Question 1

Raymond's Leasing Company signed an agreement to lease an asset that has a fair value of $800,000 on December 31, 2014. The lease will be paid in seven equal annual payments of $138,730, beginning on December 31, 2014. The interest rate included in the lease agreement is most nearly equal to

Accepted Answer

The interest rate can be found by using a financial calculator or spreadsheet to solve for the interest rate (I/Y) that equates the present value of the lease payments to the fair value of the asset. Inputting the given values (PV = $800,000, PMT = -$138,730, N = 7, and the first payment occurring immediately, which is a type of annuity due), the interest rate that aligns with these values is closest to 7%.

Question 2

Parker Posie wants to determine how much she must deposit today at 14% interest to provide four withdrawals of $26,000 at the end of each year, beginning five years from now. This is an example of the present value of

Accepted Answer

This scenario describes a deferred ordinary annuity because the withdrawals ($26,000) occur at the end of each year, starting five years from now. This means there is a deferral period before the annuity payments begin, which is characteristic of a deferred ordinary annuity. An ordinary annuity has payments at the end of each period, but without the initial deferral period.

Question 3

Stacey has $5,000,000 on deposit in a fund that earns 9% interest compounded annually. How much can Stacey withdraw annually from the fund in ten equal annual withdrawals to completely deplete the fund after the tenth draw, assuming the first withdrawal occurs today?

Accepted Answer

The correct answer can be found using the formula for the present value of an annuity due, since the first withdrawal occurs today. The formula is $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1+r)$, where PV is the present value ($5,000,000), PMT is the annual payment, r is the annual interest rate (9% or 0.09), and n is the number of periods (10 years). Solving for PMT gives us the annual withdrawal amount, which matches option A, $714,771, when calculated correctly.

Question 4

Stacey has $5,000,000 on deposit in a fund that earns 9% interest compounded annually. How much can Stacey withdraw annually from the fund in ten equal annual withdrawals to completely deplete the fund after the tenth draw, assuming the first withdrawal occurs one year from today?

Accepted Answer

The answer of Stacey has $5,000,000 on deposit in a...

Question 5

When the present value of an annuity is calculated as of two or more periods before the payment of the first cash flow, the annuity is

Accepted Answer

A deferred ordinary annuity is characterized by a delay in the start of payments. When the present value of an annuity is calculated as of two or more periods before the first cash flow, it means there's a gap between the valuation date and the start of payments, fitting the definition of a deferred ordinary annuity.

Question 6

Suppose you borrow money from your parents for college tuition on January 1, 2013. Your parents require four annual payments of $1,000 each, with the first payment due on January 1, 2017. They are charging you 6% annual interest. What is the cost of the college tuition?

Accepted Answer

The cost of the college tuition is the present value of the four $1,000 payments, discounted at 6% per year over the period from 2017 to 2013. Calculating the present value gives $2,909.37.

Question 7

For which of the following transactions would the present value of an annuity due concept be most appropriate for calculating the present value of the asset acquired or liability assumed?

Accepted Answer

The present value of an annuity due concept is most appropriate for calculating the present value of transactions where payments are made at the beginning of each period. Choice A, a rental agreement with the initial payment due immediately, fits this description, as the payments start at the beginning of the period.

Question 8

Marcus Jones wants to invest $10,000 on January 1, 2014, so that he may withdraw 10 annual payments of equal amounts beginning January 1, 2029. If the fund earns 10% annual interest over its life, what will be the amount of each of the withdrawals?

Accepted Answer

To solve this, we use the formula for the present value of an annuity. First, we find the present value of the annuity on January 1, 2029, which is when the withdrawals start. The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment amount, r is the interest rate per period, and n is the number of periods. However, since we're given the present value ($10,000) and need to find PMT, we rearrange the formula to solve for PMT. The $10,000 needs to be grown for the 15 years (2014 to 2029) at 10% to find the future value on January 1, 2029, which then serves as the present value for the annuity calculation. The future value is calculated as $10,000 * (1 + 0.10)^15 = $41,772.18. Then, using the annuity formula for PMT with n = 10 and r = 10%, we find PMT = $41,772.18 * [0.10 / (1 - (1 + 0.10)^-10)] = $16,181.

Question 9

Charlie's Construction Co. acquired a new $800,000 backhoe on April 1, 2014. Charlie's will make six annual payments based upon 8% interest compounded annually, starting on March 31, 2015. How much will each payment be?

Accepted Answer

The payments can be calculated using the formula for the present value of an annuity because Charlie's Construction Co. is essentially taking out a loan that it will pay back in equal annual installments. The formula is P = PMT * [(1 - (1 + r)^-n) / r], where P is the present value of the loan ($800,000), PMT is the annual payment, r is the annual interest rate (0.08), and n is the number of payments (6). Rearranging the formula to solve for PMT gives PMT = P / [(1 - (1 + r)^-n) / r]. Plugging in the numbers gives PMT = $800,000 / [(1 - (1 + 0.08)^-6) / 0.08], which calculates to approximately $173,052.

Question 10

On July 7, 2014, Lawrence Company sold some machinery to Johnson Construction Company. The sales contract requires Johnson to pay five equal annual payments of $75,000 each, beginning on July 7, 2014. What present value concept is most appropriate for this situation?

Accepted Answer

Since the payments start immediately on the date of the sale (July 7, 2014), this situation represents an annuity due, where payments are made at the beginning of each period.

Question 11

Balance sheet values are calculated using compound interest present value) calculations for all of the following except

Accepted Answer

Deferred income taxes are not calculated using compound interest present value calculations; they are based on differences between accounting and tax bases of assets and liabilities.

Question 12

To determine the converted table factor for the present value of an annuity due, one must find the factor for the present value of an ordinary annuity for

Accepted Answer

The answer of To determine the converted table factor for...

Question 13

On June 1,2016, Molser Company acquired a new machine by agreeing to pay five equal annual payments of $20,000, with the first payment due that day. Assuming an interest rate of 14% compounded annually, Molser should record the acquisition cost of the machine as

Accepted Answer

The answer of On June 1,2016, Molser Company acquired a...

Question 14

On September 1, 2014, Watson Company received a loan of $44,940 from One Finance Company. To pay off this loan, Watson Company will have to pay One Finance $10,000 each year for ten years. The first payment is due September 1, 2015. Which interest rate compounded annually is Watson paying on this loan?

Accepted Answer

The answer of On September 1, 2014, Watson Company received...

Question 15

Joshua desires to purchase an annuity on January 1, 2014, that yields him five annual cash flows of $10,000 each, with the first cash flow to be received on January 1, 2017. The interest rate is 10% compounded annually. The cost present value) of the annuity on January 1, 2014, is

Accepted Answer

The present value of the annuity is calculated by discounting each of the $10,000 cash flows back to January 1, 2014, using the 10% interest rate. The first cash flow occurs on January 1, 2017, which is 3 years from January 1, 2014. The present value of the annuity is $31,328.81.

Question 16

Samuel just inherited an annuity. He will receive six equal annual payments of $18,000, beginning today. Assuming a 10% interest rate compounded annually, the present value today of all receipts is

Accepted Answer

The present value of an annuity due (since payments begin today) can be calculated using the formula: $PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where $P$ is the payment amount, $r$ is the interest rate, and $n$ is the number of periods. Plugging in the values: $PV = 18,000 \times \left(\frac{1 - (1 + 0.10)^{-6}}{0.10}\right) \times (1 + 0.10)$, the calculation gives a present value of approximately $86,234, making option C correct.

Question 17

David Company borrowed $550,000 on December 31, 2014. The loan will be paid with six equal annual payments of $115,388, beginning on December 31, 2015. The rate of interest compounded annually for the loan is most nearly equal to

Accepted Answer

The loan is an annuity problem where the present value of the annuity (loan amount) is $550,000, the annual payment is $115,388, and the number of periods is 6. Using the formula for the present value of an annuity, the interest rate that satisfies these conditions is approximately 7%.

Question 18

What is the formula for the present value of an annuity due?

Accepted Answer

The formula for the present value of an annuity due is $ C \times\left[\frac{1-\frac{1}{(1+i)^{n-1}}}{i}+1\right] $, which accounts for payments at the beginning of each period by adding 1 to the standard present value of an ordinary annuity formula.

Question 19

On January 31, 2016, Manning Company acquired a new machine by paying $40,000 cash and agreeing to pay $20,000 annually for four years, beginning on January 31, 2017. Assuming an interest rate of 10%, Manning should record the acquisition cost of the machine on January 31, 2016, at

Accepted Answer

The acquisition cost includes the cash payment and the present value of the future payments. The present value of the $20,000 annual payments for four years at a 10% interest rate is calculated using the present value of an annuity formula. Adding this to the $40,000 cash payment gives the total acquisition cost.

Question 20

Norah has $2,000,000 in her retirement account. She wants to make 20 equal withdrawals, beginning today and each year thereafter. The investment plan earns 8%. What is the amount of annual withdrawals that would completely deplete the fund after the 20th withdrawal?

Accepted Answer

The problem is a present value of annuity due problem. Using the formula for annuity due, the annual withdrawal amount is calculated to be approximately $188,615.

Quiz 23: Understanding Time Value of Money Formulas and Concepts