384
20.17 What is the equivalent annual worth of the cash flow given in the accompanying
figure? Assume i = 8%.
20.18 What are the equivalent present worth, annual worth, and future worth of the cash
flow given in the accompanying figure? Assume i = 8%.
385
SOLUTION
20.19 You are to consider the following projects. Which project would you approve if
each project creates the same income? Assume i = 8%, and a period of 15 years.
Project X
Project Y
Initial cost
$55,000
$80,000
Annual operating cost
$15,000
$10,000
Annual maintenance cost
$6,000
$4,000
Salvage value at the end of
$10,000 $15,000
SOLUTION
386
20.20 In order to purchase a new car, imagine that you recently have borrowed $15,000
from a bank that charges you according to a nominal rate of 8%. The loan is
payable in 60 months. (a) Calculate the monthly payments, (b) Assume the bank
charges a loan fee of 4.5% of the loan amount payable at the time they give you
the loan. What is the effective interest rate that you actually are being charged?
SOLUTION
387
20.21 Imagine the company that you work for borrows $8,000,000 at 8% interest, and
the loan is to be paid in seven years according to the schedule shown. Determine
the amount of the last payment.
Ye
ar
Amount
1
$1,000,000
2
$1,000,000
3
$1,000,000
4
$1,000,000
5
$1,000,000
6
$1,000,000
7
$?
20.22 You need to borrow $12,000 to buy a car, so you visit two banks and are given
two alternatives. The first bank allows you to pay $2595.78 at the end of each
year for six years. The first payment is to be made at the end of the first year. The
second bank offers equal monthly loan payments of $198.87, starting at the end of
first month. What are the interest rates that the banks are charging? Which
alternative is more attractive?
SOLUTION
20.23 What is the value of X if the given cash flow diagrams are equivalent. Assume i =
8%.
20.24 Your future company has been presented with an opportunity to invest in a project
with the following cash flow for ten years. If the company would like to make at
least 8% on its investment, would you invest in the project?
Initial investment
$10,000,000
Income
(annual)
$3,000,000
Labor cost
(annual)
$400,000
Material cost
(annual)
$150,
000
Maintenance cost
(annual)
$80,000
Utility cost
(annual)
$200,000
389
20.25 Your future company has purchased a machine and has entered into a contract
that requires the company to pay $2000 each year for the upgrade of machine
components at the end of years 6, 7, and 8. In anticipation of the upgrade cost,
your company has decided to deposit equal mounts (X) at the end of each year for
5 years in a row in an account that pays i = 6%. The first deposit is made at the
end of the first year. What is the value of X?
20.26 Your car loan payment extends for 6 years at 8% interest compounded monthly.
After how many months do you pay off half of your loan?
SOLUTION
20.27 What are the equivalent annual worth and future worth of the cash flow given in
Problem 20.15? Assume i = 8%.
SOLUTION
20.28 What are the equivalent present worth and annual worth of the cash flow given in
Problem 20.16? Assume i = 8%.
20.29 What are the equivalent present worth and future worth of the cash flow given in
Problem 20.17? Assume i = 8%.
20.30 The cash flow given in Problem 20.18 is to be replaced by an equivalent cash
flow with equal amounts (X) at the end of years 6, 7, 8, 9, and 10. What is the
value of X?
20.31 The cash flow given in Problem 20.15 is to be replaced by an equivalent cash
flow with equal amounts (X) at the end of years 5 through10. What is the value of
X?
392
20.32 The cash flow given in Problem 20.16 is to be replaced by an equivalent cash
flow with equal amounts (X) at the end of years 9 and 10. What is the value of X?
20.33 Solve Problem 20.1 using Excel.
20.34 Solve Problem 20.3 using Excel.
SOLUTION
20.35 Solve Problem 20.4 using Excel.
SOLUTION
20.36 Solve Problem 20.5 using Excel.
SOLUTION
20.37 Solve Problem 20.11 using Excel.
SOLUTION
20.38 Solve Problem 20.15 using Excel.
20.39 Solve Problem 20.16 using Excel.
20.40 Solve Problem 20.17 using Excel.
395
20.41 Solve Problem 20.18 using Excel.
SOLUTION
20.42 Solve Problem 20.19 using Excel.
20.43 Solve Problem 20.21 using Excel.
20.44 Solve Problem 20.22 using Excel.
20.45 Solve Problem 20.23 using Excel.
20.46 Solve Problem 20.24 using Excel.
20.47 Solve Problem 20.25 using Excel.
20.48 Solve Problem 20.26 using Excel.
20.49 Solve Problem 20.31 using Excel.
400
20.50 Solve Problem 20.32 using Excel.
SOLUTION