Werkcollege financiering voor vastgoedkunde
Hoofdstuk 7. Stock Valuation.
Vraag 8. Suppose Acap Corporation will pay a dividend of $2.80 per share at the end of this
year and a dividend of $3 per share next year. You expect Acap’s stock price to be $52 in
two years. Assume that Acap’s equity cost of capital is 10%.
a) What price would you be willing to pay for a share of Acap stock today, if you planned
to hold the stock for two years?
P0= 2,80/1,1^1 + 3+52/1,1^2 = 48
b) Suppose instead you plan to hold the stock for one year. For what price would you
expect to be able to sell a share of Acap stock in one year?
P1= 3+52/1,1 = 50
c) Given your answer to part (b), what price would you be willing to pay for a share of
Acap stock today, if you planned to hold the stock for one year? How does this price
compare to your answer in part (a)?
P0= 2,80+50/1,1 = 48
d) When you compare your answer in part (a) to the answer in part (c)
The price in part (a) is the same as the price in part (c).
Vraag 9. Krell Industries has a share price of $22.00 today. If Krell is expected to pay a
dividend of $0.88 this year and its stock price is expected to grow to $23.54 at the end of the
year, what is Krell’s dividend yield and equity cost of capital?
0,88 / 22 = 4% > Dividend yield (antwoord op de vraag)
The capital gain rate is
(23,54 – 22) / 22 = 0,07 = 7.0%
The total return is
0,88+23,54/22 – 1 = 0,11 = 11% > equity cost of capital
Vraag 14. DFB, Inc., expects earnings this year of $5 per share, and it plans to pay a $3
dividend to shareholders. DFB will retain $2 per share of its earnings to reinvest in new
projects that have an expected return of 15% per year. Suppose DFB will maintain the same
dividend payout rate, retention rate, and return on new investments in the future and will not
change its number of outstanding shares.
a) What growth rate of earnings would you forecast for DFB?
G = (1-payback)x ROE
G = 0,4 x 0,15
G = 0,06 = 6%
b) If DFB’s equity cost of capital is 12%, what price would you estimate for DFB stock?
P0= Div1/Re-G = 3/0,12-0,06 = $50
c) Suppose instead that DFB paid a dividend of $4 per share this year and retained only
$1 per share in earnings. That is, it chose to pay a higher dividend instead of
reinvesting in as many new projects. If DFB maintains this higher payout rate in the
future, what stock price would you estimate for the firm now? Should DFB follow this
new policy?
G= 0,2 x 0,15 = 3%
P0= 4/0,12-0,03 = $44,44
d) Should DFB follow this new policy?
No, DFB should not raise dividends because the projects are positive NPV.
Hoofdstuk 8. Investment Decision Rules.
Vraag 11. OpenSeas, Inc., is evaluating the purchase of a new cruise ship. The ship would
cost $500 million, but would operate for 20 years. OpenSeas expects annual cash flows from
operating the ship to be $70 million and its cost of capital is 12%.
a.
b. The IRR is the point at which the line crosses the x-axis. In this case, it falls very close to
13%. Using Excel, the IRR is 12.72%.
c. Yes, because the NPV is positive at the discount rate of 12%.
d. The discount rate could be off by 0.72% before the investment decision would change.
Vraag 26. You are considering the following two projects and can only take one. Your cost of
capital is 11%.
0
1
2
3
4
A
-100
25
30
40
50
B
-100
50
40
30
20
Plan: Compute the NPV and the IRR of each project.
Execute: The timeline of the investment opportunity is:
0
1
2
3
4
–100
–100
25
50
30
40
40
30
50
20
a. NPVA  100 
NPVB  100 
25
30
40
50



 9.06
2
3
1  0.11 (1  0.11)
(1  0.11) (1  0.11)4
50
40
30
20



 12.62
2
3
1  0.11 (1  0.11)
(1  0.11) (1  0.11)4
b. Solving for the discount rate that results in zero NPV
IRR(A)  14.7%
IRR(B)  17.8%
c. This can be solved two ways. One is to calculate the IRR of the difference in cash flows
between the two projects. The other is to create NPV profiles of both investments and
determine the cost of capital at which the NPVs of both projects are the same.
0
1
2
3
4
–100
–100
0
25
50
–25
30
40
–10
40
30
10
50
20
30
25
10
10
30



2
3
1  r (1  r ) (1  r ) (1  r )4
IRR  5.567%
NPV  0 
NPV Profiles of investments A and B:
The profiles cross at a cost of capital of 5.567%.
Evaluate:
d. You should invest in B, as it has a higher NPV.
Hoofdstuk 9. Fundamentals of Capital Budgeting.
Vraag 16. One year ago, your company purchased a machine used in manufacturing for
$110,000. You have learned that a new machine is available that offers many advantages;
you can purchase it for $150,000 today. It will be depreciated on a straight-line basis over ten
years and has no salvage value. You expect that the new machine will produce a gross
margin (revenues minus operating expenses other than depreciation) of $40,000 per year for
the next ten years. The current machine is expected to produce a gross margin of $20,000
per year. The current machine is being depreciated on a straight-line basis over a useful life
of 11 years, and has no salvage value, so depreciation expense for the current machine is
$10,000 per year. The market value today of the current machine is $50,000. You company’s
tax rate is 45%, and the opportunity cost of capital for this type of equipment is 10%. Should
your company replace its year-old machine?
Plan:
Incremental revenues: 0
Incremental costs: 150,000
Depreciation: $10,000 per year
Capital Gain on Salvage: $50,000  $0  $50,000
Cash Flow from Salvage Value: 50,000  (50,000)(0.45)  27,500
Execute: Replacing the machine increases EBITDA by 40,000  20,000  20,000.
Depreciation expenses rises by $15,000  $10,000  $5000. Therefore, FCF will increase by
(20,000) 
(1  0.45)  (0.45)(5000)  $13,250 in years 1 through 10.
In year 0, the initial cost of the machine is $150,000. Because the current machine has a
book value of $110,000  10,000 (one year of depreciation)  $100,000, selling it for
$50,000 generates a capital gain of 50,000  100,000  50,000. This loss produces tax
savings of 0.45  50,000  $22,500, so that the after-tax proceeds from the sales including
this tax savings is $72,500. Thus, the FCF in year 0 from replacement is 150,000  72,500
 $77,500.
NPV of replacement  77,500  13,250  (1/0.10)(1  1/1.1010)  $3,916. There is a small
profit from replacing the machine.
Evaluate: Even though the decision has no impact on revenues, it still matters for cash
flows because it reduces costs. Further, both selling the old machine and buying the new
machine involve cash flows with tax implication.
Vraag 22. Home Builder Supply, a retailer in the home improvement industry, currently
operates seven retail outlets in Georgia and South Carolina. Management is contemplating
building an eighth retail store across town from its most successful retail outlet. The company
already owns the land for this store, which currently has an abandoned warehouse located
on it. Last month, the marketing department sent $10,000 on market research to determine
the extent of customer demand for the new store. Now Home Builder Supply must decide
whether to build and open the new store.
Which of the following should be included as part of the incremental earnings for the
proposed new retail store?
a) The original purchase price of the land where the store will be located.
Nee, is een sunk cost
b) The cost of demolishing the abandoned warehouse and clearing the lot.
Ja, sloop is gevolg van de beslissing om nieuw te bouwen > incrementeel
c) The loss of sales in the existing retail outlet, if customers who previously drove across
town to shop at the existing outlet become customers of the new store instead.
Ja, externe effecten
d) The $10,000 in market research spent to evaluate customer demand.
Nee, is ook sunk cost
e) Construction costs for the new store.
Ja, dit is de investering <(een van je belangrijkste kasstroom)
f)
The value of the land if sold.
Ja, opportunity cost
g) Interest expense on the debt borrowed to pay the construction costs.
Nee, verschil tussen financiering- en investeringskosten.
Hoofdstuk 10. Stock Valuation: A Second Look.
Vraag 7a. Sora Instustries has 60 million outstanding share, $120 million in debt, $40 million
in cash, and the following projected free cash flow for the next four years:
Year
0
1
2
3
4
Earnings and FCF Forecast ($ million)
Sales
433.0 468.0
516.0
547.0
574.3
Growth versus Prior Year
8.1%
10.3% 6.0%
5.0%
Cost of Goods Sold
-313.6
-345.7 -366.5 -384.8
Gross Profit
154.4
170.3
180.5
189.5
Selling, General, and Administrative
-93.6
-103.2 -109.4 -114.9
Depreciation
-7.0
-7.5
-9.0
-9.5
EBIT
53.8
59.6
62.1
65.2
Less: Income Tax at 40%
-21.5
-23.8
-24.8
-26.1
Plus: Depreciation
7.0
7.5
9.0
9.5
Less: Capital Expenditures
-7.7
-10.0
-9.9
-10.4
Less: Increase in NWC
-6.3
-8.6
-5.6
-4.9
Free Cash Flow
25.3
24.6
30.8
33.3
a) Suppose Sora’s revenues and free cash flow are expected to grow at 5% rate beyond
year 4. If Sora’s weighted average cost of capital is 10%, what is the value of Sora’s
stock based on this information?
P0 = V0 + cash0 – debt0
V0 = 25,3/1,1 + 24,6/1,1^2 + 30,8/1,1^3 + 33,3/1,1^4 + 699,3/1,1^4 = 566,84
VN = (1+Gfcf/Rwass-Gfcf) x FCF4
V1 = (1,05/01,-0,05) x 33,3 = 699,3
P0= CF1/1+r
P0=5,66,84 + 40 – 120/60 = $8,11
Vraag 14. Suppose Rocky Shoes and Boots has earnings per share of $2.30 and EBITDA of
$30.7 million. The firm also has 5.4 million shares outstanding and debt of $125 million (net
of cash). You believe Deckers Outdoor Corporation is comparable to Rocky Shoes and
Boots in terms of its underlying business, but Deckers has no debt. If Deckers has a P/E of
13.3 and an enterprise value to EBITDA multiple of 7.4, estimate the value of Rocky Shoes
and Boots stock using both multiples. Which estimate is likely to be more accurate?
The total value of Rocky Shoes and Boots using the P/E ratio is:
(2.3 x 5.4) x 13.3 = $165.2 million
The total value of Rocky Shoes and Boots using the EBITDA ratio is
(30.7 x 7.4) – 125 = $102.2 million.
Enterprise Value to EBITDA Ratio is the more accurate valuation method.