The Time Value of Money ♦ 273
Each of the following factors appear in the various present value and future value tables. Select
the letter that matches up with the factor in the correct table. All answers are based on a 5%
interest rate.
a.
12.57789
b.
1.62889
c.
7.72173
d.
0.61391
13. Future value of a single amount
14. Future value of an annuity
15. Present value of a single amount
16. Present value of an annuity
274 ♦ Chapter 8
PROBLEM
1. a. Levinson Corporation wants to accumulate a fund to replace its equipment in 5 years. If it
invests $200,000 today at 7%, what amount will it have in 5 years?
b. Assume the same facts as in (a) except that Levinson invests $40,000 per year. What amount
will it have in 5 years?
2. Assume that Sanders Co. has promised to make four payments to Johnson, Inc. Each payment is
in the amount of $1,000.
Required:
What is the present value of these cash flows if the annual rate is 12%, and the payments begin:
a.
one year from today, and are paid annually?
b.
six months from today, and are paid semiannually?
c.
three months from today, and are paid quarterly?
Which method of payments do you think each company would prefer and why? Carefully show
your work and label it clearly.
a.
PV = amount of annuity x interest factor
= $3,037.35
b.
PV = amount of annuity x interest factor
= $3,465.11
c.
PV = amount of annuity x interest factor
= $3,717.10
The Time Value of Money ♦ 275
3.
a.
What is the present value of $200,000 to be paid at the end of 10 years, assuming an 8%
interest rate?
b.
What is the present value of $20,000 per year for 10 years, assuming an 8% interest
rate?
4.
a.
What is the present value of $75,000 to be paid at the end of 10 years, assuming a 9%
interest rate?
b.
What is the present value of $7,500 per year for 10 years, assuming an 9% interest
rate?
5.
a.
Koslovsky Corporation wants to accumulate a fund to replace its equipment in 8
years. If it invests $400,000 today at 8%, what amount will it have in 8 years?
b.
Assume the same facts as in (a) except that Koslovsky invests $50,000 per year.
What amount will it have in 8 years?
6. Santander Enterprises has purchased new equipment on a long-term payment plan. The contract
calls for Santander to pay $50,000 at the end of each year for 6 years, at an interest rate of 8%. At
what amount should Santander record this equipment and what total amount of interest will it pay
over the 6 years?
276 ♦ Chapter 8
7. Silverstone Co. is considering two options for acquiring a new company car. Details on the two
options are:
Option 1. Lease the car for 4 years at an annual payment of $14,000; an additional $24,000
payment would be required at the end of the lease. The interest rate on this option is 11%.
Option 2. Purchase the car on a 4 year note at an annual payment of $18,000. The interest rate on
this option is 11%.
Which option should Silverstone select? Show supporting computations in good form.
8. Your company is “right sizing” and offers you the option of receiving one year’s salary of $70,000
today or deferring your severance 20 years and receiving $150,000. Assume a reasonable rate of
interest of 8%. Which settlement should you accept? (Ignore any tax consequences.) (Show your
work.)
9. Assume that upon retirement, you wish to receive $40,000 per year for the first ten years. How
much will you need in a fund to assure yourself of your desired financial arrangement upon
retirement? Assume an interest rate of 12%. (Show your work.)
The Time Value of Money ♦ 277
10. Yellow Strawberry borrowed $45,000 to start a traveling fast-pitch softball team for girls age
sixteen and under. The note signed at the bank requires Strawberry to make five equal annual
payments, with the first payment due one year from the date the note was signed. Assuming the
bank’s borrowing rate is 6%, what will be the amount of Yellow Strawberry’s five payments?
(Show your work.)
11. Your company was fined by a regulatory agency. The agency has given your company two
methods of paying its debt. It can either make a payment today of $450,000, or it can make
periodic (annual) payments of $60,000 at the end of each period for 10 periods. Which option
would you suggest your company select, assuming an interest rate of 7%? (Show your work.)
12. Synergistic Corporation has purchased new equipment on a long-term payment plan. The contract
calls for Synergistic to pay $30,000 at the end of each year for 7 years, at an interest rate of 6%. At
what amount should Synergistic record this equipment and what total amount of interest will it pay
over the 7 years?
13. On January 1, 2007, Simmons Company adopted a plan to accumulate funds to retire $10,000,000
of bonds payable which are due on December 31, 2016. Simmons plans to make ten annual
deposits that will earn 9%. The first payment will be made on December 31, 2007. What annual
payment should Simmons make?
278 ♦ Chapter 8
14. Stevens Co. is considering two options for acquiring 2 new company cars. Details on the two
options are:
Option 1. Lease the cars for 3 years at an annual payment of $16,000; an additional $30,000
payment would be required at the end of the lease. The interest rate on this option is 10%.
Option 2. Purchase the cars on a 3-year note at an annual payment of $20,000. The interest rate on
this option is 8%.
Which option should Stevens select? Show supporting computations in good form.
15. Lancaster Corporation is considering an investment in new equipment which will cost $600,000
and is expected to last for 5 years. The firm estimates that it will generate net operating cash flows
from the equipment of $150,000 per year. Assuming that Lancaster requires a 10% return on
investment, what is the present value of the future operating cash flows? Show supporting
computations in good form.
16. On January 1, 2007 The Corgy Company adopted a plan to accumulate funds to retire $8,000,000
of bonds payable which are due on December 31, 2016. Corgy plans to make ten annual deposits
that will earn 10%. The first payment will be made on December 31, 2007 What annual payment
should Corgy make?
The Time Value of Money ♦ 279
17. Starlight Ventures is considering an investment in new equipment which will cost $200,000 and is
expected to last for 6 years. Starlight estimates that it will generate net operating cash flows from
the equipment of $50,000 per year. Assuming that Starlight requires a 12% return on investment,
compute the present value of its estimated future net operating cash flows? Show supporting
computations in good form.
18. On January 1, 2007 All-Appliance Company purchased a building by signing a note for the
purchase price. The note required three equal end-of-year payments, with interest to be paid on the
unpaid balance. The following amortization table provides information about this note:
Year
Beginning of
year balance
Interest Expense
Payment
End of year
balance
2007
$379,694.20
$34,172.48
$150,000
?
2008
263,866.68
23,748.00
150,000
?
2009
137,614.68
12,385.32
150,000
?
Required:
Answer the following questions:
a.
What was the purchase price of the building?
b.
What was the interest rate on the note?
c.
What amount would All-Appliance report on its income statement for the year ended
December 31, 2007 What would it be labeled?
d.
What amount would All-Appliance report on its December 31, 2007 balance sheet?
What would it be labeled?
e.
By what amount was the principal balance reduced during 2007?
a.
$379,694.20
b.
9%= ($34,172.48 / 379,694.20)
c.
$34,172.48; interest expense
d.
263,866.68 ; note payable
e.
$115,827.52= ($379,694.20 – 263,866.68) or ($150,000 – $34,172).
280 ♦ Chapter 8
19. Assume the following series of cash flows:
Period
Amount
1
$ 900
2
8,500
3
4,400
4
750
Required:
What is the present value of these amounts when discounted at:
a.
1%
b.
12%
State one conclusion you can draw from the results.
Carefully show your work and label it clearly.
20. Jose is considering expansion of his miniature golf course. He expects that incremental cash
inflows from this expansion would be $16,000 for the first year and $24,000 for the second year.
Each succeeding year through the 5th year is projected to grow by 10%. At the end of the 5th year
he plans to sell the golf course and believes the expansion would bring an extra $100,000 in
selling price.
Required:
a.
What is the present value of these expected incremental cash inflows if Jose requires
a 12% return on investment? Carefully show your work and label it clearly.
b.
Assume the answer to part (a) is $140,000 and that Jose goes ahead with the
expansion. Also assume that the cost of the expansion is $136,000. What can you
determine about the rate of return that Jose will earn on this project? Be specific.
The Time Value of Money ♦ 281
21. Valerie Sport has just acquired a new Corvette (for business purposes, of course) at a cash price of
$70,000. Unfortunately, Valerie only had $10,000 available and had to finance the balance with
the dealer over 5 years at 9%. The sales contract calls for Valerie to make 5 equal annual year-end
payments to retire the debt.
Required:
a.
What is the amount of each payment?
b.
What is Valerie’s interest expense for year 2? Prepare an amortization table.
c.
What is Valerie’s total interest cost over the 5-year term of the loan?
282 ♦ Chapter 8
22. Golden Mermaid is considering a major expansion of its operating capacity. The expansion will
require the acquisition of $400,000 of new assets having an expected life of 8 years. The company
expects to generate net operating cash flows from the assets of $75,000 per year. The expansion
will only be undertaken if a return on investment of at least 12% can be expected. Should the new
assets be acquired? Clearly state your answer and carefully label all supporting computations.
The Time Value of Money ♦ 283
23. One for All Bicycle Rental Company can modernize its fleet by spending $6,500,000 for new
equipment. Management estimates additional net operating cash flows of $1,600,000 per year for
the first 3 years and $1,900,000 per year for another 3 years. Generally, this business does not take
on new investments unless a 12% return can be earned.
Required:
a.
Should the firm take on this new investment? Why or why not? Neatly and precisely
show your work for any supporting computations.
b.
What additional factors must be considered other than just the numerical
computations you made in part (a)?
a.
Yes, the investment should be adopted. The company could pay up to $7,091,130
284 ♦ Chapter 8
24. The Gold Star Delivery Service is for sale at a price of $700,000. You have satisfied yourself as to
the accuracy of the financial statements which show fairly stable revenues at about $600,000 per
year and expenses of about $440,000 per year. All transactions are in cash. After studying the
operations thoroughly, you are quite sure that you could increase revenues by about 10% and cut
expenses by about 4%. You believe these changes would occur the first year and then stay at these
new levels for about 5 years. At the end of 5 years you estimate you could sell the business for
about $750,000. A return of 12% is required for you to proceed.
Required:
Will this acquisition meet your investment objective? Discuss. Clearly and neatly label any
supporting computations.
25. Space Travel borrowed $400,000 at 10% annual interest. The loan is to be repaid in three equal
year-end installments.
Required:
a.
Determine the size of the required payments.
b.
Complete the amortization table below:
Year
Beginning
Principal
Payment
Interest
Expense
Principal
Repaid
Ending
Principal
1
2
3
0
The Time Value of Money ♦ 285
26. Green Hills Condominiums borrowed $150,000 on a three-year bank loan to finance roof repairs.
The interest rate was 12% and three equal year-end payments were required to pay off the debt.
Required:
a.
Determine the size of the required payments.
b.
Complete the amortization table.
c.
Determine the interest revenue that the bank should recognize for each year of the
loan.
$150,000 ÷ 2.40183 = $62,452
$160,486; ($400,000 ÷ 2.48685)
286 ♦ Chapter 8
27. The beneficiary of a life insurance policy can choose one of three options of receiving benefits:
1.
$120,000 in cash upon selecting the option.
2.
$6,000 at the end of each quarter for five years.
3.
$30,000 in cash plus $9,000 at the end of each quarter for 3 years.
The person asks you which option to exercise. What option would you suggest? Assume an annual
interest rate of 12%. (Be careful.) (Show your work.)
ESSAY
1. Describe the difference between present value and future value?
2. Explain the relationship between the future value of a sum of money and its present value.
The Time Value of Money ♦ 287
3. Define an annuity.
4. Assume you have negotiated a deal with a car dealer to purchase a new Lexus. You must now
decide how to finance the purchase. The dealer gives you a number of options. These options
range from paying the entire amount in cash today to making monthly payments of various
amounts over various numbers of periods. Describe what you would do to select the best financing
package for you. (Assume all options are within your reach financially.)
5. Assume you are inspecting a time value of money table labeled “Present Value of $1.” In the row
labeled 13 periods and under the 4% column, the number .60057 is found. How should that factor
be interpreted? What does it mean? Don’t merely tell how the interest factor would be used
mechanically, but discuss what it means.
6. Assume you have just won the Florida lottery. You have a choice of receiving $150,000 today or
$25,000 per year for eight years. Discuss what you would do to make your decision. (Ignore
income taxes.)
288 ♦ Chapter 8
7. Johnson Fluids can expand production 32% by investing $425,000 in additional manufacturing
equipment. The firm’s accountants have estimated that the incremental production has a sales
value of $300,000 at current prices and would cost $215,000 (not including the cost of the
equipment). The estimated life of this equipment is 10 years. Furthermore, the accountants have
determined that the present value of these cash flows, when discounted at 15%, is $426,595.
Should this investment be adopted? What other information might be helpful to the decision?
Discuss.
8. Happy Cow Farms borrowed $93,000 from its local bank on a 7-year note payable. Terms of the
note require that Happy Cow repay the note via seven equal-sized year-end payments which
include 11% interest. Consider the third year of this note. In what way will the interest revenue
earned by the bank on this note and the interest expense incurred by Happy Cow Farms differ? Be
specific.