Question 1

How much must be deposited on January 1, 2010 in a savings account paying 6% annually in order to make annual withdrawals of $20,000 at the end of the years 2010 and 2011? The present value of one at 6% for one period is .9434.

Accepted Answer

Step 1: Use the present value of an annuity formula to find the amount that needs to be deposited today: 
PV = (Annuity amount) x (PV factor)
PV = $20,000 x (0.9434 + 0.889)
PV = $37,740
Step 2: The amount that needs to be deposited today is $37,740. Therefore, the best choice is B, $37,740.

Question 2

Jenks Company financed the purchase of a machine by making payments of $18,000 at the end of each of five years.The appropriate rate of interest was 8%.The future value of one for five periods at 8% is 1.46933.The future value of an ordinary annuity for five periods at 8% is 5.8666.The present value of an ordinary annuity for five periods at 8% is 3.99271.What was the cost of the machine to Jenks?

Accepted Answer

The answer of Jenks Company financed the purchase of a...

Question 3

Pearson Corporation makes an investment today (January 1, 2012).They will receive $10,000 every December 31st for the next six years (2012 - 2017).If Pearson wants to earn 12% on the investment, what is the most they should invest on January 1, 2012?

Accepted Answer

The answer of Pearson Corporation makes an investment today (January...

Question 4

Stemway requires a new manufacturing facility.Management found three locations; all of which would provide needed capacity, the only difference is the price.Location A may be purchased for $500,000.Location B may be acquired with a down payment of $100,000 and annual payments at the end of each of the next twenty years of $50,000.Location C requires $40,000 payments at the beginning of each of the next twenty-five years.Assuming Stemway's borrowing costs are 8% per annum, which option is the least costly to the company?

Accepted Answer

The cost of location A is $500,000 upfront.
The cost of location B is a down payment of $100,000 and annual payments of $50,000 for 20 years. To calculate the present value of the annuity, we can use the formula: PMT*[1-(1+r)^(-n)]/r. In this case, PMT is $50,000, r is 8%, and n is 20. Plugging in these values, we get a present value of $634,894. Adding the down payment of $100,000, the total cost of location B is $734,894.
The cost of location C is $40,000 payments at the beginning of each of the next 25 years. To calculate the present value of this annuity, we can use the same formula as above, but with n equal to 25. Plugging in the values, we get a present value of $529,387.
Therefore, the least costly option is location B, with a total cost of $734,894.

Question 5

If an annuity due and an ordinary annuity have the same number of equal payments and the same interest rates, then

Accepted Answer

CAn annuity due involves payments at the beginning of each period, while an ordinary annuity involves payments at the end. For the present value, payments made sooner (as in an annuity due) are worth more today due to the time value of money, making the present value of an annuity due greater than that of an ordinary annuity. For the future value, both types of annuities will have different future values due to the timing of payments, but the statement C is incorrect as it suggests equality; the correct relationship is that the future value of an annuity due is greater because payments have more time to earn interest. However, since this specific comparison was not an option, the correct understanding is that their future values are not equal, with the annuity due generally having a higher future value.

Question 6

Lane Co.has a machine that cost $200,000.It is to be leased for 20 years with rent received at the beginning of each year.Lane wants a return of 10%.Calculate the amount of the annual rent.

Accepted Answer

The answer of Lane Co.has a machine that cost $200,000.It...

Question 7

Paula purchased a house for $300,000.After providing a 20% down payment, she borrowed the balance from the local savings and loan under a 30-year 6% mortgage loan requiring equal monthly installments at the end of each month.Which time value concept would be used to determine the monthly payment?

Accepted Answer

The monthly payment is determined by calculating the present value of the loan amount, which is the present value of an ordinary annuity.

Question 8

How much must be invested now to receive $10,000 for 15 years if the first $10,000 is received today and the rate is 9%?

Accepted Answer

The answer of How much must be invested now to...

Question 9

John won a lottery that will pay him $100,000 at the end of each of the next twenty years.Assuming an appropriate interest rate is 8% compounded annually, what is the present value of this amount?

Accepted Answer

This is a case of an annuity with a fixed amount to be paid each year. We can use the formula for present value of an annuity to calculate the present value of the payments.

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

Where PV is the present value, Payment is the annual payment, r is the interest rate, and n is the number of years.

Plugging in the given values, we get:

PV = $100,000 x ((1 - (1 + 0.08)^-20) / 0.08)
PV = $981,815

Therefore, the present value of the 20-year annuity is $981,815.

Question 10

What amount should be recorded as the cost of a machine purchased December 31, 2010, which is to be financed by making 8 annual payments of $6,000 each beginning December 31, 2011? The applicable interest rate is 8%.

Accepted Answer

The answer of What amount should be recorded as the...

Question 11

An accountant wishes to find the present value of an annuity of $1 payable at the beginning of each period at 10% for eight periods.The accountant has only one present value table which shows the present value of an annuity of $1 payable at the end of each period.To compute the present value, the accountant would use the present value factor in the 10% column for

Accepted Answer

The correct approach is to use the present value factor for eight periods and then multiply by (1 + .10) because the payments are made at the beginning of each period, effectively moving the entire annuity one period forward in time, which is equivalent to multiplying by (1 + the interest rate).

Question 12

James leases a ski chalet to his best friend, Janet.The lease term is five years with $22,000 annual payments due at the beginning of each year.What is the present value of the payments discounted at 8% per annum?

Accepted Answer

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

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

where r is the discount rate, n is the number of periods, and Payment is the annual payment.

Plugging in the given values, we get:

Present value = $22,000 x [(1 - (1 + 0.08)^-5) / 0.08] x (1 + 0.08)
Present value = $87,840

Therefore, the present value of the lease payments is $87,840, and the best choice is B.

Question 13

A machine is purchased by making payments of $5,000 at the beginning of each of the next five years.The interest rate was 10%.The future value of an ordinary annuity of 1 for five periods is 6.10510.The present value of an ordinary annuity of 1 for five periods is 3.79079.What was the cost of the machine?

Accepted Answer

We need to use the formula for the present value of an annuity due.

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

where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of periods.

Using the given values, we have:

PV = $5,000 x ((1 - (1 + 0.1)^-5)/0.1) x (1 + 0.1)
PV = $5,000 x 3.79079 x 1.1
PV = $20,849

Therefore, the cost of the machine was $20,849. So, the answer is (C).

Question 14

Garretson Corporation will receive $10,000 today (January 1, 2010), and also on each January 1st for the next five years (2013 - 2017).What is the present value of the six $10,000 receipts, assuming a 12% interest rate?

Accepted Answer

To calculate the present value of multiple future cash flows, we use the formula:

PV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + ... + CFn / (1+r)^n

where PV is the present value, CF is the cash flow in a given period (year), r is the interest rate, and n is the total number of periods.

Using this formula, we can calculate the present value of the six $10,000 receipts as:

PV = 10,000/(1+0.12)^1 + 10,000/(1+0.12)^2 + 10,000/(1+0.12)^3 + 10,000/(1+0.12)^4 + 10,000/(1+0.12)^5 + 10,000/(1+0.12)^6

= $81,152.

Therefore, the answer is option C, $81,152.

Question 15

Hiller Corporation makes an investment today (January 1, 2012).They will receive $20,000 every December 31st for the next six years (2012 - 2017).If Hiller wants to earn 12% on the investment, what is the most they should invest on January 1, 2012?

Accepted Answer

The present value of an annuity formula is used to calculate the maximum investment: PV = PMT × [(1 - (1 + r)^-n) / r]. Here, PMT = $20,000, r = 0.12, n = 6. Calculating gives PV ≈ $82,228.

Question 16

Sue Gray wants to invest a certain sum of money at the end of each year for five years.The investment will earn 6% compounded annually.At the end of five years, she will need a total of $40,000 accumulated.How should she compute her required annual invest-ment?

Accepted Answer

To determine the required annual investment, we need to find the present value of a 5-year, 6% ordinary annuity of 1 that will accumulate to $40,000 in five years. Therefore, we should divide $40,000 by the present value of a 5-year, 6% ordinary annuity of 1. Choice D is the correct formula for this calculation.

Question 17

Use the following 8% interest factors for questions . 
-Al Darby wants to withdraw $20,000 (including principal) from an investment fund at the end of each year for five years.How should he compute his required initial investment at the beginning of the first year if the fund earns 10% compounded annually?

Accepted Answer

To find the required initial investment, we need to calculate the present value of an annuity that pays $20,000 annually for five years at a 10% annual interest rate. This can be done using the formula for the present value of an ordinary annuity:
PV = PMT x [1 - (1+r)^-n] / r
where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.
Substituting the values, we get:
PV = $20,000 x [1 - (1+0.10)^-5] / 0.10
PV = $20,000 x [1 - 0.6209] / 0.10
PV = $20,000 x 3.791
PV = $75,820.61
Therefore, the required initial investment at the beginning of the first year is $75,820.61, which is option C.

Question 18

What amount should an individual have in a 10% bank account today before withdrawal if $5,000 is needed each year for four years with the first withdrawal to be made today and each subsequent withdrawal at one-year intervals? (The balance in the bank account should be zero after the fourth withdrawal.)

Accepted Answer

The correct answer involves calculating the present value of each withdrawal, including the one made today (which does not need to be discounted). Choices B, C, and D either incorrectly calculate the present value or apply the formula incorrectly. The correct approach is to discount each future withdrawal by the appropriate discount factor for a 10% interest rate (1/(1+0.10)^n, where n is the number of years until the withdrawal), and then sum these present values with the amount withdrawn today, which does not need to be discounted.

Question 19

Jonas won a lottery that will pay him $100,000 at the end of each of the next twenty years.Zebra Finance has offered to purchase the payment stream for $1,359,000.What interest rate (to the nearest percent) was used to determine the amount of the payment?

Accepted Answer

The answer of Jonas won a lottery that will pay...

Question 20

Find the present value of an investment in plant and equipment if it is expected to provide annual earnings of $21,000 for 15 years and to have a resale value of $40,000 at the end of that period.Assume a 10% rate and earnings at year end.The present value of 1 at 10% for 15 periods is .23939.The present value of an ordinary annuity at 10% for 15 periods is 7.60608.The future value of 1 at 10% for 15 periods is 4.17725.

Accepted Answer

Using the present value of an ordinary annuity formula:

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

where PV is the present value, A is the annual earnings, r is the rate, n is the number of periods, and FV is the resale value.

Plugging in the given values:

PV = 21,000 x [(1 - (1 + 0.1)^-15) / 0.1] + 40,000 / (1 + 0.1)^15 
PV = 21,000 x 7.60608 + 40,000 / 4.17725 
PV = 169,303

Therefore, the present value of the investment in plant and equipment is $169,303. Choice B is the correct answer.

Quiz 6: Accounting and the Time Value of Money