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New
heritage
case
新文物箱

Capital Budgeting  資本預算

MGMT 408: Foundations of Finance Tyler Muir
MGMT 408: 財務基礎 Tyler Muir

Introduction to Capital Budgeting
資本預算簡介

Big picture question  大圖問題
What is the goal of a firm?
公司的目標是什麼？
make money  生財
societal good  社會公益
mission statement  使命聲明
spend money efficiently max ROI
有效運用資金，達到最大 ROI
Create Value for sharehoiders
為分享者創造價值
Prob of Success Capital budgeting “Pagback period” Givel these goals, how should firens choose projects in which to invest? ↑ ↑ uarr\uparrow
成功的概率 資本預算「Pagback period」 給出這些目標，firens 應該如何選擇投資的專案？ ↑ ↑ uarr\uparrow
Diversity time to breakeven
多樣性達到收支平衡的時間
ROI  投資回報率
No loss ~ minimize loss seasonality 4 case! How to fund them?
不虧損 ~ 盡量減少虧損的季節性 4 案例！如何提供資金？
Debt / equity, /internal funds?
債務/股票/內部資金？
Choals a bruad awareness market share maximize Value ∼ N P V ∼ N P V ∼NPV\sim N P V
選擇一個bruad意識市場份額最大化價值 ∼ N P V ∼ N P V ∼NPV\sim N P V 。

How can we use the concept of present value to make better decisions?
我們如何使用現值的概念來做出更好的決策？

■ Many decisions (e.g. to invest in a new project or not) come down to a trade-off between costs and benefits.
許多決策 (例如是否投資新專案) 都需要在成本與效益之間權衡取捨。
  • Take actions for which the benefits outweigh the costs
    採取利大於弊的行動
■ These costs and benefits often occur at different points in time.
這些成本和效益通常發生在不同的時間點。
  • Present value gives a consistent measure for such costs and benefits.
    現值為此類成本和效益提供了一致的衡量標準。
  • Net Present Value (NPV): The present value of benefits minus the present of value of costs
    淨現值 (NPV)：效益的現值減去成本的現值

Learning objectives  學習目標

Goal:
How should firms invest their capital?
目標：公司應如何投資資本？

  • Fundamentals of Capital Budgeting
    資本預算基礎
■ The NPV Rule
NPV 規則
  • Free Cash Flow  自由現金流
■ Capital Budgeting in Practice
資本預算實務
  • Building the cash flow pro forma
    建立現金流量預測
■ Alternatives to the NPV Rule
NPV 規則的替代方案
  • Profitability Index  獲利指數
■ Internal Rate of Return
內部回報率
  • Payback Period  回本期

Warm up case: HG Surfboards
熱身箱HG 衝浪板

Rob HG owns a surfboard company and has $ 1 $ 1 $1\$ 1 million to invest in one of two projects:
Rob HG 擁有一間衝浪板公司，並擁有 $ 1 $ 1 $1\$ 1 百萬元投資在兩個專案中的其中一個：
Option 1: The Custom Surfboard Machine HG currently holds a patent for a machine that can rapidly produce custom surfboards and be installed in any surf shop in the world. The technology combines a computer controlled (C&C) router with a new automated epoxy resin based fiberglassing module for a one-button production process. Rob estimates that by investing $ 150 K $ 150 K $150K\$ 150 \mathrm{~K} today he can develop the technology into a working prototype in one year. At the end of the year, he projects that he would be able to sell the technology to Firewire Surfboards (a larger surfboard manufacturer) for $ 480 K $ 480 K $480K\$ 480 \mathrm{~K}.
方案 1：客製化衝浪板機器 HG 目前擁有一種機器的專利，該機器可快速生產客製化衝浪板，並可安裝在世界上任何一家衝浪板店。該技術結合了電腦控制 (C&C) 刳刨機與新型自動化環氧樹脂基玻璃纖維模組，可實現一鍵式生產流程。Rob 估計，只要今天投資 $ 150 K $ 150 K $150K\$ 150 \mathrm{~K} ，他就能在一年內將這項技術發展成工作原型。到了年底，他預計可以 $ 480 K $ 480 K $480K\$ 480 \mathrm{~K} 的價格將這項技術賣給 Firewire Surfboards（一間較大的衝浪板製造商）。

Warm up case: HG Surfboards
熱身箱HG 衝浪板

Option 2: Retail Outlet HG Surfboards currently does not have a retail outlet, preferring to sell its quality surfboards exclusively over the internet. However, following the lead of other boutique internet brands like Warby Parker and Bonobos, Rob thinks that a bricks and mortar location in Venice Beach could do a lot to help him market his boards. He estimates that by investing $ 550 K $ 550 K $550K\$ 550 \mathrm{~K} today he could develop a retail shop. To keep his focus on designing great boards, he would sell the shop in one year for a price of $ 780 K $ 780 K $780K\$ 780 \mathrm{~K}. For simplicity, assume that the sales price includes the added profits that HG will get from selling more boards.
方案 2：零售店 HG Surfboards 目前沒有零售店，只選擇在網路上銷售高品質的衝浪板。然而，Rob 認為，效仿 Warby Parker 和 Bonobos 等其他精品網路品牌，在威尼斯海灘開設一家實體店面可以大大幫助推廣他的衝浪板。他估計，只要今天投資 $ 550 K $ 550 K $550K\$ 550 \mathrm{~K} ，他就可以發展一家零售店。為了讓他專注於設計很棒的衝浪板，他將在一年內以 $ 780 K $ 780 K $780K\$ 780 \mathrm{~K} 的價格賣掉這家店。為了簡單起見，假設銷售價格包含 HG 因銷售更多木板而獲得的額外利潤。

Warm up case: HG Surfboards
熱身箱HG 衝浪板

The opportunity cost of Rob’s time Rob estimates that either Option 1 or 2 will be a full time job for him and the opportunity cost of his time for a year of work is $ 150 K $ 150 K $150K\$ 150 \mathrm{~K} in present value terms. Also, because either project would take up all his time, he can’t do both.
Rob 的時間機會成本 Rob 估計，無論是方案 1 還是方案 2，對他來說都是一份全職工作，以現值計算，他工作一年的時間機會成本為 $ 150 K $ 150 K $150K\$ 150 \mathrm{~K} 。此外，由於任一個專案都會佔據他所有的時間，因此他無法兩者兼顧。

Warm up case: HG Surfboards
熱身箱HG 衝浪板

Assume that Rob faces the interest rate of 20 % 20 % 20%20 \%, in other words that he can borrow and lend at 20%
假設 Rob 面臨 20 % 20 % 20%20 \% 的利率，換句話說，他可以以 20% 的利率借貸
  • Which project should Rob choose and why?
    Rob 應該選擇哪個專案，為什麼？
  • Should Rob just use the cash he has to buy a house for $ 1 $ 1 $1\$ 1 million on Kauai instead of growing his company? Why or why not? Assume the house creates zero financial NPV (but provides some emotional benefit).
    Rob 應該直接用他手頭的現金在考愛島上花 $ 1 $ 1 $1\$ 1 百萬元買一棟房子，而不是發展他的公司嗎？為什麼？假設這棟房子創造的財務淨現值為零（但提供一些情感上的好處）。

Buying the vacation home
購買度假屋

■ Rob should create the most value for his company in terms of NPV.
從淨現值的角度來看，Rob 應該為他的公司創造最大的價值。
■ We’ve assumed the house creates zero NPV for the company.
我們假設這棟房子為公司創造的淨現值為零。
  • That doesn’t mean he shouldn’t buy the house! He can then borrow against the value he has created investing in positive NPV projects to finance the purchase.
    這並不表示他不應該買這棟房子！然後，他可以利用投資正 NPV 專案所創造的價值來借款，為購屋提供資金。
  • By using his opportunity cost of capital in our calculations, we’ve taken into account the cost the borrowing will impose on Rob.
    透過在計算中使用他的資本機會成本，我們已經考慮到借貸對 Rob 造成的成本。
  • THe $1M that Rob has in cash doesn’t actually affect any of the decisions that Rob has to make.
    羅伯持有的 100 萬美元現金實際上不會影響羅伯必須做出的任何決策。

Fundamentals of Capital Budgeting
資本預算基礎

The NPV rule  NPV 規則

NPV Investment Rule: When making an investment decision, take the option with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.
NPV 投資規則：做出投資決策時，選擇淨現值最高的方案。選擇此選項等於今天以現金收取其淨現值。

The NPV rule and Free Cash Flow
淨現值規則和自由現金流

Need to apply the formula
需要套用公式
N P V = P V ( Benefits ) − P V ( Costs ) N P V = P V (  Benefits  ) − P V (  Costs  ) NPV=PV(" Benefits ")-PV(" Costs ")N P V=P V(\text { Benefits })-P V(\text { Costs })
But how do we quantify (measure) benefits and costs?
但我們如何量化（衡量）效益與成本？

The NPV rule and Free Cash Flow
淨現值規則和自由現金流

Need to apply the formula
需要套用公式
N P V = P V ( Benefits ) − P V ( Costs ) N P V = P V (  Benefits  ) − P V (  Costs  ) NPV=PV(" Benefits ")-PV(" Costs ")N P V=P V(\text { Benefits })-P V(\text { Costs })
But how do we quantify (measure) benefits and costs?
但我們如何量化（衡量）效益與成本？
Free Cash Flow: The incremental effect of a project on the firm’s available cash.
自由現金流： 項目對公司可用現金的增量影響。
F C F = ( Revenues - Costs - Depreciation ) ( 1 − τ c ) ⏞ unlevered net income IIfau ′ ′ corp. tax rate r=0.2 ( 1 − y ) = 0.8 F C F = (  Revenues - Costs - Depreciation  ) 1 − τ c ⏞ unlevered net income   IIfau  ′ ′ corp.   tax rate   r=0.2  ( 1 − y ) = 0.8 {:[{:FCF= obrace((" Revenues - Costs - Depreciation ")(1-tau_(c)))^("unlevered net income ")" IIfau "^('')_("corp. ")" tax rate ":}],[" r=0.2 "],[(1-y)=0.8]:}\begin{aligned} & \begin{aligned} F C F= & \overbrace{(\text { Revenues - Costs - Depreciation })\left(1-\tau_{c}\right)}^{\text {unlevered net income }} \text { IIfau }{ }^{\prime \prime}{ }_{\text {corp. }} \text { tax rate } \end{aligned} \\ & \text { r=0.2 } \\ & (1-y)=0.8 \end{aligned}
Should these be included? Why or why not?
是否應該包含這些內容？為什麼或為什麼不？
in the discount rate (in week 8-9)
中的貼現率（在第 8-9 周）
Net working capital (NWC)
淨營運資金 (NWC)
Net Working Capital is defined as
淨營運資金定義為
N W C = Cash + Inventory + Recievables − Payables N W C =  Cash  +  Inventory  +  Recievables  −  Payables  NWC=" Cash "+" Inventory "+" Recievables "-" Payables "N W C=\text { Cash }+ \text { Inventory }+ \text { Recievables }- \text { Payables }
Why remove changes in NWC, as given by
為什麼要移除 NWC 中的變更，如下所示
Δ N W C t = N W C t − N W C t − 1 Δ N W C t = N W C t − N W C t − 1 Delta NWC_(t)=NWC_(t)-NWC_(t-1)\Delta N W C_{t}=N W C_{t}-N W C_{t-1},
from unlevered net income? Change in NWC
來自非平均淨收入？NWC 變化
Cash tied up in project
項目中的現金結存
receirables ∼ ∼ ∼\sim sale but hasn 4 come in as W 2 W 2 W^(2)W^{2}
應收帳款 ∼ ∼ ∼\sim 銷售，但尚未以 W 2 W 2 W^(2)W^{2} 進帳。

Coca-Cola Energy Drink Case
可口可樂能量飲料案例

Applying Capital Budgeting Techniques
應用資本預算技術

  • Take a moment and read the document “Capital Budgeting Minicase: The Coca-Cola Company Energy Drink”
    花點時間閱讀「資本預算迷你案例」文件：可口可樂公司能量飲料"
  • Download the excel template “coke_template.xlsx”
    下載 excel 範本 "coke_template.xlsx"

Steps to calculate NPV
計算 NPV 的步驟

Use the template, it will make your life easier!
使用範本，它會讓您的生活更輕鬆！
1 Project Sales, COGS, SG&A, Depreciation using assumptions given in case
1 計劃銷售額、COGS、SG&A、折舊，使用案例中的假設。
12 Calculate:  12 計算：
  • EBIT (Earnings Before Interest and Taxes)
    EBIT（息稅前盈利）
  • Taxes  稅項
■ Unlevered Net Income  非平均淨收入
3 Project NWC and △ N W C △ N W C /_\NWC\triangle N W C
3 NWC 項目和 △ N W C △ N W C /_\NWC\triangle N W C
4 Calculate FCF  4 計算 FCF
5 Discount FCF to get NPV
5 折現 FCF 以獲得 NPV
Y e s N P r > 0 Y e s N P r > 0 {:[Yes],[NPr > 0]:}\begin{aligned} & Y e s \\ & N P r>0 \end{aligned}

Projecting Sales  預測銷售額

Sales Projections  銷售預測

End of Year  年終
0 1
Units Sold (in 000's)
銷售單位 (單位：千)		 5000
Avg. Price Per Unit
平均值每單位價格		 $ 1.60 $ 1.60 $1.60\$ 1.60
Sales (in 0 0 0\boldsymbol{0} 000s)
銷售額 (單位： 0 0 0\boldsymbol{0} 000s)		 $ 8 , 000 $ 8 , 000 $8,000\$ 8,000 = = == Units Sold*Avg Price Per Unit
= = == 銷售單位*每單位平均價格
End of Year 0 1 Units Sold (in 000's) 5000 Avg. Price Per Unit $1.60 Sales (in 0 000s) $8,000 = Units Sold*Avg Price Per Unit| | End of Year | | | :--- | :---: | ---: | | | 0 | 1 | | Units Sold (in 000's) | | 5000 | | Avg. Price Per Unit | $\$ 1.60$ | | | Sales (in $\boldsymbol{0}$ 000s) | $\$ 8,000$ | $=$ Units Sold*Avg Price Per Unit |

Projecting Costs  預測成本

Cash Flow Pro Forma
現金流量預估

End of Year  年終
0 1
Sales (in $000s)  銷售額（千美元） $ 8 , 000 $ 8 , 000 $8,000\$ 8,000
Cost of Goods Sold
銷售成本		 $ 6 , 000 = ( 1 − $ 6 , 000 = 1 − $6,000=(1-:}\$ 6,000=\left(1-\right. Gross Profit Margin) ⋆ ⋆ ^(***){ }^{\star} Sales
$ 6 , 000 = ( 1 − $ 6 , 000 = 1 − $6,000=(1-:}\$ 6,000=\left(1-\right. 毛利率） ⋆ ⋆ ^(***){ }^{\star} 銷售額
Gross Profit  毛利 $ 2 , 000 = $ 2 , 000 = $2,000=\$ 2,000= Sales - COGS   $ 2 , 000 = $ 2 , 000 = $2,000=\$ 2,000= 銷售 - COGS
SG&A $ 480 = 6 % ∗ $ 480 = 6 % ∗ $480=6%^(**)\$ 480=6 \%{ }^{*} Sales   $ 480 = 6 % ∗ $ 480 = 6 % ∗ $480=6%^(**)\$ 480=6 \%{ }^{*} 銷售
Depreciation  折舊 $ 1 , 000 = $ 1 , 000 = $1,000=\$ 1,000= CAPEX/# Years of Depreciation
$ 1 , 000 = $ 1 , 000 = $1,000=\$ 1,000= 資本支出/#折舊年數
End of Year 0 1 Sales (in $000s) $8,000 Cost of Goods Sold $6,000=(1-:} Gross Profit Margin) ^(***) Sales Gross Profit $2,000= Sales - COGS SG&A $480=6%^(**) Sales Depreciation $1,000= CAPEX/# Years of Depreciation | | End of Year | | | :--- | :--- | :--- | | | 0 | 1 | | Sales (in $000s) | $\$ 8,000$ | | | Cost of Goods Sold | $\$ 6,000=\left(1-\right.$ Gross Profit Margin) ${ }^{\star}$ Sales | | | Gross Profit | $\$ 2,000=$ Sales - COGS | | | SG&A | $\$ 480=6 \%{ }^{*}$ Sales | | | Depreciation | $\$ 1,000=$ CAPEX/# Years of Depreciation | |

Calculating EBIT, Taxes, and UNI
計算 EBIT、稅項和 UNI

Cash Flow Pro Forma
現金流量預估
End of Year  年終
0 1 0 1 0quad10 \quad 1
Sales (in $ 000s)
銷售額（千美元）		 $8,000
Cost of Goods Sold
銷售成本		 $6,000
Gross Profit  毛利 $2,000
SG&A $480
Depreciation  折舊 $1,000
EBIT $520.00 =Gross Profit - SG&A - Depreciation
= 毛利 - SG&A - 折舊
Taxes  稅項 $ 208.00 =Corporate Tax Rate * EBIT
= 公司稅率 * EBIT
Unlevered Net Income  非槓桿淨收入 $312.00 =EBIT-Taxes
Cash Flow Pro Forma End of Year 0quad1 Sales (in $ 000s) $8,000 Cost of Goods Sold $6,000 Gross Profit $2,000 SG&A $480 Depreciation $1,000 EBIT $520.00 =Gross Profit - SG&A - Depreciation Taxes $ 208.00 =Corporate Tax Rate * EBIT Unlevered Net Income $312.00 =EBIT-Taxes| Cash Flow Pro Forma | | | | :---: | :---: | :---: | | | End of Year | | | | $0 \quad 1$ | | | Sales (in $ 000s) | $8,000 | | | Cost of Goods Sold | $6,000 | | | Gross Profit | $2,000 | | | SG&A | $480 | | | Depreciation | $1,000 | | | EBIT | $520.00 | =Gross Profit - SG&A - Depreciation | | Taxes | $ 208.00 | =Corporate Tax Rate * EBIT | | Unlevered Net Income | $312.00 | =EBIT-Taxes |

Projecting NWC and △ △ /_\\triangle NWC
預測 NWC 和 △ △ /_\\triangle NWC

Net Working Capital Projections
淨營運資金預測

End of Year  年終
0 1
0 $ 160 $ 160 $160\$ 160
= 2 % ∗ = 2 % ∗ =2%**=2 \% * Sales   = 2 % ∗ = 2 % ∗ =2%**=2 \% * 銷售
Cash  現金 0 $ 240 = 3 % ∗ $ 240 = 3 % ∗ $240=3%**\$ 240=3 \% * Sales   $ 240 = 3 % ∗ $ 240 = 3 % ∗ $240=3%**\$ 240=3 \% * 銷售
Inventory  庫存 0 $ 1 , 200 = 15 % ∗ $ 1 , 200 = 15 % ∗ $1,200=15%^(**)\$ 1,200=15 \%{ }^{*} Sales   $ 1 , 200 = 15 % ∗ $ 1 , 200 = 15 % ∗ $1,200=15%^(**)\$ 1,200=15 \%{ }^{*} 銷售
Recievables  可回收物品 0 $ 900 = 15 % ∗ $ 900 = 15 % ∗ $900=15%^(**)\$ 900=15 \%{ }^{*} COGS
Payables  應付款項 0 $ 700.00 = $ 700.00 = $700.00=\$ 700.00= Cash + Inventory+Recievables-Payables
$ 700.00 = $ 700.00 = $700.00=\$ 700.00= 現金+存貨+應收賬款-應付賬款
Net Working Capital  淨營運資金 $ 700.00 = $ 700.00 = $700.00=\$ 700.00= NWC(EOY) - NWC(EOY-1)
Increase in NWC  增加 NWC
End of Year 0 1 0 $160 =2%** Sales Cash 0 $240=3%** Sales Inventory 0 $1,200=15%^(**) Sales Recievables 0 $900=15%^(**) COGS Payables 0 $700.00= Cash + Inventory+Recievables-Payables Net Working Capital $700.00= NWC(EOY) - NWC(EOY-1) Increase in NWC | | End of Year | | | :--- | :---: | :---: | | | 0 | 1 | | | 0 | $\$ 160$ | | $=2 \% *$ Sales | | | | Cash | 0 | $\$ 240=3 \% *$ Sales | | Inventory | 0 | $\$ 1,200=15 \%{ }^{*}$ Sales | | Recievables | 0 | $\$ 900=15 \%{ }^{*}$ COGS | | Payables | 0 | $\$ 700.00=$ Cash + Inventory+Recievables-Payables | | Net Working Capital | | $\$ 700.00=$ NWC(EOY) - NWC(EOY-1) | | Increase in NWC | | |

Projecting Free Cash Flow and PV of FCF
預測自由現金流和 FCF 的 PV

Cash Flow Pro Forma
現金流量預估

End of Year  年終
0 1
Sales (in $ 000 $ 000 $000\$ 000 s)  銷售額（以 $ 000 $ 000 $000\$ 000 秒為單位） $ 8 , 000 $ 8 , 000 $8,000\$ 8,000
Cost of Goods Sold
銷售成本		 $ 6 , 000 $ 6 , 000 $6,000\$ 6,000
Gross Profit  毛利 $ 2 , 000 $ 2 , 000 $2,000\$ 2,000
SG&A $ 480 $ 480 $480\$ 480
Depreciation  折舊 $ 1 , 000 $ 1 , 000 $1,000\$ 1,000
EBIT $ 520.00 $ 520.00 $520.00\$ 520.00
Taxes  稅項 $ 208.00 $ 208.00 $208.00\$ 208.00
Unlevered Net Income  非槓桿淨收入 $ 312.00 $ 312.00 $312.00\$ 312.00
Depreciation  折舊 $ 1 , 000 $ 1 , 000 $1,000\$ 1,000
Capital Expenditures  資本支出 5,000
Increase in NWC  增加 NWC $ 700.00 $ 700.00 $700.00\$ 700.00
Free Cash Flow  自由現金流 − 5 , 000 − 5 , 000 -5,000-5,000 612
PV(FCF) − 5 , 000 − 5 , 000 -5,000-5,000 556 = 556 = 556=556= FCF/
End of Year 0 1 Sales (in $000 s) $8,000 Cost of Goods Sold $6,000 Gross Profit $2,000 SG&A $480 Depreciation $1,000 EBIT $520.00 Taxes $208.00 Unlevered Net Income $312.00 Depreciation $1,000 Capital Expenditures 5,000 Increase in NWC $700.00 Free Cash Flow -5,000 612 PV(FCF) -5,000 556= FCF/| | End of Year | | | :--- | :--- | ---: | | | 0 | 1 | | Sales (in $\$ 000$ s) | $\$ 8,000$ | | | Cost of Goods Sold | | $\$ 6,000$ | | Gross Profit | $\$ 2,000$ | | | SG&A | $\$ 480$ | | | Depreciation | $\$ 1,000$ | | | EBIT | $\$ 520.00$ | | | Taxes | $\$ 208.00$ | | | Unlevered Net Income | $\$ 312.00$ | | | Depreciation | $\$ 1,000$ | | | Capital Expenditures | 5,000 | | | Increase in NWC | | $\$ 700.00$ | | Free Cash Flow | $-5,000$ | 612 | | PV(FCF) | $-5,000$ | $556=$ FCF/ |

The completed Pro Forma
已完成的備考

Cash Flow Pro Forma
現金流量預估
End of Year  年終
0 1 2 3 4 5
Sales (in $ 000s)
銷售額（千美元）		 $8,000 $11,200 $17,500 $14,000 $7,000
Cost of Goods Sold
銷售成本		 $6,000 $8,400 $13,125 $10,500 $5,250
Gross Profit  毛利 $2,000 $2,800 $4,375 $3,500 $1,750
SG&A $480 $672 $1,050 $840 $420
Depreciation  折舊 $1,000 $1,000 $1,000 $1,000 $1,000
EBIT $520.00 $1,128.00 $2,325.00 $1,660.00 $330.00
Taxes  稅項 $208.00 $ 451.20 $930.00 $664.00 $132.00
Unlevered Net Income  非槓桿淨收入 $312.00 $ 676.80 $1,395.00 $996.00 $198.00
Depreciation  折舊 $1,000 $1,000 $1,000 $1,000 $1,000
Capital Expenditures  資本支出 5,000
Increase in NWC  增加 NWC $700.00 $280.00 $551.25 - $ 306.25 $ 306.25 $306.25\$ 306.25 - 1 1,225.00
Free Cash Flow  自由現金流 -5,000 612 1,397 1,844 2,302 2,423
PV(FCF) -5,000 556 1,154 1,385 1,572 1,504
NPV 1,173 M(PV(FCF)
End of Year 0 1 2 3 4 5 Sales (in $ 000s) $8,000 $11,200 $17,500 $14,000 $7,000 Cost of Goods Sold $6,000 $8,400 $13,125 $10,500 $5,250 Gross Profit $2,000 $2,800 $4,375 $3,500 $1,750 SG&A $480 $672 $1,050 $840 $420 Depreciation $1,000 $1,000 $1,000 $1,000 $1,000 EBIT $520.00 $1,128.00 $2,325.00 $1,660.00 $330.00 Taxes $208.00 $ 451.20 $930.00 $664.00 $132.00 Unlevered Net Income $312.00 $ 676.80 $1,395.00 $996.00 $198.00 Depreciation $1,000 $1,000 $1,000 $1,000 $1,000 Capital Expenditures 5,000 Increase in NWC $700.00 $280.00 $551.25 - $306.25 - 1 1,225.00 Free Cash Flow -5,000 612 1,397 1,844 2,302 2,423 PV(FCF) -5,000 556 1,154 1,385 1,572 1,504 NPV 1,173 M(PV(FCF) | | End of Year | | | | | | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | | 0 | 1 | 2 | 3 | 4 | 5 | | Sales (in $ 000s) | | $8,000 | $11,200 | $17,500 | $14,000 | $7,000 | | Cost of Goods Sold | | $6,000 | $8,400 | $13,125 | $10,500 | $5,250 | | Gross Profit | | $2,000 | $2,800 | $4,375 | $3,500 | $1,750 | | SG&A | | $480 | $672 | $1,050 | $840 | $420 | | Depreciation | | $1,000 | $1,000 | $1,000 | $1,000 | $1,000 | | EBIT | | $520.00 | $1,128.00 | $2,325.00 | $1,660.00 | $330.00 | | Taxes | | $208.00 | $ 451.20 | $930.00 | $664.00 | $132.00 | | Unlevered Net Income | | $312.00 | $ 676.80 | $1,395.00 | $996.00 | $198.00 | | Depreciation | | $1,000 | $1,000 | $1,000 | $1,000 | $1,000 | | Capital Expenditures | 5,000 | | | | | | | Increase in NWC | | $700.00 | $280.00 | $551.25 | - $\$ 306.25$ | - 1 1,225.00 | | Free Cash Flow | -5,000 | 612 | 1,397 | 1,844 | 2,302 | 2,423 | | PV(FCF) | -5,000 | 556 | 1,154 | 1,385 | 1,572 | 1,504 | | NPV | 1,173 | M(PV(FCF) | | | | |
Coca-cola Energy Drink Case - Mutually exclusive production technologies Which production technology should Coca-cola use? Why?
Coca-cola Energy Drink 個案 - 相互排斥的生產技術 Coca-cola 應該使用哪種生產技術？為什麼？
2ad one Greater NPV
2ad 一個更大的 NPV

Which production technology to choose?
選擇何種生產技術？

Cash Flow Pro Forma - Alternative Production Process
現金流量預測 - 替代生產流程

End of Year  年終
0 1 2 3 4 5
Sales (in $000s)  銷售額（千美元） $8,000 $11,200 $17,500 $14,000 $7,000
Cost of Goods Sold
銷售成本		 $6,400 $8,960 $12,250 $9,800 $4,900
Gross Profit  毛利 $1,600.00 $2,240.00 $5,250.00 $4,200.00 $2,100.00
SG&A $480 $672 $1,050 $840 $420
Depreciation  折舊 $1,000 $1,000 $1,000 $1,000 $1,000
EBIT $120.00 $568.00 $3,200.00 $2,360.00 $680.00
Taxes  稅項 $48.00 $227.20 $1,280.00 $944.00 $272.00
Unlevered Net Income  非槓桿淨收入 $72.00 $340.80 $1,920.00 $1,416.00 $408.00
Depreciation  折舊 $1,000 $1,000 $1,000 $1,000 $1,000
Capital Expenditures  資本支出 5,000
Increase in NWC  增加 NWC $640.00 $256.00 $766.50 - $ 332.50 $ 332.50 $332.50\$ 332.50 - $ 1,330.00
Free Cash Flow  自由現金流 -5,000 432 1,085 2,154 2,749 2,738
PV(FCF) -5,000 393 897 1,618 1,877 1,700
NPV 1,485
End of Year 0 1 2 3 4 5 Sales (in $000s) $8,000 $11,200 $17,500 $14,000 $7,000 Cost of Goods Sold $6,400 $8,960 $12,250 $9,800 $4,900 Gross Profit $1,600.00 $2,240.00 $5,250.00 $4,200.00 $2,100.00 SG&A $480 $672 $1,050 $840 $420 Depreciation $1,000 $1,000 $1,000 $1,000 $1,000 EBIT $120.00 $568.00 $3,200.00 $2,360.00 $680.00 Taxes $48.00 $227.20 $1,280.00 $944.00 $272.00 Unlevered Net Income $72.00 $340.80 $1,920.00 $1,416.00 $408.00 Depreciation $1,000 $1,000 $1,000 $1,000 $1,000 Capital Expenditures 5,000 Increase in NWC $640.00 $256.00 $766.50 - $332.50 - $ 1,330.00 Free Cash Flow -5,000 432 1,085 2,154 2,749 2,738 PV(FCF) -5,000 393 897 1,618 1,877 1,700 NPV 1,485 | | End of Year | | | | | | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | | 0 | 1 | 2 | 3 | 4 | 5 | | Sales (in $000s) | | $8,000 | $11,200 | $17,500 | $14,000 | $7,000 | | Cost of Goods Sold | | $6,400 | $8,960 | $12,250 | $9,800 | $4,900 | | Gross Profit | | $1,600.00 | $2,240.00 | $5,250.00 | $4,200.00 | $2,100.00 | | SG&A | | $480 | $672 | $1,050 | $840 | $420 | | Depreciation | | $1,000 | $1,000 | $1,000 | $1,000 | $1,000 | | EBIT | | $120.00 | $568.00 | $3,200.00 | $2,360.00 | $680.00 | | Taxes | | $48.00 | $227.20 | $1,280.00 | $944.00 | $272.00 | | Unlevered Net Income | | $72.00 | $340.80 | $1,920.00 | $1,416.00 | $408.00 | | Depreciation | | $1,000 | $1,000 | $1,000 | $1,000 | $1,000 | | Capital Expenditures | 5,000 | | | | | | | Increase in NWC | | $640.00 | $256.00 | $766.50 | - $\$ 332.50$ | - $ 1,330.00 | | Free Cash Flow | -5,000 | 432 | 1,085 | 2,154 | 2,749 | 2,738 | | PV(FCF) | -5,000 | 393 | 897 | 1,618 | 1,877 | 1,700 | | NPV | 1,485 | | | | | |
Higher NPV, you should choose this process!
較高的 NPV，您應該選擇此流程！

Using one alternative as an opportunity cost of the other
將一種選擇作為另一種選擇的機會成本

Free Cash Flow of Alternative Process with Free Cash Flow of Original Process as an Opportunity Cost
替代製程的自由現金流量與原始製程的自由現金流量作為機會成本
0 End of Year  年終
0 2 3 4 5
FCF of alternive production process
替代生產流程的 FCF		 − $ 5 , 000 − $ 5 , 000 -$5,000-\$ 5,000 $ 432 $ 432 $432\$ 432 $ 1 , 085 $ 1 , 085 $1,085\$ 1,085 $ 2 , 154 $ 2 , 154 $2,154\$ 2,154 $ 2 , 749 $ 2 , 749 $2,749\$ 2,749 $ 2 , 738 $ 2 , 738 $2,738\$ 2,738
Less: FCF of original process
減去原始流程的 FCF		 − $ 5 , 000 − $ 5 , 000 -$5,000-\$ 5,000 $ 612 $ 612 $612\$ 612 $ 1 , 397 $ 1 , 397 $1,397\$ 1,397 $ 1 , 844 $ 1 , 844 $1,844\$ 1,844 $ 2 , 302 $ 2 , 302 $2,302\$ 2,302 $ 2 , 423 $ 2 , 423 $2,423\$ 2,423
Free Cash Flow  自由現金流 0 -180 -312 310 446 315
PC(FCF) 0 -164 -258 233 305 196
NPV 312
0 End of Year 0 2 3 4 5 FCF of alternive production process -$5,000 $432 $1,085 $2,154 $2,749 $2,738 Less: FCF of original process -$5,000 $612 $1,397 $1,844 $2,302 $2,423 Free Cash Flow 0 -180 -312 310 446 315 PC(FCF) 0 -164 -258 233 305 196 NPV 312 | | 0 | End of Year | | | | | | :--- | ---: | ---: | ---: | ---: | ---: | ---: | | | 0 | 2 | 3 | 4 | 5 | | | FCF of alternive production process | $-\$ 5,000$ | $\$ 432$ | $\$ 1,085$ | $\$ 2,154$ | $\$ 2,749$ | $\$ 2,738$ | | Less: FCF of original process | $-\$ 5,000$ | $\$ 612$ | $\$ 1,397$ | $\$ 1,844$ | $\$ 2,302$ | $\$ 2,423$ | | Free Cash Flow | 0 | -180 | -312 | 310 | 446 | 315 | | PC(FCF) | 0 | -164 | -258 | 233 | 305 | 196 | | | | | | | | | | NPV | 312 | | | | | |

Coca-cola Energy Drink Case - Salvage value
可口可樂能量飲料盒 - 殘值

Would your recommendations change if Coca-cola can sell the equipment it used to produce the energy drink at the end of the product cycle? Why?
如果 Coca-cola 可以在產品週期結束時出售用於生產能量飲料的設備，您的建議會改變嗎？為什麼？

NPV ↑↑↑ ↑↑↑ uarr uarr uarr\uparrow \uparrow \uparrow

Salvage value and NPV
殘值與淨現值

Complexity / flexiblity Competition growth ratecoparapla, Enetgy Drink Case - Your thoughts
複雜性 / 靈活性 競爭成長率coparapla, Enetgy Drink Case - 您的想法
Are there any considerations soo think we have left out? Are there any considerations you think we have left out? synergies tares regulation Bud debt (receivables)
您認為我們遺漏了哪些考慮因素？您認為我們是否遺漏了任何考慮因素？ 協同效應 稗子 法規 花蕾 債務（應收賬款）
New suppliers /  新供應商 /
Non fin cost  非翅片成本
new relationships  新關係
Cost of time  時間成本
Social impact production synergies
社會影響生產協同效益
brand equity  品牌價值
add to sales elsewtedre
加入銷售
cannibalize sales of rea. Coke 5 years of it ends?
蠶食 rea.可口可樂 5 年結束了嗎？

The Profitability Index  獲利指數

Profitability Index and Scarce Resources
獲利指數與稀缺資源

Investment opportunities often consume scarce resources within a firm, to maxmize the NPV created by new projects can use the
投資機會通常會消耗公司內部的稀缺資源，為了使新專案所創造的 NPV 最大化，可以使用
Profitiability Index = Value Created Resource Consumed = N P V Resource Consumed  Profitiability Index  =  Value Created   Resource Consumed  = N P V  Resource Consumed  " Profitiability Index "=(" Value Created ")/(" Resource Consumed ")=(NPV)/(" Resource Consumed ")\text { Profitiability Index }=\frac{\text { Value Created }}{\text { Resource Consumed }}=\frac{N P V}{\text { Resource Consumed }}
■ Examples of scarce resources: capital, production capacity, human resources, etc
稀有資源的例子：資本、生產能力、人力資源等
  • Profitability Index Rule: Take the projects with the highest profitability index until the scarce resource is consumed.
    獲利指數規則：採取獲利指數最高的專案，直到稀有資源耗盡為止。

Example: Using the Profitability Index
範例：使用獲利指數

Suppose you must choose how to invest $ 60 $ 60 $60\$ 60 million in capital among the following investment opportunities
假設您必須在下列投資機會中選擇如何投資 $ 60 $ 60 $60\$ 60 百萬資金
Project  專案 NPV Initial Investment  初始投資 Profitability Index  獲利指數
A 10.1 10 1.01
B 19.0 15 1.27
C 22.0 15 1.47
D 25.0 22 1.14
E 60.2 30 2.01
Project NPV Initial Investment Profitability Index A 10.1 10 1.01 B 19.0 15 1.27 C 22.0 15 1.47 D 25.0 22 1.14 E 60.2 30 2.01| Project | NPV | Initial Investment | Profitability Index | | :---: | :---: | :---: | :---: | | A | 10.1 | 10 | 1.01 | | B | 19.0 | 15 | 1.27 | | C | 22.0 | 15 | 1.47 | | D | 25.0 | 22 | 1.14 | | E | 60.2 | 30 | 2.01 |
Use the profitability index to choose the project(s) in which should you invest.
使用獲利指數選擇您應該投資的專案。

Example Solution  解決方案範例

Suppose you must choose how to invest $ 60 $ 60 $60\$ 60 million in capital among the following investment opportunities
假設您必須在下列投資機會中選擇如何投資 $ 60 $ 60 $60\$ 60 百萬資金
Project  專案 NPV Initial Investment  初始投資 Profitability Index  獲利指數 Rank  等級
  累計已用資本
Cumulative
Capital Used
Cumulative Capital Used| Cumulative | | :---: | | Capital Used |
E 60.2 30 2.01 1 30
C 22.0 15 1.47 2 45
B 19.0 15 1.27 3 60
D 25.0 22 1.14 4 82
A 10.1 10 1.01 5 92
Project NPV Initial Investment Profitability Index Rank "Cumulative Capital Used" E 60.2 30 2.01 1 30 C 22.0 15 1.47 2 45 B 19.0 15 1.27 3 60 D 25.0 22 1.14 4 82 A 10.1 10 1.01 5 92| Project | NPV | Initial Investment | Profitability Index | Rank | Cumulative <br> Capital Used | | :---: | :---: | :---: | :---: | :---: | :---: | | E | 60.2 | 30 | 2.01 | 1 | 30 | | C | 22.0 | 15 | 1.47 | 2 | 45 | | B | 19.0 | 15 | 1.27 | 3 | 60 | | D | 25.0 | 22 | 1.14 | 4 | 82 | | A | 10.1 | 10 | 1.01 | 5 | 92 |

Shortcomings of the Profitability Index
獲利指數的缺點

The ultimate goal of an capital budgeting analysis is to create the most NPV for the firm. The profitability index is an algorithm to find the set of projects that achieves that goal. But it only works if
資本預算分析的最終目標是為公司創造最大的 NPV。盈利能力指數是一種運算方法，用來找出能達到該目標的專案集。但它只有在以下情況下才有效
1 The set of projects selected by the profitability index completely exhausts the available resources.
1 由獲利指數選出的專案集完全耗盡可用資源。
2 There is only one resource constraint.
2 只有一個資源限制。
If either of these two criteria fail, then you have to go back to old fashion guessing and checking.
如果這兩個標準中的任何一個失敗，那麼您就必須回到老式的猜測和檢查。

Example: When the Profitability Index Doesn't work
範例：當盈利指數失效時

Suppose you must choose how to invest $ 60 $ 60 $60\$ 60 million in capital among the following investment opportunities
假設您必須在下列投資機會中選擇如何投資 $ 60 $ 60 $60\$ 60 百萬資金
Project  專案 NPV Initial Investment  初始投資 Profitability Index  獲利指數 Rank  等級
  累計已用資本
Cumulative
Capital Used
Cumulative Capital Used| Cumulative | | :---: | | Capital Used |
A 50 40 1.25 1 40
B 30 30 1 2 70
C 25 +30 .83 3 100
Project NPV Initial Investment Profitability Index Rank "Cumulative Capital Used" A 50 40 1.25 1 40 B 30 30 1 2 70 C 25 +30 .83 3 100| Project | NPV | Initial Investment | Profitability Index | Rank | Cumulative <br> Capital Used | | :---: | :---: | :---: | :---: | :---: | :---: | | A | 50 | 40 | 1.25 | 1 | 40 | | B | 30 | 30 | 1 | 2 | 70 | | C | 25 | +30 | .83 | 3 | 100 |
  • A is the most profitable, but uses too much capital to be combined with any other project.
    A 的利潤最高，但使用的資本太多，無法與其他專案結合。
  • Investing in both B and C creates more value than investing in A alone.
    同時投資 B 和 C 比單獨投資 A 創造更多價值。

The Internal Rate of Return IRR
內部回報率 IRR

Internal Rate of Return
內部回報率
Internal Rate of Return: The interest rate that sets the NPV of a project to zero. If y y yy is IRR, then y y yy solves
內部回報率：將專案的 NPV 設定為零的利率。如果 y y yy 是 IRR，則 y y yy 解得
∑ t = 0 T C t ( 1 + y ) t = 0 y > r ? ∑ t = 0 T   C t ( 1 + y ) t = 0 y > r ? {:[sum_(t=0)^(T)(C_(t))/((1+y)^(t))=0],[y > r?]:}\begin{aligned} \sum_{t=0}^{T} \frac{C_{t}}{(1+y)^{t}} & =0 \\ y & >r ? \end{aligned}
Internal Rate of Return Rule: Take any investment opportunity where the IRR exceeds the opportunity cost of capital (hurdle rate). Turn down any opportunity whose IRR is less than the opportunity cost of capital
內部回報率規則：把握任何內部回報率超過資本機會成本（階段回報率）的投資機會。拒絕任何內部回報率低於資本機會成本的投資機會。
I R R ∼ < 480 300 = 1 + y I R R ∼ < 480 300 = 1 + y IRR∼ < (480)/(300)=1+y\underset{\sim}{I R R}<\frac{480}{300}=1+y

Example: Simple IRR Calculation
範例：簡單 IRR 計算

Suppose you have project with the following free cash flows:
假設您有以下自由現金流量的專案：
C 0 C 1 C 2 C 3 − 5 , 000 2 , 000 2 , 000 2 , 000 C 0 C 1 C 2 C 3 − 5 , 000 2 , 000 2 , 000 2 , 000 {:[C_(0),C_(1),C_(2),C_(3)],[-5","000,2","000,2","000,2","000]:}\begin{array}{cccc} C_{0} & C_{1} & C_{2} & C_{3} \\ \hline-5,000 & 2,000 & 2,000 & 2,000 \end{array}
Calculate the IRR. Should you invest in the project?
計算內部回報率。您是否應該投資該專案？
5000 = 2000 1 + y + 2000 ( 1 + y ) 2 + 2000 ( 1 + y ) 3 5000 = 2000 1 + y + 2000 ( 1 + y ) 2 + 2000 ( 1 + y ) 3 5000=(2000)/(1+y)+(2000)/((1+y)^(2))+(2000)/((1+y)^(3))5000=\frac{2000}{1+y}+\frac{2000}{(1+y)^{2}}+\frac{2000}{(1+y)^{3}}

Solution  解決方案

A B C D E
1 EOY
2 0 1 2 3
3 C_EOY -5000 2000 2000 2000
4
5 IRR 9.70% B3:E3)
A B C D E 1 EOY 2 0 1 2 3 3 C_EOY -5000 2000 2000 2000 4 5 IRR 9.70% B3:E3) | | A | B | C | D | E | | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | EOY | | | | | | 2 | | 0 | 1 | 2 | 3 | | 3 | C_EOY | -5000 | 2000 | 2000 | 2000 | | 4 | | | | | | | 5 | IRR | 9.70% | B3:E3) | | |
We don’t have enough information to decide if we should take the project. We don’t know our opportunity cost of capital!
我們沒有足夠的資訊來決定是否應該接下這個專案。我們不知道我們的資本機會成本！

IRR and NPV  內部回報率與淨現值

■ Is there a difference between the IRR rule and the NPV Rule for the preceding example?
■ 前述範例的 IRR 規則與 NPV 規則是否有差異？
■ Is there a reason to use one over the other?
是否有理由使用其中一種而非另一種？

Example: IRR and lending or borrowing
範例：內部回報率與借貸

Suppose you have two projects with the following free cash flows:
假設您有兩個專案，其自由現金流量如下：
Project  專案 C 0 C 0 C_(0)C_{0} C 1 C 1 C_(1)C_{1} C 2 C 2 C_(2)C_{2}
A − 5 , 000 − 5 , 000 -5,000-5,000 3,000 3,000
B 5,000 − 3 , 000 − 3 , 000 -3,000-3,000 − 3 , 000 − 3 , 000 -3,000-3,000
Project C_(0) C_(1) C_(2) A -5,000 3,000 3,000 B 5,000 -3,000 -3,000| Project | $C_{0}$ | $C_{1}$ | $C_{2}$ | | :---: | :---: | :---: | :---: | | A | $-5,000$ | 3,000 | 3,000 | | B | 5,000 | $-3,000$ | $-3,000$ |
Calculate the IRR of each project. If your opportunity cost of capital is 10 % 10 % 10%10 \% which project should you take?
計算每個專案的 IRR。如果您的資本機會成本是 10 % 10 % 10%10 \% ，您應該選擇哪一個項目？
Project A A AA extra return = 13.07 % − 10 % = 3.07 % = 13.07 % − 10 % = 3.07 % =13.07%-10%=3.07%=13.07 \%-10 \%=3.07 \%
專案 A A AA 額外回傳 = 13.07 % − 10 % = 3.07 % = 13.07 % − 10 % = 3.07 % =13.07%-10%=3.07%=13.07 \%-10 \%=3.07 \%
Project B B BB extra return = 10 % − 13.07 % = − 3.07 % = 10 % − 13.07 % = − 3.07 % =10%-13.07%=-3.07%=10 \%-13.07 \%=-3.07 \%
專案 B B BB 額外回傳 = 10 % − 13.07 % = − 3.07 % = 10 % − 13.07 % = − 3.07 % =10%-13.07%=-3.07%=10 \%-13.07 \%=-3.07 \%
Take project A !
以專案 A ！

Solution  解決方案

Example: IRR and clean up costs
範例：內部回報率和清理成本

Suppose you have two mutually exclusive projects with the following free cash flows:
假設您有兩個互斥的專案，其自由現金流量如下：
Project  專案 C 0 C 0 C_(0)C_{0} C 1 C 1 C_(1)C_{1} C 2 C 2 C_(2)C_{2}
A − 1 , 000 − 1 , 000 -1,000-1,000 2,300 − 1 , 320 − 1 , 320 -1,320-1,320
B − 1 , 000 − 1 , 000 -1,000-1,000 3,000 − 2 , 320 − 2 , 320 -2,320-2,320
Project C_(0) C_(1) C_(2) A -1,000 2,300 -1,320 B -1,000 3,000 -2,320| Project | $C_{0}$ | $C_{1}$ | $C_{2}$ | | :---: | :---: | :---: | :---: | | A | $-1,000$ | 2,300 | $-1,320$ | | B | $-1,000$ | 3,000 | $-2,320$ |
Calculate the IRR of each project. If your opportunity cost of capital is 15 % 15 % 15%15 \% which project(s) should you take?
計算每個專案的 IRR。如果您的資本機會成本是 15 % 15 % 15%15 \% ，您應該選擇哪一個項目？

Solution  解決方案

A B C D
1 EOY
2 0 1 2
3 Project AC_EOY  專案 AC_EOY -1000 2300 -1320
4 Project B C_EOY  專案 B C_EOY -1000 3000 -2320
5
6 IRR Project A  IRR 專案 A 10.00% = IRR = IRR =IRR=\operatorname{IRR} (B3:E3,   = IRR = IRR =IRR=\operatorname{IRR} (B3:E3、
7 IRR Project A  IRR 專案 A 20.00% = lRR = lRR =lRR=\operatorname{lRR} (B3:E3,   = lRR = lRR =lRR=\operatorname{lRR} (B3:E3、
8 IRR Project B  內部回報率專案 B #NUM! =IRR(B4:E4,  =IRR(B4:E4、
A B C D 1 EOY 2 0 1 2 3 Project AC_EOY -1000 2300 -1320 4 Project B C_EOY -1000 3000 -2320 5 6 IRR Project A 10.00% =IRR (B3:E3, 7 IRR Project A 20.00% =lRR (B3:E3, 8 IRR Project B #NUM! =IRR(B4:E4, | | A | B | C | D | | :---: | :---: | :---: | :---: | :---: | | 1 | | EOY | | | | 2 | | 0 | 1 | 2 | | 3 | Project AC_EOY | -1000 | 2300 | -1320 | | 4 | Project B C_EOY | -1000 | 3000 | -2320 | | 5 | | | | | | 6 | IRR Project A | 10.00% | $=\operatorname{IRR}$ (B3:E3, | | | 7 | IRR Project A | 20.00% | $=\operatorname{lRR}$ (B3:E3, | | | 8 | IRR Project B | #NUM! | =IRR(B4:E4, | |
These projects don’t have well defined IRR’s!!
這些專案沒有明確的內部回報率！！
Project A has two IRR’s!!
專案 A 有兩個 IRR!
Project B does not have an IRR!!
專案 B 沒有 IRR!

Example: IRR and mutually exclusive projects
範例：內部回報率和互斥專案

Suppose you have two mutually exclusive projects with the following free cash flows:
假設您有兩個互斥的專案，其自由現金流量如下：
Project  專案 C 0 C 0 C_(0)C_{0} C 1 C 1 C_(1)C_{1} C 2 C 2 C_(2)C_{2}
A − 2 , 000 − 2 , 000 -2,000-2,000 1,500 1,500
B − 5 , 000 − 5 , 000 -5,000-5,000 1,000 6,500
Project C_(0) C_(1) C_(2) A -2,000 1,500 1,500 B -5,000 1,000 6,500| Project | $C_{0}$ | $C_{1}$ | $C_{2}$ | | :---: | :---: | :---: | :---: | | A | $-2,000$ | 1,500 | 1,500 | | B | $-5,000$ | 1,000 | 6,500 |
Calculate the IRR of each project.
計算每個專案的內部回報率。
  • If your opportunity cost of capital is 15 % 15 % 15%15 \% which project should you take?
    如果您的資本機會成本是 15 % 15 % 15%15 \% ，您應該選擇哪個專案？
  • What if your cost of capital is 22 % 22 % 22%22 \% ?
    如果您的資本成本是 22 % 22 % 22%22 \% 呢？

Example solution  解決方案範例

A B C D
1 EOY
2 0 1 2
3 Project AC_EOY  專案 AC_EOY -2000 1500 1500
4 Project B C_EOY  專案 B C_EOY -5000 1000 6500
5
6 IRR Project A  IRR 專案 A 31.87% =IRR(B3:E3)
7 IRR Project B  內部回報率專案 B 24.46% =IRR(B4:E4)
A B C D 1 EOY 2 0 1 2 3 Project AC_EOY -2000 1500 1500 4 Project B C_EOY -5000 1000 6500 5 6 IRR Project A 31.87% =IRR(B3:E3) 7 IRR Project B 24.46% =IRR(B4:E4) | | A | B | C | D | | :---: | :---: | :---: | :---: | :---: | | 1 | EOY | | | | | 2 | | 0 | 1 | 2 | | 3 | Project AC_EOY | -2000 | 1500 | 1500 | | 4 | Project B C_EOY | -5000 | 1000 | 6500 | | 5 | | | | | | 6 | IRR Project A | 31.87% =IRR(B3:E3) | | | | 7 | IRR Project B | 24.46% =IRR(B4:E4) | | |
IRR can be misleading, these projects have different sizes! IRR rule does not say choose project with highest IRR!
IRR 可能會產生誤導，這些專案有不同的規模！IRR 規則並沒有說要選擇 IRR 最高的專案！

Example solution  解決方案範例

Which project has higher NPV depends on the opportunity cost of capital.
哪個專案的 NPV 較高，取決於資本的機會成本。

The Payback Rule  回報規則

The Payback Rule  回報規則

Payback investment rule: Accept a project if its cash flows pay back its initial investment within the payback period.
回報投資規則：如果一個專案的現金流能在投資回收期內收回其初始投資，則接受該專案。
This investment rule ignores important features of a given project:
這種投資規則忽略了特定專案的重要特點：
  • The cost of capital.
    資本成本。
  • Long term cash flows.
    長期現金流量。
It also relies on an ad hoc payback period.
它還依賴於臨時投資回收期。

Example: Applying the Payback Rule
範例：應用投資回收法則

  • Your company has set a pay back period of 5 years.
    貴公司設定的還款期為 5 年。
  • You have access to a project that will require $ 60 $ 60 $60\$ 60 million capital investment at EOY 0 . The project will produce a free cash flow of $ 10 $ 10 $10\$ 10 million a year for 10 years beginning at EOY 1.
    您可以獲得一個項目，該項目在 EOY 0 時需要 $ 60 $ 60 $60\$ 60 百萬資本投資。從 EOY 1 開始的 10 年中，該項目將每年產生 $ 10 $ 10 $10\$ 10 百萬的自由現金流。
  • Your discount rate is 8 % 8 % 8%8 \%.
    您的貼現率為 8 % 8 % 8%8 \% 。
  • Apply the payback rule to this project. What is the NPV of this project?
    將回收期規則應用於此專案。這個專案的 NPV 是多少？

Why do Firms Use the Payback Rule
公司為何使用回報率規則

  • Provides some information about the length of time capital will be committed to a project.
    提供一些有關資金投入專案時間長度的資訊。
  • With a short payback period, most projects that satisfy the payback rule will also be positive NPV.
    由於投資回收期短，符合投資回收規則的多數專案也會是正淨現值。
  • It’s very simple.  非常簡單。

Concept Check  概念檢查

Capital Budgeting: Concept Check
資本預算：概念檢查

The rules of capital budgeting
資本預算規則
  • NPV: The present value of benefits minus the present value of costs
    NPV：效益的現值減去成本的現值
  • The NPV rule: Choose projects with the highest NPV
    NPV 法則：選擇 NPV 最高的專案
  • Correctly accounts for the time value of money
    正確計算貨幣的時間價值
  • Corresponds to value creation in measured dollars today
    相對應於今日以計量美元計算的價值創造
  • Free Cash Flow: The cash available to distribute to investors, the right way to measure costs and benefits.
    自由現金流： 可分配給投資者的現金，衡量成本與效益的正確方法。
  • Allocating scarce resources: the profitability index.
    分配稀缺資源：獲利能力指數。
  • Other approaches to capital budgeting
    資本預算的其他方法
■ Internal Rate of Return
內部回報率
  • Payback Period  回本期