P5-51 Growth rates (LG 6; Basic)
To find average annual growth rate, use the future-value framework and solve for the
P5-52 Personal finance: Rate of return (LG 6, Intermediate)
a. Use the future-value framework, and solve for the interest rate (r) that makes the investment
the RATE function, but PV must be entered as a negative number.
the same amount of risk.
P5-53 Personal finance: Rate of return and investment choice (LG 6; Intermediate)
a.
In Excel, use RATE function, but PV must be entered as a negative number.
b. Investment C provides the highest return of the four alternatives. Assuming all investments
have equal risk, Clare should choose C.
P5-54 Rate of return-annuity (LG 6; Basic)
Use the framework for an ordinary annuity with n 10, PMT $2,000, PV $10,606, and solve
P5-55 Personal finance: Choosing the best annuity (LG 6; Intermediate)
Note: In Excel, use RATE function, but PV must be entered as a negative number.
a. Annuity A Annuity B
n 20, PV $30,000, PMT $3,100 n 10, PV $25,000, PMT
n 15, PV $40,000, PMT $4,200 n 12, PV $35,000, PMT
b. Annuity B offers the highest return at 9.03%. Because Raina considers all four annuities
equally risky and is indifferent about their differing lives, she should choose Annuity B.
P5-56 Personal finance: Interest rate for an annuity (LG 6; Challenge)
Note: In Excel, use RATE function, but PV must be entered as a negative number.
a. Defendant’s interest rate assumption: n 25, PV $2,000,000, and PMT $156,000
Solve for r 12.0%.
P5-57 Personal finance: Loan rates of interest (LG 6; Intermediate)
Note: In Excel, use RATE function, but PV must be entered as a negative number.
a. Loan A: n 5, PV $5,000, PMT $1,352.81. Solve for r 11.0%
b. Mr. Fleming should choose Loan B, which has the lowest interest rate.
P5-58 Number of years to equal future amount (LG 6; Intermediate)
Note: In Excel, use NPER function, but PV must be entered as a negative number.
A Given r 7%, PV $300, and FV $1,000, solve for n 17.79 years.
P5-59 Personal finance: Time to accumulate a given sum (LG 6; Intermediate)
Note: In Excel, use NPER function, but PV must be entered as a negative number.
d. The higher the rate of interest, the less time is required to accumulate a given future sum.
P5-60 Number of years to provide a given return (LG 6; Intermediate)
Note: In Excel, use the NPER function, but PV must be entered as a negative number.
A: Given r 11%, PV $1,000, and PMT $250, solve for n 5.56 years.
P5-61 Personal finance: Time to repay installment loan LG 6; Intermediate
Note: In Excel, use the NPER function, but PV must be entered as a negative number.
a. r 12%, PV $14,000, PMT $2,450. Solve for n 10.21 years.
P5-62 Ethics problem (LG 6; Intermediate)
To find average annual return, use the future-value equation – plugging in purchase price
($545,000) for PV, sales price ($1,500,000) for FV17, and 17 for the number of periods (n):
As to Samantha “swindling” Michael by selling the house 17 years later for nearly three times the
price she paid him for it, if stocks offer a risk-adjusted return comparable to the return on home
Case: “Finding Jill Moran’s Retirement Annuity”
Case studies are available on www.pearson.com/mylab/finance.
Chapter 5’s case challenges the student to apply present and future value techniques to a real-world situation.
annual deposits can be determined.
a.
b. Total amount needed at the end of year 12 is the present value of future annuity payments to Ms.
c. End-of-year deposits necessary over 12 years to fund Mr. Moran’s annuity may be found with the
next 12 years to accumulate the funds needed to pay $42,000 for 20 years.
d. If the interest rate rises to 10%, needed deposits fall to $14,670.43—Sunrise must deposit $14,670.43 at
the end of years 1–12 to provide Ms. Moran a $42,000 in years 13 to 32.
e. Step one is determining the present value of the $42,000 perpetuity to Ms. Moran; the present value of
this perpetuity equals annual cash flows ($42,000) divided by the interest rate (12%) or $350,000.
Spreadsheet Exercise
Answers to Chapter 5’s Uma Corporation spreadsheet problem are available on
www.pearson.com/mylab/finance.
Group Exercise
Group exercises are available on www.pearson.com/mylab/finance .
This chapter’s exercises provide each group with opportunities to use time value of money techniques on
their fictitious firm. In part (a), students analyze options for leasing a new copy machine to replace the
current unreliable one. In part (b), students analyze options for buying a replacement copier outright.
Students are asked to furnish a discount rate; instructors should discuss various market rates as candidates.
[A good source for interest-rate data is the Federal Reserve Economic Data (FRED), the data website of the
Federal Reserve Bank of St. Louis (https://fred.stlouisfed.org/).] In part (c), students are asked to create an
amortization schedule for a loan to upgrade the firm’s computer systems. Finally, in part (d), students are
asked to compute the present value of a four-year stream of settlement payments, given a 6% discount rate.
Integrative Case 2: Track Software, Inc.
Integrative Case 2, Track Software, Inc., places the student in the role of financial manager to introduce basic
concepts like setting financial goals, measuring firm performance, and analyzing firm condition. This
seven-year-old company has cash-flow problems, so the student must prepare/analyze the statement of cash
flows. Interest expense is increasing, and the firm’s financing strategy should be evaluated in view of current
yields on loans of different maturities. Ratio analysis of Track’s financial statements provides additional
insight into firm condition. The student must then confront a cost/benefit tradeoff: Is the additional expense of
a new software developer (which depresses short-term profitability) a good long-term investment? Wrestling with
such decisions highlight the importance of financial decisions to day-to-day firm operations and long-term
profitability.
a. 1. Stanley has focused on maximizing profit, as suggested by the rise in net profits from
2013 to 2019. His concern about adding a software designer, which would depress near-term
(cash flow, timing, risk) into decision-making.
2. An agency problem exists when managers place personal goals ahead of corporate goals. Stanley
b. Earnings per share (EPS) calculation:
Year Net Profits After
Taxes EPS (NPAT 50,000 shares)
2013 ($50,000) $ 0
2014 (20,000) 0
EPS has increased steadily, suggesting Stanley has been focused on profit maximization.
c. Operating and Free Cash Flows
OCF EBIT (1 T) depreciation = $89 (1 0.2) 11 $82.2
Track Software is generating good cash flow from operating activities. OCF is sufficient to provide
needed cash for investment in fixed assets and net working capital, with $20,200 left over for investors
(creditors and equity holders).
d. Ratio Analysis -Track Software, Inc
Actual Industry Avg. TS: Time Series
Ratio 2018 2019 2019 CS: Cross
Section
Net working
CS: Poor
Avg. collection
period 29.6 35.8 20.2 TS:
Deteriorating
(days) CS: Poor
Total asset
Debt ratio 0.78 0.73 0.55 TS:
Decreasing
CS: Poor
Times interest
CS: Poor
Net profit
margin 3.0% 3.1% 4.0% TS: Stable
CS: Fair
Ratio analysis of Track Software:
1. Liquidity: Track’s liquidity (based on its current ratio, net working capital, and quick ratio) has
been stable or improved slightly but remains well below peer (industry average).
2. Activity: Inventory turnover has deteriorated considerably and is now much worse than peer.
3. Debt: Track’s debt ratio improved slightly from 2018 but remains higher than the industry
4. Profitability: Track’s gross, operating, and net profit margins improved slightly in 2019 but
5. Stanley should find the cash to hire the software developer. Adding a new product would increase
sales and lead to greater earnings for Track Software over the long term.
e. Stanley should seek to maximize the value of Track Software, not earnings in any one period.
f. The investor should view a $5,000 annual payment as a perpetuity, with a present value equal to