Principles of Corporate Finance, 11/e solutions manual and test bank 0078034760
Richard A. Brealey, London Business School
Stewart C. Myers, Massachusetts Institute of Technology
Franklin Allen, University of Pennsylvania
ISBN: 0078034760
Copyright year: 2014
brealey - principles of corporate finance - 11e, solutions manual and test bank 0078034760
THE JONES FAMILY, INCORPORATED
Minicase Solution
Principles of Corporate
Finance, 11th Edition
R. A. Brealey, S. C. Myers
and F. Allen
If the wildcat well is a success, it should produce 75×365 = 27,375 barrels per year. Suppose production starts after one year. The net cash flow per barrel, after pipeline and shipping costs and including one year’s inflation at 2.5%, is (100 – 20) ×1.025 = $82. Total cash flow is C1 = 27,375×82 = $2,245,000 (we will round to the nearest $1000). Production will decline by 5% per year, but prices are projected to grow at 2.5% per year. The net growth rate is (1.025×.95) – 1 = –.026 or –2.6%.
Johnny used the CAPM to get a discount rate. The interest rate is 6%, the market risk premium is 7% and the beta is .8. Thus:
The cash flows from the oil well are a 15-year annuity declining at 2.6% per year.[1] Johnny decided to use the short-cut formula in Table 2.2. The short cut starts with the formula for a growing (in this case declining) perpetuity, but subtracts the PV of another declining perpetuity. Let T = the date of the last cash flow from the declining annuity:
The second term inside the brackets subtracts the present value of an annuity starting in year 16 and discounts it back to the present. Note that the cash flow for year 16 is
C1×(1 - .026)15.
Of course there was a 30 per cent chance of a dry hole, so Johnny multiplied his PV of $13,757,000 by 1 - .3 = .7 and subtracted the $5 million investment.
NPV = .7 ´ 13,757,000 – 5,000,000 = + $4,630,000
What about the operating leverage that so concerned Johnny’s father? Operating leverage is caused by fixed costs, in this base by the pipeline and shipping costs. These costs start at 20×1.025 = $20.50 per barrel in year 1 and are expected to grow at 2.5% per year. The calculation above folds them into net cash flows and discounts them at 11.6%, as if they were just as risky as the revenues. If they are really fixed, they should be discounted at a lower rate, for example at the 7% long-term borrowing rate for Jones Family Oil, Inc.
Johnny decided to see how the PV of the fixed costs would change when discounted at 7 vs. 11.6%. The PV per barrel at 11.6%, which was included in the PV calculated above, is:
The PV at 7% increases to:
Thus recognizing operating leverage could decrease overall PV by
(161.4 – 125.6) × 27,375 = $980,000 and decrease NPV to 13,757,000 – 980,000 = $12,777,000.[2] The wildcat well’s NPV is still positive, however, because .7 × 12,777,000 = $8,944,000 is still greater than the $5 million outlay.
It seems that Marsha’s oil well is an excellent investment. In fact it remains a good investment (ignoring any adjustment for operating leverage) even if production lasts only 6 years. You can check this by recalculating the declining annuity formula with T = 6, multiplying by the 0.7 probability of finding oil and subtracting the investment of $5 million. The resulting NPV is still positive.
[1] This assumes that the well produces one lump-sum cash flow per year at dates 1, 2, … , 15. This timing may not be right. If the cash flows are spread evenly over each year, and the well starts production at date 1, then it would be better to assume receipt at dates 1.5, 2.5, … , 15.5 (the mid-year convention). In this case you could discount the present values by an extra half year to account for the six-month delays. Or you could switch over to continuous compounding.
[2] This holds the 11.6% discount rate for revenues constant. If that rate was right for net cash flows (revenues less fixed costs), it is too high for revenues alone. Operating leverage adds risk to net cash flows, not to revenue. A lower discount rate for revenues would increase NPV and make the Marsha’s investment still more attractive.
Chapter 2 How
to Calculate Present Values
OVERVIEW
This
chapter introduces the concept of present value and shows why a firm should
maximize the market value of the stockholders’ stake in it. It describes the mechanics of calculating
present values of lump sum amounts, perpetuities, annuities, growing
perpetuities, growing annuities and unequal cash flows. Other related topics
like simple interest, frequent compounding, continuous compounding, and nominal
and effective interest rates are discussed.
The net present value rule and the rate of return rule are explained in
great detail.
LEARNING
OBJECTIVES
- To
learn how to calculate present value of lump sum cash flows.
- To
understand and use the formulas associated with the present value of
perpetuities;
growing
perpetuities; annuities; and growing annuities.
- To
understand more frequent compounding including continuous compounding.
- To
understand the important difference between nominal and effective interest
rates.
- To
understand value-additive property and the concept of arbitrage.
- To
understand the net present value rule and the rate of return rule.
CHAPTER
OUTLINE
Future
values and present values
The concepts of future value, present
value, net present value (NPV) and the opportunity cost of capital (hurdle
rate) are introduced. The authors show, using several numerical examples, that
simple projects with rates of return exceeding the opportunity cost of capital
have positive net present values. The
“Net present value rule” and the “Rate of return rule” are stated here.
This chapter also extends the
concept of discounting to assets, which produce a series of cash flows. The possibility of arbitrage restricts the
relative values of discount factors DF1, DF2,…. DFt
–.The main point is that money machines cannot exist in well-functioning
financial markets. Using numerical
examples it shows how to calculate PV and NPV of a series of cash flows over a
number of periods (years).
Looking for shortcuts – perpetuities and annuities
This
section is devoted to developing formulae for perpetuities and annuities. It explains the difference between an ordinary
annuity and an annuity due. It also explains how the future value of an annuity
is calculated. The present value of an
annuity can be thought of as the difference between two perpetuities
beginning
at different times. Using this simple
idea, the formula for the present value of an annuity is derived. The future value of an annuity formula is also
derived. These have numerous
applications in pension funds, mortgages and valuation of financial assets.
More shortcuts – growing perpetuities and annuities
Some
applications need the present value of a perpetual cash flow growing at a
constant rate, as well as annuities that grow at a constant rate. The formula for the present value of a growing
perpetuity is derived. The present value
of a growing annuity can be thought of as the difference between two growing
perpetuities starting at different times. Using this simple idea, the formula for the
present value of a growing annuity is also derived. These formulas have many applications in the
valuation of assets.
How Interest Is Paid and Quoted
This section explains the
differences between compound interest and simple interest, as well as the
differences between effective annual rates and annual percentage rates. It deals with how each interest rate is used
in the market place and the math necessary to move between the two kinds of
interest rates.
TEACHING
TIPS FOR POWERPOINT SLIDES
Slide 1 - Title slide
Slide 2
Explain
the terms “future value” and “present value”. The concept must be emphasized at this point.
Consequently, it may be necessary to spend some time explaining real world
examples of how present value and future value relate. A good example to use is retirement planning.
Slide 3
FV = PV× [(1
+ r)^ t ]
Define
the terms: FV = Future value
PV = Present value
r = interest rate
t = number of years (Periods)
Explain
the time value of money and its importance to financial decision making.
Walk
through each step in the math process and show how the value increases. If you
plan to have your students use a financial calculator, you can skip the details
of the basic math. Be aware, students often stumble when doing simple math
calculations.
How to Calculate
Present Values
Multiple Choice
Questions
|
1.
|
The present value of
$100.00 expected two years from today at a discount rate of 6% is:
|
|
2.
|
Present value is defined
as:
|
A.
|
future cash
flows discounted to the present by an appropriate discount rate.
|
|
B.
|
inverse of
future cash flows.
|
|
C.
|
present cash
flows compounded into the future.
|
|
D.
|
future cash
flows multiplied by the factor (1 + r)t.
|
|
|
3.
|
If the annual
interest rate is 12.00%, what is the two-year discount factor?
|
|
4.
|
If the present value
of cash flow X is $240, and the present value of cash flow Y is $160, then
the present value of the combined cash flows is:
|
|
5.
|
The rate of return
is also called the: I) discount rate; II) hurdle rate; III) opportunity cost
of capital
|
|
6.
|
The present value of
$121,000 expected one year from today at an interest rate (discount rate) of
10% per year is:
|
|
7.
|
The one-year
discount factor, at a discount rate of 25% per year, is:
|
|
8.
|
The one-year
discount factor, at an interest rate of 100% per year, is:
|
|
9.
|
The present value of
$100,000 expected at the end of one year, at a discount rate of 25% per year,
is:
|
|
10.
|
If the one-year
discount factor is 0.8333, what is the discount rate (interest rate) per
year?
|
|
11.
|
If the present value
of $480 to be paid at the end of one year is $400, what is the one-year
discount factor?
|
|
12.
|
If the present value
of $250 expected one year from today is $200, what is the one-year discount
rate?
|
|
13.
|
If the one-year
discount factor is 0.90, what is the present value of $120 expected one year
from today?
|
|
14.
|
If the present value
of $600, expected one year from today, is $400, what is the one-year discount
rate?
|
|
15.
|
The present value
formula for a cash flow expected one period from now is:
|
|
16.
|
The net present
value formula for one period is:
|
A.
|
NPV = C0 + [C1/(1 + r)].
|
|
B.
|
NPV = PV
required investment.
|
|
|
17.
|
An initial investment
of $400,000 is expected to produce an end-of-year cash flow of $480,000. What
is the NPV of the project at a discount rate of 20%?
|
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