Question 1

Suppose you have a winning lottery ticket and you are given the option of accepting $3,000,000 three years from now or taking the present value of the $3,000,000 now. The sponsor of the prize uses a 6% discount rate. If you elect to receive the present value of the prize now, the amount you will receive is

Accepted Answer

To calculate the present value of the prize, we need to use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the discount rate, and n is the number of years.

In this case, FV is $3,000,000, r is 6%, and n is 3 years. Therefore,

PV = $3,000,000 / (1 + 0.06)^3
PV = $2,518,860

So the best choice is to take the present value of the prize now, which is $2,518,860, because it is worth more than the $3,000,000 you would receive in three years due to the time value of money.

Question 2

Present value is based on

Accepted Answer

Present value takes into account all three factors; the dollar amount to be received, the length of time until the amount is received, and the interest rate. Therefore, all of the given answer choices are correct.

Question 3

If you are able to earn an 8% rate of return, what amount would you need to invest to have $30,000 one year from now?

Accepted Answer

The answer of If you are able to earn an...

Question 4

The amount you must deposit now in your savings account, paying 6% interest, in order to accumulate $6,000 for a down payment 5 years from now on a new car is

Accepted Answer

To find the present value (the amount you must deposit now) to accumulate a future sum, you use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($6000), r is the interest rate per period (6% or 0.06), and n is the number of periods (5 years). Plugging in the values: PV = $6000 / (1 + 0.06)^5 ≈ $4484.

Question 5

In order to compute the present value of an annuity, it is necessary to know the
1) discount rate.
2) number of discount periods and the amount of the periodic payments or receipts.

Accepted Answer

To compute the present value of an annuity, we need to know both the discount rate and the number of discount periods, as well as the amount of the periodic payments or receipts. Both pieces of information are necessary to determine the present value of the annuity. Therefore, both option 1 and option 2 are required for the computation.

Question 6

In present value calculations, the process of determining the present value is called

Accepted Answer

The process of determining the present value involves discounting future cash flows to their present value, hence the term "discounting" is the correct choice. "Allocating" refers to the process of dividing a budget or resources, "pricing" refers to setting the value or cost of a product or service, and "negotiating" refers to reaching an agreement through discussion and compromise.

Question 7

If you are able to earn a 15% rate of return, what amount would you need to invest to have $15,000 one year from now?

Accepted Answer

The formula for calculating future value is:
Future Value = Present Value x (1 + Rate of Return)
We are looking for the present value, so we rearrange the formula to get:
Present Value = Future Value / (1 + Rate of Return)
Plugging in the numbers, we get: 
Present Value = 15,000 / (1 + 0.15)
Simplifying:
Present Value = 13,044. This is the closest answer choice to our calculation. Therefore, the correct answer is choice D.

Question 8

Suzy Douglas has been offered the opportunity of investing $73,540 now. The investment will earn 8% per year and at the end of its life will return $200,000 to Suzy. How many years must Suzy wait to receive the $200,000?

Accepted Answer

To find the number of years Suzy must wait to receive $200,000, we can use the formula for the future value of a single sum, which is $FV = PV(1 + r)^n$, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Rearranging the formula to solve for n gives us $n = \frac{\log(FV/PV)}{\log(1 + r)}$.Plugging in the values from the question:- $FV = $200,000$- $PV = $73,540$- $r = 8\% = 0.08$We get $n = \frac{\log(200000/73540)}{\log(1.08)}$.Calculating this gives us approximately 13 years.

Question 9

The amount you must deposit now in your savings account, paying 5% interest, in order to accumulate $10,000 for your first tuition payment when you start college in 3 years is

Accepted Answer

The formula for calculating the present value of a future amount is:

Present Value = Future Value / (1 + r)n

Where r is the annual interest rate and n is the number of years.

In this case, we want to find the present value required to accumulate $10,000 in 3 years at an interest rate of 5%. Plugging in the values, we get:

Present Value = 10,000 / (1 + 0.05)3 
            = 10,000 / 1.1576 
            = $8,637.99

Rounding off, we get $8,638 as the answer, which is choice C.

Question 10

Dexter Company is considering purchasing equipment. The equipment will produce the following cash flows:
Year 1 $120,000
Year 2 $200,000
Dexter requires a minimum rate of return of 10%. What is the maximum price Dexter should pay for this equipment?

Accepted Answer

The maximum price Dexter should pay is the present value of the cash flows discounted at the required rate of return (10%). The present value of $120,000 in Year 1 is $120,000 / (1+0.10) = $109,091, and the present value of $200,000 in Year 2 is $200,000 / (1+0.10)^2 = $165,289. The total present value is $109,091 + $165,289 = $274,380, which is closest to option A.

Question 11

If the single amount of $3,000 is to be received in 3 years and discounted at 6%, its present value is

Accepted Answer

Using the present value formula PV=FV/(1+r)^n where FV=$3,000, r=0.06, and n=3, we get PV=$2,518.66. Rounding to the nearest dollar, the answer is A) $2,519.

Question 12

Hazel Company has just purchased equipment that requires annual payments of $40,000 to be paid at the end of each of the next 4 years. The appropriate discount rate is 15%. What is the present value of the payments?

Accepted Answer

Using a financial calculator or formula, we can find the present value of the payments:
PV = 40,000/(1+0.15)^1 + 40,000/(1+0.15)^2 + 40,000/(1+0.15)^3 + 40,000/(1+0.15)^4
PV = $114,199. Therefore, the best choice is A.

Question 13

A $10,000, 6%, 5-year note payable that pays interest quarterly would be discounted back to its present value by using tables that would indicate which one of the following period-interest combinations?

Accepted Answer

We need to find the present value of a $10000 6% 5-year note payable that pays interest quarterly. Therefore, we need to use tables that show the periodic interest for quarterly payments. That is, we need the interest rate per quarter. The formula to calculate this interest rate is:

(1 + periodic interest rate)^number of periods = 1 + annual interest rate
(1 + i)^4 = 1 + 0.06
(1 + i) = (1 + 0.06)^(1/4)
(1 + i) = 1.01477
i = 0.01477 or 1.477%

Therefore, we need to use tables that indicate 20 interest periods (5 years * 4 quarters per year) at a periodic interest rate of 1.5% (half of the quarterly interest rate we just calculated). Choice C is the only option that meets these criteria.

Question 14

The present value of $10,000 to be received in 5 years will be smaller if the discount rate is

Accepted Answer

When the discount rate is increased, the present value of future cash flows decreases. Therefore, if the discount rate is increased, the present value of $10,000 to be received in 5 years will be smaller.

Question 15

Peter Johnson invests $35,516.80 now for a series of $5,000 annual returns beginning one year from now. Peter will earn 10% on the initial investment. How many annual payments will Peter receive?

Accepted Answer

To solve this problem, we need to use the formula for the present value of an annuity:

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

Where:
PV = present value
PMT = payment amount (in this case, $5,000)
r = interest rate per period (10% per year)
n = number of periods

We know that the present value (PV) is $35,516.80, the payment amount (PMT) is $5,000, and the interest rate (r) is 10%. We need to solve for the number of periods (n).

35,516.80 = 5,000 x [1 - (1 + 0.10)^(-n)] / 0.10

Simplifying this equation, we get:

7.10336 = [1 - (1.10)^(-n)]

1.10^(-n) = 0.899151

Taking the logarithm of both sides, we get:

-n log(1.10) = log(0.899151)

n = log(0.899151) / log(1.10)

n ≈ 13

So Peter will receive 13 annual payments of $5,000 each, beginning one year from now. Therefore, the best choice is C.

Question 16

If the single amount of $2,000 is to be received in 2 years and discounted at 11%, its present value is

Accepted Answer

Using the formula for present value of a single amount:
PV = FV / (1 + r)^n
Where PV is present value, FV is future value, r is the discount rate, and n is the number of years.
Plugging in the given values, we get:
PV = 2,000 / (1 + 0.11)^2 = $1,623.

Question 17

Perdue Company has purchased equipment that requires annual payments of $30,000 to be paid at the end of each of the next 6 years. The appropriate discount rate is 12%. What amount will be used to record the equipment?

Accepted Answer

To record the equipment, we need to find the present value of the annual payments using the appropriate discount rate. We can use the formula:

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

Where:
Payment = $30,000 (annual payment)
r = 12% (discount rate)
n = 6 (number of years)

Plugging in the numbers, we get:

Present value = $30,000 x [1 - (1 / (1 + 0.12)^6)] / 0.12
Present value = $123,342

Therefore, the amount to record the equipment is $123,342, which is closest to choice B.

Question 18

If Sloane Joyner invests $10,514.81 now and she will receive $30,000 at the end of 11 years, what annual rate of interest will she be earning on her investment?

Accepted Answer

The answer of If Sloane Joyner invests $10,514.81 now and...

Question 19

Which of the following accounting problems does not involve a present value calculation?

Accepted Answer

Option A, C, and D require present value calculations to determine the amount to report in the financial statements. However, option B involves calculating depreciation expense using a specific method (declining-balance method) and does not require any present value calculations.

Question 20

Which of the following discount rates will produce the smallest present value?

Accepted Answer

The higher the discount rate, the lower the present value of future cash flows. Therefore, a higher discount rate would produce a smaller present value. Of the given options, 10% is the highest, thus it would produce the smallest present value.

Quiz 26: Time Value of Money