Problem 9-11 Cost of Equity Page 448
Radon Homes’ current EPS is $6.50. It was $4.42 5 years ago. The company pays out 40% of its
earnings as dividends and the stock sells for $36.
a. Calculate the historical growth rate in earnings (Hint: This is a 5 year growth period)
b. Calculate the next expected dividend per share D1 (Hint: D0 = 0.4($6.50) = $2.60)
c. What is Radon’s cost of equity rs?
Jawaban:
a. EPS this period = $6.50
EPS 5 years ago = $4.42
t = 5 years
Compounded EPS growth = [(EPS this period)/EPS t periods ago)]^(1/t) – 1
= [$6.50/$4.42]^(⅕) - 1
= 1.470588^(⅕)-1
= 0.080185 equivalent with 8.0185%
b. Next expected dividend = current EPS x (1+growth rate) + payout ratio
= $6.50 x (1+0.080185 ) + 40%
= $6.50 x 1.080185 + 40%
= $2.80848 equivalent with $2.81
c. Cost of equity = (expected dividend/stock price) + growth rate
= ( $2.80848/$36) + 0.080185
= 0.158198 equivalent with 15.82%
Problem 9-16 Market Value Capital Structure Page 449
Suppose the Schoof Company has this book value balance sheet:
Current Assets
$30,000,000 Current Liabilities
Notes Payable
Fixed Assets
$70,000,000 Long term debt
Common stock (1 million shares)
Retained earnings
Total Assets
$100,000,000 Total liabilities and equity
$20,000,000
$10,000,000
$30,000,000
$1,000,000
$39,000,000
$100,000,000
The notes payable are to banks, and the interest rate on this debt is 10%, the same as the rate on
new bank loans. These bank loans are not used for seasonal financing but instead are part of the
company’s permanent capital structure. The long term debt consists of 30,000 bonds, each with
par value of $1,000 annual coupon interest rate of 6%, and a 20 year maturity. The going rate of
interest on new long term debt, rd is 10% and this is present yield to maturity on the bonds. The
common stock sells at a price of $60 per share. Calculate the firm’s market value capital structure.
Jawaban:
- Short term debt = notes payable → face value sama dengan market value karena tidak
terdapat perubahan suku bunga
- Nilai long term debt
Face value dari long term debt = 30,000 x $1,000
= $30,000,000
r adalah yield to maturity sehingga bernilai 10%
n adalah jumlah annual coupon yang harus dibayarkan yaitu 20 cupon dalam 20 tahun
Annual coupon = face value x coupon rate
= $30,000,000 x 6%
= $1,800,000
Price = face value / (1+r)n + (annual coupon x (1-(1+r)-n / r)
Price = $30,000,000 / (1+10%)20+($1,800,000 x (1-(1+10%)-20/10%)
= $30,000,000/6.7275 + ($1,800,000 x 8.513564)
= $4,459,309+$15,324,414
=$19,783,723.5
1
Value of equity = share price x number of shares
= $60 x 1,000,000
= $60,000,000
Total capital = value of equity + Price + notes payable
= $60,000,000 + $19,783,723.5 + $10,000,000
= $89,783,723.54
Short term debt = notes payable / total capital
= $10,000,000 / $89,783,723.54
= 0.1114 equivalent with 11.14%
Long term debt = price / total capital
= $19,783,723.5/ 8$9,783,723.54
= 0.2203 equivalent with 22.03%
Equity = value of equity / total capital
= $60,000,000/$89,783,723.54
= 0.6683 equivalent with 66.83%
2
Problem 10-19 Multiple Rate of Return Page 488
The Ulmer Uranium Company is deciding whether or not open a strip mine whose net cost is
$4.4 million. Net cash in flows are expected to be $27.7 million, all coming at the end of Year 1.
The land must be returned to its natural state at a cost of $25 million payable at the end of Year
2.
a. Plot the project’s NPV profile
b. Should the project be accepted ir r = 8%? If r = 14%? Explain your reasoning
c. Can you think of some other capital budgeting situations in which negative cash flows
during or at the end of the project’s life might lead to multiple IRRs?
d. What is the project’s MIRR at r=8%? At r = 14%? Does the MIRR method lead to the
same accept reject decision as the NPV method?
Jawaban:
a. Plot the project’s NPV profile
Rate
NPV
0%
-$1,700,000.00
1%
-$1,481,658.66
2%
-$1,272,356.79
3%
-$1,071,693.84
4%
-$879,289.94
5%
-$694,784.58
6%
-$517,835.53
3
Rate
NPV
7%
-$348,117.74
8%
-$185,322.36
14%
$661,557.40
20%
$1,322,222.22
25%
$1,760,000.00
50%
$2,955,555.56
100%
$3,200,000.00
150%
$2,680,000.00
200%
$2,055,555.56
250%
$1,473,469.39
500%
-$477,777.78
600%
-$953,061.22
b. NPV untuk r =8% adalah -$185,322.36 sehingga project ditolak
NPV untuk r =14% adalah $661,557.40 sehingga project layak untuk diterima
Jika NPV >0 maka project layak diterima
c. Terkadang kita menemukan situasi dimana penganggaran modal yang memiliki arus kas
negatif pada akhir umur proyek sebagai contoh:
- Sewa dengan menggunakan leverage
Leverage adalah penggunaan dana utang atau pinjaman yang dipergunakan untuk
meningkatkan return atau keuntungan dalam sebuah bisnis atau investasi sehingga
jumlah nominal yang dipinjam akan dibayar pada akhir masa pakai proyek. Jumlah
yang dibayarkan pada akhirnya lebih tinggi dari pendapatan yang diperoleh dari
pinjaman. Hal ini dapat menyebabkan arus kas negatif pada akhir umur proyek.
d. MIRR
4
= MIRR(-4400000,27700000,-25000000,8%,8%)
= 7.61%
= MIRR(-4400000,27700000,-25000000,14%,14%)
= 15.58%
Ya, metode MIRR memberikan kesimpulan yang sama dengan perhitungan NPV.
Tolak project jika r=8% karena r > dari MIRR = 7.61%
Terima project jika r=14% karena r < MIRR=15.58%
5
Problem 10-20 Present Value of Cost, Page 489
The Aubey Coffee Company is evaluating the within plant distribution system for its new roasting,
grinding, and packing plant distribution system for its new roasting, grinding and packing plat.
The two alternatives are (1) a conveyor system with a high initial cost but low annual operating
costs and (2) several forklift trucks, which cost less but have considerably higher operating costs.
The decision to construct the plant has already been made and the choice here will have no effect
on the overall revenues of the project. The cost of capital for the plant is 8% and the project
expected net costs are listed in the following table:
Expected Net Cost
Year
Conveyor
Forklift
0
-$500,000
-$200,000
1
-120,000
-160,000
2
-120,000
-160,000
3
-120,000
-160,000
4
-120,000
-160,000
5
-20,000
-160,000
a. What is the IRR of each alternative?
b. What is the present value of the costs of each alternative? Which method should be
chosen?
Jawaban:
a. Menurut Ser Keng Ang et al. (2021), p. 459. IRR proyek adalah tingkat diskonto yang
memaksa PV dari arus masuk sama dengan awal biaya (atau sama dengan PV dari semua
biaya jika biaya dikeluarkan selama beberapa tahun). Ini setara untuk memaksa NPV
sama dengan nol. IRR adalah perkiraan tingkat pengembalian proyek, dan sebanding
dengan YTM pada obligasi.
IRR pada kasus ini tidak dapat tidak dapat ditentukan karena tidak ada perubahan cash
flow. Cash flow tahun 0 = cash flow tahun 1 s/d 5 yaitu -$500,000
6
b. Cost of capital: 8%
Present value=Cash flows x Present value of discounting factor(rate%,time period)
Conveyor:
Present value = future value / (1+r)n
= CF0 + CF1 +CF2+CF3+CF4+CF5
= (500,000/(1+8%)0+(120,000/(1+8%)1 + (120,000/(1+8%)2 + (120,000/(1+8%)3
+ (120,000/(1+8%)4 + (120,000/(1+8%)5
=-$500,000 - $111,111.11 - $102,880.66 - $95,259.87 - $88,203.58 - $13,611.66
=$-911,066.88
Forklift:
Present value = future value / (1+r)n
= CF0 + CF1 +CF2+CF3+CF4+CF5
= (200,000/(1+8%)0+(160,000/(1+8%)1 + (160,000/(1+8%)2 + (160,000/(1+8%)3
+ (160,000/(1+8%)4 + (160,000/(1+8%)5
=-$200,000 - $148,148.151 - $137,174.21 - $127,013.16 - $117,604.78 - $108,893.31
=$-838,833.61
7
PV biaya untuk sistem conveyor adalah =$-911,066.88, sedangkan PV biaya untuk sistem
forklift adalah $-838,833.61.
Sehingga sistem forklift diharapkan menjadi: -$838.833.61 - (-$911,066.88) = $72,233.28 lebih
murah daripada sistem konveyor, dan karenanya sistem forklift harus digunakan.
8
Problems CH11: 11-6 New Project Analysis page 533
The Campbell Company is considering adding a robotic paint sprayer to its production line.
The sprayer’s base price is $920,000, and it would cost another $20,000 to install it. The machine
falls into the MACRS 3-year class, and it would be sold after 3 years for $500,000. The MACRS
rates for the first three years are 0.333,0.4445 and 0.1481. The machine would require an increase
in net working capital (inventory) of $15,500. The Sprayer would not changes
on revenues, but it is expected to save the firm $304,000 per year in before-tax operating
costs, mainly labor. Campbell’s marginal tax rate is 25%.
a. What is the Year-0 net cash flow?)
b. What are the cash flows in Years 1, 2, and 3?
c. What is the additional Year-3 cash flow (i.e., the after-tax salvage and the return of
working capital)?
d. If the project’s cost of capital is 12%, what is the NPV?
Jawaban:
a. Year 0 net cash flow = base price + installation cost + net working capital
= $920,000 + $20,000 + $15,500
= $955,500
b. Initial cost = $920,000+$20,000
= $940,000
9
c.
Additional Year 3 cash flow = sale value - [sale value-(initial cost-total depreciation)]x tax + net
working capital
=$500,000-[$500,000–($940,000-$870,3460]x 0.25 + $15,500
=$500,000 -($500,000-$69,654 x 0.25) +$15,500
= $500,000 - $107,586.5 +$15,500
= $407,913.5
d. NPV
NPV if project cost of capital is 12% would be $60,441.11
10
Problems CH11: 11-13 Replacement Analysis, Page 535
The Everly Equipment Company’s flange lipping machine was purchased 5 years ago at a cost
for $55,000. it had an expected life of 10 years when it was bought, and its remaining
depreciationis $5,500 per year for each year of its remaining life. As older flange clippers are
robust and useful machine, this one can be sold for $20,000 at the end of its useful life.
As new high efficiency digital controlled flange lipper can be purchased for $120,000
including installation cost. During its 5 year life, it will reduce cash operating expenses by $30,000
per year, although it will not affect sales. At the end of its useful life, the high efficiency machine
is estimated to be worthless. MACRS depreciation will be used and the machine will be
depreciated rates are 33.33%, 44.45%, 14.81% and 7.41%
The old machine can be sold today for $35,000. The firm tax rate is 25% and the
appropriate cost of capital is 16%.
a. If the new flange lipper is purchased, what is the amount of the initial cash flow at year 0?
b. What are the incremental cash flow that will occur at the end of Years 1 through 5?
c. What is the NPV of this project? Should Everly replace the flange lipper?
Jawaban:
a. Depresiasi untuk 5 tahun ke depan adalah $5,500 dan biaya mesinnya $55,000
Realizable book value = Cost of the machine - (depreciation x 5)
= $55,000 - ($5,500x5)
= $27,500
Tax rate : 25%
Amount from sale of machine: $35,000
CF0=(Cost of new machine + selling price of old machine)-tax on sale of new machine
=( -$120,000+$35,000)-$1,875
= -$86,875
11
b.
Arus kas tambahan di tahun ke-5 akan menjadi nilai sisa setelah pajak dari mesin lama.
Mesin lama akan disusutkan secara penuh sehingga nilai buku mesin tersebut pada akhir
tahun ke-5 adalah $0
After tax salvage value = salvage value - (salvage value - book value) x tax rate
= $20,000 - ($20,000-$0) x 25%
= $15,000
Incremental cash flow:
CF0: -$86,875
CF1: $31,124
CF2: $34,460
CF3: $25,568
CF4: $23,348
CF5: $6,125
12
NPV = CF0 + CF1/(1+r)1+CF2/(1+r)2+CF3/(1+r)3+CF4/(1+r)4+CF5/(1+r)5
= $86,875 + $31,124/(1+16%)1+ $34,460/(1+16%)2+ $25,568/(1+16%)3+
$23,348/(1+16%)4+ $6,125/(1+16%)5
= -$2,243.152
Analisis: Jika NPV positive maka project dapat diterima, namun karena hasil perhitungan
NPV adalah -$2,243.152 sehingga penggantian mesin flange lipper seharusnya tidak
dilakukan
12-5 Long Term Financing Needed Page 577
At year-end 2010, Wallace Landscaping’s total assets were $2.17 million and its accounts
payable were $560,000. Sales, which in 2019 were $3.5 million, are expected to increase
13
by 35% in 2020. Total assets and accounts payable are proportional to sales, and that
relationship will be maintained. Wallace typically uses no current liabilities other than
accounts payable. Common stock amounted to $625,000 in 2019, and retained earnings
were $395,000. Wallace has arranged to sell $195,000 of new common stock in 2020 to
meet some of its financing needs. The remainder of its financing needs will be met by
issuing new long-term debt at the end of 2020. (Because the debt is added at the end of the
year, there will be no additional interest expense due to the new debt.) Its profit margin on
sales is 5%, and 45% of earnings will be paid out as dividends.
a. What were Wallace’s total long-term debt and total liabilities in 2019?
b. How much new long-term debt financing will be needed in 2020?
(Hint: AFN − New stock = New long-term debt.)
Jawaban:
Account payable : $560,000
Common stock :$625,000
Retained earnings: $395,000
Total assets = account payable + long term debt + common stock + retained earnings
$2,170,000 = $560,000 + long term debt + $625,000 + $395,000
a. Long term debt = $2,170,000 - ( $560,000+ $625,000 + $395,000)
= $2,170,000 - $1,150,000
= $590,000
Total assets = Total liabilities + Total shareholder equity
$2,170,000 = Total liabilities + (common stock + retained earnings)
$2,170,000 = Total liabilities + ($1,020,000)
Total liabilities = $2,170,000 - $1,020,000
= $1,150,000
b. Increase by 35%.
Asset in 2017= $2,170,000x135%= $2,929,500
accounts payable in 2016= $560,000x135%= $756,000
Total Sales in 2017 = $3,500,000x135%= $4,725,000
Profit margin = 5% of sales
= 5% x $4,725,000
= $236,250
45% is dividend therefore income after dividend = $236,250 x 55%
= $129,937.5
Retained earnings = beginning retained earnings +income after dividend paid
= $395,000 + $129,937.5
14
= $524,937.5
Long term liabilities= Asset- short term liabilities- equity
= Assets - account payable - equity
= $2,929,500 - $756,000 - ($524,937.5 +$ 625,000+ $195,000)
= $2,929,500 - $756,000 - $1,344,937.5
=$828,563
Wallace already had long term liabilities of $590,000
Additional Fund Needed (AFN)= $828,563-$590,000
= $238,563
Problem 12-7 Forecasted Statements and Ratios page 577-578
Upton Computers makes bulk purchases of small computers, stocks them in conveniently located
warehouses, ships them to its chain of retail stores, and has a staff to advise customers and help
15
them set up their new computers. Upton’s balance sheet as of December 31, 2019, is shown here
(millions of dollars):
Cash
$ 3.5 Account payable
$9.0
Receivables
26.0 Notes payable
18.0
Inventories
58.0 Line of credit
0
Accruals
Total current assets
Net fixed Assets
$87.5
8.5
Total current liabilities
$35.5
35.0 Mortgage loan
6.0
Common stock
15.0
Retained earnings
Total assets
$122.5
Total liabilities and equities
66
$122.5
Sales for 2019 were $350 million and net income for the year was $10.5 million, so the firm’s
profit margin was 3.0%. Upton paid dividends of $4.2 million to common stockholders, so its
payout ratio was 40%. Its tax rate is 25%, and it operated at full capacity. Assume that all
assets/sales ratios, spontaneous liabilities/sales ratios, the profit margin, and the payout ratio
remain constant in 2020.
a. If sales are projected to increase by $70 million, or 20%, during 2020, use the AFN
equation to determine Upton’s projected external capital requirements.
b. Using the AFN equation, determine Upton’s self-supporting growth rate. That is, what is
the maximum growth rate the firm can achieve without having to employ nonspontaneous
external funds?
c. Use the forecasted financial statement method to forecast Upton’s balance sheet for
December 31, 2020. Assume that all additional external capital is raised as a bank loan at
the end of the year and is reflected in notes payable (because the debt is added at the end
of the year, there will be no additional interest expense due to the new debt). Assume
Upton’s profit margin and dividend payout ratio will be the same in 2020 as they were in
2019. What is the amount of notes payable reported on the 2020 forecasted balance
sheets? (Hint: You don’t need to forecast the income statements because you are given
the projected sales, profit margin, and dividend payout ratio; these figures allow you to
calculate the 2020 addition to retained earnings for the balance sheet.)
Jawaban :
a. Current level of assets = $122.50
Changes in sales = $420 - $350 = $70
16
Beginning Sales Level = $350
Current level of liabilities = Account payable + Accruals = $9.0 + $8.5 = $17.5
New level of sales = $ 420
Profit margin = 3%
Payout ratio = 40%
AFN =
Current level of assets x Changes in sales
Beginning Sales Level
- Current level of liabilities x Changes in sales
Beginning Sales Level
- New level of sales x Profit margin x (1 - Payout ratio)
AFN = $122.50 x $420 - $350 - $17.5 x $420 - $350 - $ 420 x 3% x 60%
$350
$350
= $ 24.5 - $ 3.5 - $7.56
= $13.44
So, the additional fund that needed by Upton company in 2017 is 13.44 million.
b. M
POR
So
Ao
Lo
= Profit Margin
= Payout Ratio
= Sales Ratio
= Current Level of Asset
= Current Level of Liabilities
Self supporting g
=
M (1 - POR) (So)
Ao x Lo - M (1 - POR) (So)
=
3% x 60% x $350
$122.5 - $17.5- (3% x 60% x $350)
= $6.3
$105-$6.3
= $6.3
$98.7
= 6.38%
c. Forecasted 2020
Cash $ 3.5 x 120%
$ 4.2 Account payable $9.0 x 120%
$10.8
17
Receivables 26 x 120%
31.2 Notes payable
18.0
Inventories 58.0 x 120%
69.6 Line of credit
13.44
Accruals 8.5 x 120%
Total current assets
Net fixed Assets 35.0 x 120%
$105
Total current liabilities
10.2
$52.44
42 Mortgage loan
6.0
Common stock
15.0
Retained earnings (66 + 7.56)
Total assets
Line of credit 2020
$147
73.56
Total liabilities and equities
$147
= $13.44
18