Financial Data

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Chapter 13:

The Time Value of Money

Purpose

  • Computations concerning the use of money help a manager evaluate the use of available dollars
  • Make informed choices about where resources of the organization should be spent.

Computation Methods

  • These four computations will help a manager evaluate the use of money:
  • Unadjusted rate of return
  • Present value analysis
  • Internal rate of return
  • Payback period

Unadjusted Rate of Return (1 of 2)

  • This method accommodates whatever depreciation method is in use.
  • It is sometimes called the accountant’s method because information required is all obtained from financial statements.
  • Remember, the answer is only an estimate, containing no precision.
  • See the practice exercise in the textbook for an example.

Unadjusted Rate of Return (2 of 2)

  • Unadjusted rate of return computation is as follows:
  • Average annual net income divided by original investment amount equals rate of return, or
  • Average annual net income divided by average investment amount equals rate of return.

Unadjusted Rate of Return:
Example 13A (1 of 3)

  • Assumptions:
  • average annual net income = $100,000
  • original investment amount = $1,000,000
  • unrecovered asset cost at the end of useful life (salvage value) = $100,000
  • Calculation using original investment amount:

$100,000

$1,000,000

= 10% Unadjusted Rate of Return

Unadjusted Rate of Return:
Example 13A (2 of 3)

  • Calculation using average investment amount:
  • Step 1: Compute average investment amount as follows:

Total unrecovered asset cost:

at beginning of estimated useful life = $1,000,000

at end of estimated useful life = $ 100,000

Sum $1,100,000

  • divided by 2 = $550,000 average investment amount

Unadjusted Rate of Return:
Example 13A (3 of 3)

  • Step 2: Calculation of unadjusted rate of return

$100,000

$550,000

= 18.2% Unadjusted Rate of Return

Unadjusted Rate of Return:
Practice Exercise 13-1

Calculation using original investment amount:

$100,000

$500,000

Calculation using average investment amount:

Step 1: Compute average investment amount as follows:

total unrecovered asset cost:

at beginning of estimated useful life = $ 500,000

at end of estimated useful life = $ 50,000

Sum $ 550,000

divided by 2 = $275,000 average investment amount

Step 2: Calculation of unadjusted rate of return

$100,000

$275,000

= 20% Unadjusted Rate of Return

= 36.4% Unadjusted Rate of Return

Unadjusted Rate of Return: Assignment Exercise 13-1

Calculation using original investment amount:

$70,000

$410,000

Calculation using average investment amount:

Step 1: Compute average investment amount as follows:

total unrecovered asset cost:

at beginning of estimated useful life = $ 410,000

at end of estimated useful life = $ 41,000

Sum $4510,000

divided by 2 = $225,000 average investment amount

Step 2: Calculation of unadjusted rate of return

$70,000

$225,000

= 17.07% Unadjusted Rate of Return

= 31.04% Unadjusted Rate of Return

Present Value Analysis (1 of 2)

  • Present value analysis is based on the time value of the money.
  • That is, the value of the dollar today is more than the value of a dollar in the future
  • The further in the future the receipt of your dollar occurs, the less it is worth.

Present Value Analysis (2 of 2)

The methods for present value analysis are as follows:

  • It is possible to use equations to restate the present values of $1 to be paid out (or received), but present value tables can take the place of equations.
  • You can also do the computation on a business calculator.

(See the practice exercise in the textbook for an example using present value tables.)

Payback Period:
Practice Exercise 13-5 (1 of 2)

  • Assemble assumptions in an orderly manner:

Purchase price of the equipment = $500,000

Useful life of the equipment = 10 years

Revenue the machine will generate per year = $84,000

Direct operating costs associated with earning the revenue = $21,000

Depreciation expense per year (computed as purchase price per assumption #1 divided by useful life per assumption #2) = $50,000

Present Value Analysis:
Example 13C (1 of 3)

  • Betty Dylan is taking an adult education night course in personal finance at the community college.
  • The class is presently studying retirement planning.
  • Each student is to estimate the amount of funds (in addition to pension plans and social security) that they believe will be needed at retirement.

Present Value Analysis:
Example 13C (2 of 3)

  • Then they are to make a retirement plan.
  • Betty has estimated she would need $100,000 fifteen years from now.
  • In order to complete her assignment, she needs to know the present value of the $100,000.
  • Betty further assumes an interest rate of 6%.

Present Value Analysis:
Example 13C (3 of 3)

Step 1: Refer to the Present Value Table found in Appendix 13-A at the back of this chapter.

  • Reading across, or horizontally, find the 6% column.
  • Reading down, or vertically, find Year 15.
  • Trace across the Year 15 line item to the 6% column.
  • The factor is 0.4173.

Step 2: Multiply $100,000 times the factor of 0.4173 to find the present value of $41,730.

Present Value Analysis:
Practice Exercise 13-3

Step 1: Refer to the Present Value Table found in Appendix 13-A at the back of this chapter.

  • Reading across, or horizontally, find the 7% column.
  • Reading down, or vertically, find Year 15.
  • Trace across the Year 15 line item to the 7% column.
  • The factor is 0.3624.

Step 2: Multiply $150,000 times the factor of 0.3624 to find the present value of $54,360.

Present Value Analysis:
Assignment Exercise 13-3, Part 1

Step 1: Refer to the Present Value Table found in Appendix 13-A at the back of this chapter.

  • Reading across, or horizontally, find the 5% column.
  • Reading down, or vertically, find Year 6. Trace across the Year 6 line item to the 5% column.
  • The factor is 0.7462.

Step 2: Multiply $250,000 times the factor of 0.7462 to find the present value of $186,550.

Present Value Analysis:
Assignment Exercise 13-3, Part 2

Step 1: Refer to the Present Value Table.

  • Reading across, or horizontally, find the 7% column.
  • Reading down, or vertically, find Year 6.
  • Trace across the Year 6 line item to the 7% column. The factor is 0.6663.

Step 2: Multiply $250,000 times the factor of 0.6663 to find the present value of $166,575.

Step 3: The difference in present value between rates of 5% and 7% amounts to $19,975.

Internal Rate of Return (IRR) (1 of 3)

  • Internal rate of return (IRR) represents the rate of interest that discounts future net inflows (from a proposed investment) down to the amount invested.
  • IRR recognizes the time pattern in which earnings occur. This means more precision in the computation because IRR calculates from period to period.
  • This method uses a discounted cash flow technique.

Internal Rate of Return (IRR) (2 of 3)

  • IRR computation first requires three assumptions:
  • Initial cost of investment
  • Estimated annual net cash inflow
  • Useful life of asset, expressed in number of periods

Internal Rate of Return (IRR) (3 of 3)

IRR computation is then as follows:

  • Divide the initial cost of investment by the estimated annual net cash inflow—the answer will be a ratio.
  • Use the look-up table (as described in the text)— find number of periods.
  • Then find the column approximating the ratio previously computed (figure in that column that is the interest rate approximating the rate of return).
  • IRR can also be computed through equations or through a series of steps on a business calculator.

Internal Rate of Return:
Practice Exercise 13-4 (1 of 3)

  • Assemble the assumptions in an orderly manner:

Initial cost of the investment = $16,950

Estimated annual net cash inflow the investment will generate = $3,000

Useful life of the asset = 10 years

Internal Rate of Return:
Practice Exercise 13-4 (2 of 3)

  • Step 1: Divide the initial cost of the investment ($16,950) by the estimated annual net cash inflow it will generate ($3,000). The answer is a ratio amounting to 5.650.
  • Step 2: Now use the abbreviated look-up table for the Present Value of an Annuity of $1, which is found in Appendix 13-C. Find the line item for the number of periods that matches the useful life of the asset (10 years in this case).

Internal Rate of Return:
Practice Exercise 13-4 (3 of 3)

  • Step 3: Look across the 10 year line on the table and find the column that approximates the ratio of 5.650 (as computed in Step #1). That column contains the interest rate representing the rate of return. In this case the rate of return is 12%.

Internal Rate of Return:
Assignment Exercise 13-4 (1 of 3)

  • Assemble the assumptions in an orderly manner:

Initial cost of the investment = $60,000

Estimated annual net cash inflow the investment will generate = $30,000. Estimated annual net cash inflow the investment will generate after taxes = $15,000

Useful life of the asset = 6 years

Internal Rate of Return:
Assignment Exercise 13-4 (2 of 3)

  • Step 1: Divide the initial cost of the investment ($60,000) by the estimated annual net cash inflow after taxes it will generate ($15,000). The answer is a ratio amounting to 4.000.
  • Step 2: Now use the abbreviated look-up table for the Present Value of an Annuity of $1, which is found in Appendix 13-C. Find the line item for the number of periods that matches the useful life of the asset (6 years in this case).

Internal Rate of Return:
Assignment Exercise 13-4 (3 of 3)

  • Step 3: Look across the 6 year line on the table and find the column that approximates the ratio of 4.000 (as computed in Step #1). That column contains the interest rate representing the rate of return. In this case the rate of return is 12%.

Payback Period (1 of 3)

  • A payback period is the length of time required for the cash coming in from an investment to equal the amount of cash originally spent when the investment was acquired.
  • Assumptions are key to this computation. Usually a “best case” and “worst case” computation is made.
  • Payback period computations are very common when equipment purchases are being evaluated.

Payback Period (2 of 3)

  • Payback period computation first requires five assumptions:
  • Purchase price of the equipment
  • Useful life of the equipment
  • Revenue generated by year
  • Related direct operating costs
  • Depreciation expense per year

Payback Period (3 of 3)

  • Payback period computation is then as follows:

Find the machine’s expected net income after taxes.

Find the annual cash inflow after taxes the machine is expected to generate (i.e., convert net income to a cash basis).

Compute the payback period: divide the price by the annual cash inflow after taxes to find the payback period.

(See the chapter text and the practice exercises for examples.)

Payback Period:
Practice Exercise 13-5 (1 of 2)

  • Assemble assumptions in an orderly manner:

#1: Purchase price of the equipment = $500,000

#2: Useful life of the equipment = 10 years

#3: Revenue the machine will generate per year = $84,000

#4: Direct operating costs associated with earning the revenue = $21,000

#5: Depreciation expense per year (computed as purchase price per assumption #1 divided by useful life per assumption #2) = $50,000

Payback Period:
Practice Exercise 13-5 (2 of 2)

Step 1: Find the machine’s expected net income after taxes:

Revenue (assumption #3) $ 84,000

Less

Direct operating costs (assumption #4) $ 21,000

Depreciation (assumption #5) 50,000

____________

Net income $ 13,000

Step 2: Find the net annual cash inflow the machine is expected to generate:

Net income $ 13,000

Add back depreciation (a noncash expenditure) 50,000

____________

Annual net cash inflow after taxes $ 63,000

Step 3: Compute the payback period:

investment $500,000 machine cost*

net annual cash inflow $63,000**

*(assumption #1 above); **(per step 2 above)

The machine will pay back its investment under these assumptions in 7.9 years.

= 7.9 year payback period

Payback Period:
Assignment Exercise 13-5 (1 of 3)

  • Assemble assumptions in an orderly manner:

Purchase price of the equipment = $15,000 Machine A and $12,000 Machine B

Useful life of the equipment = 10 years for both Machine A and Machine B

Reduction of operating costs = $5,000 for Machine A and $5,000 for Machine B

Depreciation expense per year = $1,500 for Machine A and $1,200 for Machine B

Payback Period:
Assignment Exercise 13-5 (2 of 3)

  • Perform computation: Step 1: Find the net annual cash inflow the machine is expected to generate (in other words, convert the net income to a cash basis):

Machine A Machine B

Net income (the reduction of operating

costs is the equivalent of earning revenue) $5,000 $5,000

Add back depreciation (a noncash expenditure) 1,500 1,200

Annual net cash inflow after taxes $6,500 $6,200

Payback Period:
Assignment Exercise 13-5 (3 of 3)

Step 2: Compute the payback period:

For Choice #1:

investment $15,000 machine cost*

net annual cash inflow $6,500**

* (assumption #1 above); **(per step 1 above)

For Choice #2:

investment $12,000 machine cost*

net annual cash inflow $6,200**

* (assumption #1 above); **(per step 1 above)

The $15,000 machine will pay back its investment under these assumptions in 2.31 years while the $12,000 machine will pay back its investment under these assumptions in 1.94 years.

= 2.31 year payback period

= 1.94 year payback period

Finding the Future Value with
a Compound Interest Table

  • A compound interest table is included at the end of this chapter in Appendix 13-B.
  • Compound interest tables can take the place of equations when finding future value. (While you can also do the computation on a business calculator or on the computer, the tables are sometimes a convenient reference.)

(See the practice exercise in the textbook for an example using compound interest tables.)

Finding the Future Value
(with a Compound Interest Table):
Example 13B (1 of 3)

  • Betty Dylan is Director of Nurses at Metropolis Health System.
  • Her oldest son will be entering college in five years.
  • Today Betty is trying to figure what his college fund will amount to in five more years. (Hint: compound interest means interest is not only earned on the principal, but also is earned on the previous interest earnings that have been left in the account. Interest is thus compounded.)

Finding the Future Value
(with a Compound Interest Table): Example 13B (2 of 3)

  • The college fund savings account presently has a balance of $9,000 and any interest earned over the next five years will be left in the account.
  • Betty assumes the annual interest rate will be 6 percent.
  • How much money will be in the account at the end of five more years?

Finding the Future Value
(with a Compound Interest Table):
Example 13B (3 of 3)

Step 1: Refer to the Compound Interest Table found in Appendix 13-B at the back of this chapter.

  • Reading across, or horizontally, find the 6% column.
  • Reading down, or vertically, find Year 5.
  • Trace across the Year 5 line item to the 6% column.
  • The factor is 1.338.

Step 2: Multiply $9,000 times the factor of 1.338 to find the future value of $12,042. In five years the college fund will have a balance of $12,042.

Finding the Future Value
(with a Compound Interest Table):
Practice Exercise 13-2 (1 of 3)

  • Assume the college savings fund presently has a balance of $11,000 and any interest earned over the next six years will be left in the account.
  • Assume the annual interest rate will be 7 percent.
  • How much money will be in the account at the end of six more years?

Finding the Future Value
(with a Compound Interest Table):
Practice Exercise 13-2 (2 of 3)

  • Step 1: Refer to the Compound Interest Table found in Appendix 13-B. Reading across, or horizontally, find the 7% column. Reading down, or vertically, find Year 6. Trace across the Year 6 line item to the 7% column. The factor is 1.501.
  • Step 2: Multiply $11,000 times the factor of 1.501 to find the future value of $16,511. In six years at compound interest of 7 percent, the college fund will have a balance of $16,511.

Finding the Future Value
(with a Compound Interest Table):
Practice Exercise 13-2 (3 of 3)

John Whitten is one of the physicians on staff at Metropolis Health System. His practice is six years old. He has set up an office savings account to accumulate the funds to replace equipment in his practice. Today John is trying to figure what his equipment fund will amount to in four more years.

The equipment fund savings account presently has a balance of $63,500 and any interest earned over the next four years will be left in the account. John assumes the annual interest rate will be 5 percent. How much money will be in the account at the end of four more years?

Step 1: Refer to the Compound Interest Table found in Appendix 13-B at the back of this chapter.

Reading across, or horizontally, find the 5% column.

Reading down, or vertically, find Year 4.

Trace across the Year 4 line item to the 5% column.

The factor is 1.216.

Step 2: Multiply $63,500 times the factor of 1.216 to find the future value of $77,216. In four years the equipment fund will have a balance of $77,216.

Evaluation (1 of 2)

  • The uniform use of a chosen method makes the evaluation process more manageable.

Evaluation (2 of 2)

Evaluations should be:

  • Objective
  • Readily understood by the responsible manager
  • Not too cumbersome (that is, the method should be easily calculated)