ (2)	After-Tax Cash Flows
					Cost of new equipment	Now	$ (300,000)	0	$ (300,000)
					Working capital needed	Now	$ (75,000)	0	$ (75,000)
					Net annual cash receipts	1-10	$ 80,000	1-.30	$ 56,000
					Road repairs	6	$ (40,000)	1-.30	$ (28,000)
					Annual depreciation deductions	1-10	$ 30,000	.30	$ 9,000
					Salvage value of equipment	10	$ 100,000	1-.30	$ 70,000
					Release of working capital	10	$ 75,000	0	$ 75,000
					Net present value

Sheet2

Sheet3

McGraw-Hill/Irwin

Holland Company – An Example

Step Four: Discount all cash flows to their present value as shown.

The fourth step is to discount all cash flows to their present value as shown.

Notice that the net present value of the project is twenty four thousand seven hundred forty four dollars.

Sheet1


After-tax cost (net cash outflow)	=	(1-Tax rate) ´ Tax-deductible cash expense
			Cash receipts from ore sales	$ 250,000
			Less cash expenses for mining ore	170,000
			Net cash receipts	$ 80,000
					Holland Company
						(1)	(2)	(3)	(4)	(5)	(6)
					Items and Computations	Year	Amount		After-Tax Cash Flows	12% Factor	Present Value
					Cost of new equipment	Now	$ (300,000)	0	$ (300,000)	1.000	$ (300,000)
					Working capital needed	Now	$ (75,000)	0	$ (75,000)	1.000	(75,000)
					Net annual cash receipts	1-10	$ 80,000	1-.30	$ 56,000	5.650	316,400
					Road repairs	6	$ (40,000)	1-.30	$ (28,000)	0.507	(14,196)
					Annual depreciation deductions	1-10	$ 30,000	.30	$ 9,000	5.650	50,850
					Salvage value of equipment	10	$ 100,000	1-.30	$ 70,000	0.322	22,540
					Release of working capital	10	$ 75,000	0	$ 75,000	0.322	24,150
					Net present value						$ 24,744

Sheet2

Sheet3

Rate

Periods10%12%14%

10.909 0.893 0.877

20.826 0.797 0.769

30.751 0.712 0.675

40.683 0.636 0.592

50.621 0.567 0.519

Periods10%12%14%

10.909 0.893 0.877

21.736 1.690 1.647

32.487 2.402 2.322

43.170 3.037 2.914

53.791 3.605 3.433

Present Value of an Annuity of $1

If the Net Present

Value is . . . Then the Project is . . .

Positive . . .

Acceptable, since it promises a

return greater than the required

rate of return.

Zero . . .

Acceptable, since it promises a

return equal to the required rate

of return.

Negative . . .

Not acceptable, since it promises

a return less than the required

rate of return.

Cost $3,170

Life4 years

Salvage valuezero

Increase in annual cash inflows 1,000

ItemYear(s)

Amount of

Cash Flow

10%

Factor

Present

Value of

Cash

Flows

Initial investment (outflow)Now(3,170) 1.000 (3,170)

Annual cash inflows1-41,000$ 3.170 3,170$

Net present value$ -0-

Periods10%12%14%

10.909 0.893 0.877

21.736 1.690 1.647

32.487 2.402 2.322

43.170 3.037 2.914

53.791 3.605 3.433

Present Value of $1

After-tax cost

(net cash outflow)

=(1-Tax rate)Tax-deductible cash expense

After-tax cost

(net cash outflow)

=(1-Tax rate)Tax-deductible cash expense

$42,000=(1 - .30)$60,000

After-tax benefit

(net cash inflow)

=(1-Tax rate)Taxable cash receipt

Tax savings from

the depreciation

tax shield

=Tax rateDepreciation deduction

Tax savings from

the depreciation

tax shield

=Tax rateDepreciation deduction

$27,000=.30$90,000

Cost of equipment $ 300,000

Working capital needed $ 75,000

Estimated annual cash

receipts from ore sales

$ 250,000

Estimated annual cash

expenses for mining ore $ 170,000

Cost of road repairs

needed in 6 years $ 40,000

Salvage value of the

equipment in 10 years $ 100,000

After-tax cost of capital12%

Tax rate30%

Cash receipts from ore sales250,000$

Less cash expenses for mining ore170,000

Net cash receipts80,000$

Holland Company

(1)(2)

Items and ComputationsYearAmount

Cost of new equipmentNow(300,000)$

Working capital neededNow(75,000)$

Net annual cash receipts1-1080,000$

Road repairs6(40,000)$

Annual depreciation deductions1-1030,000$

Salvage value of equipment10100,000$

Release of working capital1075,000$

Net present value

Holland Company

(1)(2)(3)(4)

Items and ComputationsYearAmount

Tax

Effect

(1)(2)

After-Tax

Cash Flows

Cost of new equipmentNow(300,000)$ 0 $ (300,000)

Working capital neededNow(75,000)$ 0 $ (75,000)

Net annual cash receipts1-1080,000$ 1-.30 $ 56,000

Road repairs6(40,000)$ 1-.30 $ (28,000)

Annual depreciation deductions1-1030,000$ .309,000$

Salvage value of equipment10100,000$ 1-.3070,000$

Release of working capital1075,000$ 075,000$

Net present value

Holland Company

(1)(2)(3)(4)(5)(6)

Items and ComputationsYearAmount

Tax

Effect

(1)(2)

After-Tax

Cash Flows

12%

Factor

Present

Value

Cost of new equipmentNow(300,000)$ 0 $ (300,000) 1.000 $ (300,000)

Working capital neededNow(75,000)$ 0 $ (75,000) 1.000 (75,000)

Net annual cash receipts1-1080,000$ 1-.30 $ 56,000 5.650 316,400

Road repairs6(40,000)$ 1-.30 $ (28,000) 0.507 (14,196)

Annual depreciation deductions1-1030,000$ .309,000$ 5.650 50,850

Salvage value of equipment10100,000$ 1-.3070,000$ 0.322 22,540

Release of working capital1075,000$ 075,000$ 0.322 24,150

Net present value

$ 24,744