Question 1

(Ignore income taxes in this problem.) Knipper Corporation has entered into a 9 year lease for a piece of equipment. The annual payment under the lease will be $2,300, with payments being made at the beginning of each year. If the discount rate is 11%, the present value of the lease payments is closest to:
A) $18,649
B) $14,136
C) $20,700
D) $8,092

Accepted Answer

The present value of an annuity due can be calculated using the formula: PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r). Here, Pmt = $2,300, r = 0.11, n = 9. Calculating this gives a present value closest to $14,136.

Question 2

Suppose an investment has cash inflows of R dollars at the end of each year for two years. The present value of these cash inflows using a 12% discount rate will be:
A) greater than under a 10% discount rate.
B) less than under a 10% discount rate.
C) equal to that under a 10% discount rate.
D) sometimes greater than under a 10% discount rate and sometimes less; it depends on R.

Accepted Answer

As the discount rate increases, the present value of future cash inflows decreases. Therefore, if the discount rate increases from 10% to 12%, the present value of the cash inflows will decrease, resulting in a lesser value.

Question 3

The present value of a given sum to be received in five years is exactly twice as large as the present value of an equal sum to be received in ten years.

Accepted Answer

The present value of a sum decreases as the time to receive it increases, but it does not decrease linearly. The relationship depends on the discount rate, and it is unlikely for the present value of a sum in five years to be exactly twice that of the same sum in ten years without specific conditions on the discount rate.

Question 4

An increase in the discount rate:
A) will increase the present value of future cash flows.
B) will have no effect on net present value.
C) will reduce the present value of future cash flows.
D) is one method of compensating for reduced risk.

Accepted Answer

An increase in the discount rate will increase the cost of capital, which in turn will reduce the present value of future cash flows. This is because future cash flows are discounted at a higher rate, making them worth less in present value terms. Therefore, choice C is the correct answer.

Question 5

(Ignore income taxes in this problem.) White Company's required rate of return on capital budgeting projects is 12%. The company is considering an investment opportunity which would yield a cash flow of $10,000 in five years. What is the most that the company should be willing to invest in this project?
A) $36,050
B) $2,774
C) $17,637
D) $5,670

Accepted Answer

The present value (PV) of the future cash flow can be calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value ($10,000), r is the rate of return (0.12), and n is the number of years (5). This gives PV = $10,000 / (1.12)^5 = $5,670.

Question 6

(Ignore income taxes in this problem.) You have deposited $8,369 in a special account that has a guaranteed interest rate of 13% per year. If you are willing to completely exhaust the account, what is the maximum amount that you could withdraw at the end of each of the next 8 years? Select the amount below that is closest to your answer.
A) $1,046
B) $1,744
C) $2,134
D) $1,182

Accepted Answer

The answer of (Ignore income taxes in this problem.) You...

Question 7

(Ignore income taxes in this problem.) If you wanted to withdraw $12,000 from a bank account at the end of each of the next 20 years, approximately how much would you have to invest in the account today assuming a 6% interest rate?
A) $20,924
B) $38,462
C) $74,880
D) $137,604

Accepted Answer

The answer of (Ignore income taxes in this problem.) If...

Question 8

(Ignore income taxes in this problem.) You have deposited $16,727 in a special account that has a guaranteed interest rate. If you withdraw $4,300 at the end of each year for 5 years, you will completely exhaust the balance in the account. The guaranteed interest rate is closest to:
A) 6%
B) 29%
C) 9%
D) 26%

Accepted Answer

After withdrawing $4,300 each year for 5 years, the total amount withdrawn will be $21,500. Therefore, the interest earned over the 5-year period is $21,500 - $16,727 = $4,773. 
Using the formula for compound interest: 
A = P(1 + r/n)^(nt), where A = final amount, P = principal, r = annual interest rate, n = number of times interest is compounded per year, t = time in years 
Plugging in the values we know: 
$21,500 = $16,727(1 + r/n)^(5)
Simplifying: 
1.282 = (1 + r/n)^(5)
Taking the fifth root of both sides: 
1.032 =~ 1 + r/n 
0.032 =~ r/n 
The interest rate would be n*r = 12*0.032 = 0.384 or approximately 0.38. Therefore, the closest interest rate from the choices given is 9%.

Question 9

(Ignore income taxes in this problem.) Noe Corporation has entered into a 8 year lease for a building it will use as a warehouse. The annual payment under the lease will be $2,520. The first payment will be at the end of the current year and all subsequent payments will be made at year-ends. What is the present value of the lease payments if the discount rate is 12%?
A) $8,142
B) $12,519
C) $20,160
D) $18,000

Accepted Answer

The present value of an annuity formula is used to calculate the present value of the lease payments: PV = Pmt × [(1 - (1 + r)^-n) / r]. Plugging in the values: PV = $2,520 × [(1 - (1 + 0.12)^-8) / 0.12] = $12,519.

Question 10

(Ignore income taxes in this problem.) Henry wants to send his son to computer school which will start one year from today. Payments of $2,000 are due at the end of each of the next two years. What lump-sum will Henry have to invest now at 12% per year in order to have $2,000 at the end of each of the next two years?
A) $4,240
B) $3,380
C) $1,594
D) $2,508

Accepted Answer

To find the lump-sum that Henry needs to invest now, we need to find the present value of the future payments of $2,000, discounted at a rate of 12% per year.

We can use the formula for present value of an annuity:

PV = Payment x [1 - (1 + r)^(-n)] / r

where PV is the present value, Payment is the payment each period, r is the interest rate per period, and n is the number of periods.

In this case, Payment is $2,000, r is 12% per year, and n is 2 (two years).

So,

PV = $2,000 x [1 - (1 + 0.12)^(-2)] / 0.12
   = $3,380.20

Therefore, the lump-sum that Henry needs to invest now is $3,380.20, which is closest to option B, $3,380.

Question 11

The present value of a cash flow decreases as it moves further into the future.

Accepted Answer

This is because of the time value of money, which states that the value of money decreases over time due to factors such as inflation and the opportunity cost of not having the money available for other uses. Therefore, a cash flow that is received in the future is worth less in present-day dollars.

Question 12

The higher the discount rate, the higher the present value of a given future cash flow.

Accepted Answer

The higher the discount rate, the lower the present value of a given future cash flow. This is because the higher the discount rate, the more value is placed on receiving cash sooner rather than later.

Question 13

The accountant of Ronier, Inc., has prepared an analysis of a proposed capital project using discounted cash flow techniques. One manager has questioned the accuracy of the results because the discount factors employed in the analysis have assumed the cash inflows occurred at the end of the year when the cash inflows actually occurred uniformly throughout each year. The net present value calculated by the accountant:
A) will be in error and therefore not usable.
B) will be slightly overstated but usable.
C) will be slightly understated but usable.
D) will produce an error the direction of which is undeterminable.

Accepted Answer

Assuming cash flows occur at the end of each year instead of uniformly throughout each year is a common simplification used in discounted cash flow analysis. This simplification slightly understates the net present value. Therefore, the net present value calculated by the accountant is still usable, but it may be slightly understated.

Question 14

(Ignore income taxes in this problem.) How much would you have to invest today in the bank at an interest rate of 13% to have an annuity of $3,900 per year for 5 years, with nothing left in the bank at the end of the 5 years? Select the amount below that is closest to your answer.
A) $19,500
B) $17,257
C) $2,118
D) $13,716

Accepted Answer

To find the present value of an annuity, use the formula: PV = PMT × [(1 - (1 + r)^-n) / r]. Here, PMT = $3,900, r = 0.13, and n = 5. Calculating gives a present value closest to $13,716.

Quiz 31: The Concept of Present Value

Suppose an investment has cash inflows of R dollars at the end of each year for two years. The present value of these cash inflows using a 12% discount rate will be:

The present value of a given sum to be received in five years is exactly twice as large as the present value of an equal sum to be received in ten years.

An increase in the discount rate:

(Ignore income taxes in this problem.) If you wanted to withdraw $12,000 from a bank account at the end of each of the next 20 years, approximately how much would you have to invest in the account today assuming a 6% interest rate?

(Ignore income taxes in this problem.) You have deposited $16,727 in a special account that has a guaranteed interest rate. If you withdraw $4,300 at the end of each year for 5 years, you will completely exhaust the balance in the account. The guaranteed interest rate is closest to:

The present value of a cash flow decreases as it moves further into the future.

The higher the discount rate, the higher the present value of a given future cash flow.

(Ignore income taxes in this problem.) How much would you have to invest today in the bank at an interest rate of 13% to have an annuity of $3,900 per year for 5 years, with nothing left in the bank at the end of the 5 years? Select the amount below that is closest to your answer.