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*Use the following “present value of 1” factors for solving questions that require present value computations:*

1.

Which of the following models for evaluating capital expenditures considers the time value of money by discounting the future cash flows?

Accounting Rate Of Return

The accounting return uses accounting revenues and expenses (not cash flows) with NO consideration of the time value of money...no discounting.

Internal Rate Of Return

The internal rate of return model uses cash flows and then discounts them to the present. The rate that discounts the cash flows to a net present value of zero is the internal rate of return.

Payback

The payback model uses the cash flows from the project to determine the time needed to recoup the cash investment. However, the cash flows are NOT discounted.

2.

Which of the following models for evaluating capital expenditures does NOT consider the time value of money (does not discount the future cash flows)?

Accounting Rate Of Return

The accounting return uses accounting revenues and expenses without discounting or considering the time value of money.

Internal Rate Of Return

The internal rate of return model uses cash flows and then *discounts them to the present*. The rate that discounts the cash flows to a net present value of zero is the internal rate of return.

Net Present Value

The net present value is the cash flows discounted back to the present and then netted against the cash paid in the present. If this net present value is equal to zero, the project is earning exactly the rate used to discount the cash flows. If the net present value is a positive amount (the present value of all cash received is *greater* than the present value of all cash paid) the project is earning *more than the rate* used to discount the cash. If the net present value is a negative amount (present value of all cash received is *less* than the present value of all cash paid) the project is earning *less than the rate* used to discount the cash.

3.

Which of the following models does NOT use cash flows?

Accounting Rate Of Return

The accounting return does NOT use cash flows. It uses accounting revenues and expenses without discounting (without consideration of the time value of money).

Internal Rate Of Return

Payback

4.

A company used the net present value method for evaluating a project. The project requires an immediate cash outlay of $450,000. The company discounted the cash flows by 16% and determined that the net present value of the project was a negative $300. From this information it is likely that the project __________.

Had An Internal Rate Of Return That Was Slightly GREATER Than 16%

Since the net present value of the project was a negative amount, the project is expected to earn *less than 16%*. Since the **negative amount is only $300** versus the immediate cash investment of $450,000, the project is earning VERY close to 16%, *but it is slightly less than 16%.*

Had An Internal Rate Of Return That Was Slightly LESS Than 16%

Had A Negative Internal Rate Of Return

The project is expected to earn almost 16%. The small negative net present value of $300 is VERY small in relation to the cash outlay of $450,000. (It is possible that the project is earning a 15.95% return.) So while the project just missed the 16% cutoff and therefore has a negative net present value, it still had a positive internal rate of return of *almost 16%*.

5.

A company is planning to invest $100,000 in order to receive $50,000 one year later, $40,000 two years later, and $60,000 three years later. Using the present value of 1 factors for 16% (see above), the net present value of this investment is __________.

($11,000)

See the calculations for $11,000.

$11,000

The present values for the FUTURE cash INFLOWS are: ($50,000 X 0.86) + ($40,000 X 0.74) + ($60,000 X 0.64) = $111,000. The present value of the cash outflows is ($100,000 X 1.00) = $100,000. The present values IN of $111,000 vs. the present value OUT of $100,000 = the **net present value of $11,000**...a positive net IN amount.

$100,000

See the calculations for $11,000.

$111,000

See the calculations for $11,000.

6.

A $100,000 investment will be made on January 1. The cash generated from this investment is expected to be received uniformly during each year. The yearly amounts are: $50,000 in the first year; $40,000 in the second year; $60,000 in the third year. What is the expected payback period?

2.0 Years

See the calculations for 2.17 years.

2.1 Years

See the calculations for 2.17 years.

2.17 Years

Payback is the number of years it takes to recoup the initial cash outlay for the project. The time value of money is not involved. (In other words there is no discounting of the cash flows.) The cash received in years 1 + 2 = $50,000 + $40,000 = $90,000 after two years. Assuming the cash flow in year 3 is uniform throughout year 3, the remaining $10,000 needed to reach the investment amount of $100,000 occurs about 1/6 of the way into year 3 ($10,000 needed divided by the total cash in year 3 of $60,000). This makes the payback 2.17 years.

3 Years

See the calculations for 2.17 years.

7.

A project's cash flows are discounted by 16% and result is a positive net present value. The positive net present value indicates that the project __________.

Has An Internal Rate Of Return That Is GREATER Than 16%

A positive net present value indicates that the present value of the cash inflows exceeds the present value of the cash outflows. The **positive net present value indicates that the project will return more than the specified rate** used to discount the cash flows.

Has An Internal Rate Of Return That Is LESS Than 16%

8.

Depreciation Expense is a negative cash flow that needs to be discounted.

True

False

9.

While depreciation does not result in a payment of cash, tax depreciation does reduce the cash payments for income taxes.

True

Depreciation Expense shown on the tax return does reduce taxable income, which in turn does reduce the amount of cash paid for income taxes.

False

10.

Depreciation Expense can be ignored when computing the accounting rate of return.

True

The accounting rate of return uses accounting revenues and accounting expenses. **Depreciation Expense** is indeed an accounting expense and *cannot* be ignored. (However, **Depreciation Expense** is considered a noncash expense.)

False

11.

If the net present value of a project is $0, the project should be rejected.

True

If you reject this project, you are rejecting earning the rate that was used to discount the cash flows.

False

If a project has a net present value of $0, the project is earning exactly the rate that was used to discount the cash flows. If that rate is the desired or targeted rate, the project is providing the desired or targeted rate...nothing more, nothing less.

12.

A project whose future cash flows are discounted by 10% will have a larger net present value than the same cash flows discounted by 8%?

True

If you discount by a larger rate, the present value will be *smaller*. In other words, a higher discount rate means you must earn a higher return and therefore will invest less for the future cash flows. (Also see the present value factors at the beginning of this quiz. The higher the discount rate, the smaller are the present value factors.)

False

13.

What amount would you invest today in return for a one-time $10,000 receipt one year from today, if you want to earn 8%? (Use the factors above.)

$9,200

The correct answer is $9,300 ($10,000 x 0.93)

$9,300

$10,000 x 0.93 = $9,300.

$9,920

The correct answer is $9,300 ($10,000 x 0.93)

14.

How much would you invest today in return for $20,000 to be received two years from today, if you want to earn 10%? (Use the factors above.)

$16,000

The correct answer is $16,600 ($20,000 x 0.83)

$16,600

$20,000 x 0.83 = $16,600.

$18,260

The correct answer is $16,600 ($20,000 x 0.83)

15.

$4,260

See the calculation for $4,620.

$4,620

($2,000 x 0.89) + ($4,000 x 0.71) = $4,620.

$4,980

See the calculation for $4,620.

16.

If you invest $68,000 today and get repaid $100,000 at the end of five years, what is the internal rate of return on your investment? (Use the factors above.)

6%

See the calculation for 8%.

8%

$68,000 is the present value of $100,000 received at the end of five years. This means the present value of 1 factor for an amount received at the end of five years is 0.68 ($68,000 divided by $100,000). The factor of 0.68 at the end of five years **appears in the column headed 8%**. (See the present value of 1 table at the beginning of this quiz.)

10%

See the calculation for 8%.

12%

See the calculation for 8%.

16%

See the calculation for 8%.

17.

If you invest $15,900 today and receive $10,000 at the end of one year plus $10,000 at the end of four years, what is the internal rate of return on your investment? (Use the factors above.)

6%

See the calculation for 10%.

8%

See the calculation for 10%.

10%

$15,900 is the present value of ($10,000 x 0.91) + ($10,000 x 0.68).

12%

See the calculation for 10%.

16%

See the calculation for 10%.

18.

If you invest $15,300 today and receive $10,000 at the end of one year and $10,000 at the end of four years, what is the internal rate of return on your investment? (Use the factors above.)

16%

8%

10%

12%

$15,300 is the present value of ($10,000 x 0.89) + ($10,000 x 0.64).

6%

19.

You invest $10,000 immediately plus an additional $100,000 at the end of one year. If the time value of money is 10%, what is the present value of your investment? (Use the factors above.)

$100,000

See the calculation for $101,000.

$101,000

($10,000 x 1.00) + ($100,000 x 0.91) = $101,000.

$110,000

See the calculation for $101,000.

20.

The state lottery offers a $500,000 prize consisting of $100,000 immediately and then four annual payments of $100,000 each. If the winner prefers to receive an immediate lump sum, the state discounts the future payments by 6%. What will be the immediate lump sum amount before any taxes? (Use the factors above.)

$346,000

See the calculation for $446,000.

$400,000

See the calculation for $446,000.

$446,000

The immediate lump sum is $446,000 calculated as follows: ($100,000 x 1.00) + ($100,000 x 0.94) + ($100,000 x 0.89) + ($100,000 x 0.84) + ($100,000 x 0.79)

$470,000

See the calculation for $446,000.

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