Download CORPORATE FINANCE (5122) – DIEM

CHAPTER 2: Practice questions
10. A parcel of land costs $500,000. For an additional $800,000 you can build a motel
on the property. The land and the motel should be worth $1,500,000 next year. Suppose
that common stocks with the same risk as this investment offer a 10 percent expected
return. Would you construct the motel? Why or why not?
Land = $500, 000
Motel = $800, 000
FV (exp) = 1,500, 000
r = 10%
C1
NPV = −Co +
(1 + r )
(1,500, 000)
(1 + 0,10)
(1,500, 000)
NPV = −1,300, 000 +
(1,10)
NPV = 63, 636.36
NPV = −(500, 000 + 800, 000) +
Since the NPV of the project is positive, you would construct the motel.
Alternatively, we can compute the return of the project as follows:
r =
1,500,000 − 1,300,000
= 0,1539 = 15,39%
1,300,000
Since the rate of return is greater than the cost of capital, you would construct the motel.
11. Calculate the NPV and rate of return for each of the following investments. The
opportunity cost of capital is 20% for all four investments.
Investment
1
2
3
4
Initial Cash Flow Cash Flow Year 1
(10.000,00)
18.000,00
(5.000,00)
9.000,00
(5.000,00)
5.700,00
(2.000,00)
4.000,00
1
C1
By using the NPV formula NPV = −Co + (1 + r ) where r=20% you obtain:
Investment
1
2
3
4
NPV
18,000
− 10,000 +
= $5,000
1.20
9,000
− 5,000 +
= $2,500
1.20
5,700
− 5,000 +
= −$250
1.20
4,000
− 2,000 +
= $1,333.33
1.20
Return
18,000 − 10,000
= 0.80 = 80.0%
10,000
9,000 − 5,000
= 0.80 = 80.0%
5,000
5,700 − 5,000
= 0.14 = 14.0%
5,000
4,000 − 2,000
= 1.00 = 100.0%
2,000
(a) Which investment is most valuable?
Investment 1 is the most valuable for shareholders because it has the highest NPV.
(b) Suppose each investment would require use of the same parcel of land.
Therefore you can take only one. Which one?
Investment 1 is the best choice because it has the highest (combined) IRR and NPV.
Although project 1 and 2 offer the same rate of return, project 1 maximizes shareholders’
wealth by offering also the highest NPV.
13. Norman Gerrymander has just received a $1 million bequest. How should he invest it?
There are four immediate alternatives.
a. Investment in one-year U.S. government securities yielding 5%.
b. A loan to nephew Gerald, who has for years aspired to open a big Cajun restaurant in
Duluth. Gerald has arranged a one-year bank loan for $900,000 at 10%, but asks for a
$1 million loan from Norman at 9%.
c. Investment in the stock market. The expected rate of return is 12%.
d. Investment in local real estate, which Norman judges is about as risky as the stock
market. The opportunity at hand would cost $1 million and is forecasted to be worth
$1.1 million after one year.
Which of these investments have positive NPVs? Which would you advise Norman to take?
C1
By using the NPV formula NPV = −Co + (1 + r ) obtain:
2
1, 050, 000
=0
(1, 05)
(a) NPVa = −1, 000, 000 +
(b) Assuming that 10% is the appropriate discount rate for an investment with the level of
risk inherent in Gerald’s restaurant:
NPVb = −1, 000, 000 +
1, 000, 000(1, 09)
= −9, 090.91
(1,10)
(c) NPVc = −1, 000, 000 +
1,120, 000
=0
(1,12)
(d) NPVd = −1, 000, 000 +
1,100, 000
= −17,857.1
(1,12)
Norman shouldn’t invest in projects (b) and (d) because they yield a negative NPV. On
the other hand, projects (a) and (c) –investing in a government bond or the stock marketwould yield him a NPV=0 (this is because correctly priced securities always have an
NPV = 0).
14. Show that your answers to question 13 are consistent with the rate of return rule
for investment decisions.
The following table summarizes the results obtained in question 13:
Investment
NPV
One-year U.S. government securities
Loan to nephew Gerald
Investment in the stock market
Investment in local real estate
$0
-$9,090.91
$0
-$17,857.1
*** Note that none of the investment projects has a positive NPV. The investment in the
government securities and the stock market have NPV = 0 because correctly priced
securities always have an NPV = 0.
Now, to compute the rate of return of each project we proceed:
(a)
Expected rate of return on project A: ra =
1, 050, 000 − 1, 000, 000
= 5.0%
1, 000, 000
*** ra is equal to the return on the government securities (which is consistent with a
NPV=0).
3
(b)
Expected rate of return on project B: rb =
1, 090, 000 − 1, 000, 000
= 9.0%
1, 000, 000
*** rb is less than the return for investments with similar risk paying 10% (which is
consistent with a negative NPV).
(c)
Expected rate of return on project C: rc =
1,120, 000 − 1, 000, 000
= 12.0%
1, 000, 000
*** rc is equal to the rate of return of the stock market (which is consistent with a
NPV=0).
(d)
Expected rate of return on project = rd =
1,100, 000 − 1, 000, 000
= 10.0%
1, 000, 000
*** rd is less than the 12% rate of return for investment in the equally risky stock market
(which is consistent with a negative NPV).
19. For an outlay of $8 million you can purchase a tanker load of bucolic acid
delivered in Rotterdam one year hence. Unfortunately the net cash flow from selling
the tanker load will be very sensitive to the growth rate of the world economy:
Slump Normal Boom
$8
$12
$16
(a) What is the expected cash flow? Assume the three outcomes for the economy
are equally likely.
Expected cash flow = 1/3*(8+12+16) =12
(b) What is the expected rate of return on the investment in the project?
Expected rate of return = (12-8)/8 = 0.5
(c) One share of stock Z is selling for $10.The stock has the following payoffs after
one year
Slump Normal Boom
$8
$12
$16
Calculate the expected rate of return offered by stock Z. Explain why this is the
opportunity cost of capital for your bucolic acid project.
Expected rate of return = (12-10)/10 = 0.2
4
This is the return foregone by investing in the project and not in a share with identical
risk
(d) Calculate the project’s NPV. Is the project a good investment? Explain why.
NPV = 12/(1+0.2)-8 = 2 > 0. It is a good project, since its has positive NPV.
CHAPTER 2: Challenge questions
20. (Tutorial) In real life the future health of the economy cannot be reduced to three
equally probable states like slump, normal, and boom. But we’ll keep that
simplification for one more example.
Your company has identified two more projects, B and C.
Each will require a $5 outlay immediately. The possible payoffs at year 1, are in
millions:
Slump Normal Boom
Project B $4
$6
$8
Project C 5
5,5
6
You have identified the possible payoffs to investors in three stocks X, Y, and Z:
Current Price
per Share
Payoff at Year 1
Slump Normal Boom
X
$95,65
$80
$110
$140
Y
40
40
44
48
Z
10
8
12
16
(a) What are the expected cash inflows of project B and C?
Expected cash inflow of project B = 1/3*(4+6+8) = 6
Expected cash inflow of project C = 1/3*(5+5.5+6) = 5.5
5
(b) What are the expected rates of return offered by stocks X,Y, and Z?
⎞
⎛1
⎜ (80 + 110 + 140 )⎟ − 95.65
3
⎠
Expected rate of return for stock X = ⎝
≈ 0.15
95.65
⎛1
⎞
⎜ (40 + 44 + 48)⎟ − 40
3
⎠
Expected rate of return for stock Y = ⎝
= 0.10
40
⎛1
⎞
⎜ (8 + 12 + 16 )⎟ − 10
3
⎠
Expected rate of return for stock Z = ⎝
= 0.20
10
(c) What are the opportunity costs of capital for projects B and C? (Hint: Calculate
the percentage differences, slump versus normal and boom versus normal, for
stocks X,Y, and Z. Match up to the percentage differences in B’s and C’s
payoffs.)
Notice that 0.5 times stock Z has the same payoffs as project B and 1/8 of stock Y has the
same payoffs as project C. Therefore we can choose 0.2 and 0.1 respectively as discount
rates.
(d) What are the NPVs of projects B and C?
Project B: NPV = 6/(1+0.2) – 5 = 0
Project C: NPV = 5.5/(1+0.1) – 5 = 0
(e) Suppose B and C are launched and $5 million are invested in each. How much
will they add to the market value of your company’s shares?
Since the NPV is zero no value would be added to the company.
6