Capital Budgeting - Value of Investment Is Pv of Expected Cash Flows Discounted at Risk-Adjusted Rate
By: RTTT • January 31, 2018 • Thesis • 2,239 Words (9 Pages) • 1,117 Views
Capital Budgeting
- Cash Flow
Value of investment is PV of expected cash flows discounted at risk-adjusted rate
- Free cash flow
FCF is cash flow available for shareholders and debtholders.
Calculate tax on before-interest basis and use tax-adjusted WACC for discounting
FCF = EBIT (1−tc) + Dep – CapEx − ∆NWC
• EBIT = Revenues – COGS – SGA – Depreciation
• CapEx = New PPE – Old PPE + Dep
• NWC (Net working capital) = Current assets – Current liabilities
= Inventory + Accounts Receivables – Accounts Payables
E.g. Value the firm Anacott Steel in 2012. Forecasting period is 2013 to infinity.
• Net revenues of Anacott Steel in 2012 were $1,000. Revenues grow at 10% through 2013-2014. The 2015 revenues match revenues in 2014.
• EBIT is 30% of revenues (operating margin).
• Depreciation is $100 p.a.
• CapEx is $150 p.a. And reduces to $100 from 2015 onwards.
• Change in net working capital is $25 and reduces to $21.1 from 2015 onwards.
• Corporate tax rate is 30%
• Before-tax WACC is 14.29%.
• Market value of debt is $696.9.
• After 2015, FCF of Anacott Steel will grow at 2% p.a. in perpetuity.
2012 | 2013 | 2014 | 2015 | ||
Sales | 1,000 | 1,100 | 1,210 | 1,210 | |
Operating Margin | 30% | 30% | 30% | ||
EBIT | 330 | 363 | 363 | ||
EBIT*(1 – tc) | 231 | 254.1 | 254.1 | ||
Plus | Depreciation | 100 | 100 | 100 | |
Minus | CapEx | 150 | 150 | 150 | 100 |
Minus | ∆ NWC | 25 | 25 | 25 | 21.1 |
FCF | 156 | 179.1 | 233 |
Discount FCF with after-tax WACC to get PV
After-tax WACC = before-tax WACC × (1 – tc) = 14.29% × (1 – 30%) = 10%
PV = 156/1.1 + 179.1/1.12 + 233/1.13 + (233 × 1.02)/(0.1 – 0.02) × 1/1.13
= $2,696,9 → Market value of assets
• Equity = Assets – Debt = $2696.9 - $696.9 = $2,000
* PV (Perpetuity) = A/i，从第n年起perpetuity， 每年增长m，
先把第n年的值推到t=0 → FCF (0) = A × (1+m)/(1+i)n-1
再带入计算PV = A × (1+m)/(1+i)n-1 /(i – m)
- Capital Budgeting
Decision-making process for accepting or rejecting projects
Use NPV rule as basic investment rule:
- NPV > 0 → accept
- NPV < 0 → reject
BUT basic NPV only applies to independent projects.
Mutually exclusive projects with different lives require adjustment.
- Independent projects
Two projects are independent if acceptance or rejection of one has no effect on acceptability of the other (and/or) → can be accepted simultaneously
- Mutually exclusive projects
Two projects are mutually exclusive if acceptance of one project precludes acceptance of the other (either or)
- Constant chain of replacement (CCR)
Assumes identical replication of projects through time.
The replacement chains are continued until both chains are of equal length.
Three alternative methods
(a) Lowest Common Multiple (LCM) Method
(b) Perpetuity Method
(c) Equivalent Annual Value Method
In most cases all three methods give the same decision.
E.g.
The student union is considering investing in either a Beverage Automatic Distributor (BAD) or a Sweet-And-Direct (SAD) machine.
Assume an opportunity cost of capital (OCC) of 10% p.a.
Time BAD SAD
0 (100) (50)
1 60 40
2 50 30
3 40
* Basic NPV rule:
NPV (BAD) = -100 + 60/1.1 + 50/1.12 + 40/1.13 = $25.92
NPV (SAD) = -50 + 20/1.1 + 30/1.12 = $11.15
Therefore accept BAD
BUT different length (BAD – 2, SAD – 3) →LCM
* Lowest common multiple
Replicate BAD twice and SAD three times (LCM = 6)
Time BAD SAD
0 (100) (50)
1 60 40
2 50 30 – 50 = -20
3 40 – 100 = -60 40
4 60 30 – 50 = -20
5 50 40
6 40 30
NPV (BAD×2) = $45.39
NPV (SAD×3) = $28.00
Therefore accept BAD
Problem with LCM method is that it can be very cumbersome. (E.g. 11 and 13-year projects require calculation of PV for 143 years)
→ Perpetuity method
Both projects are replicated forever.
The chains of cash flows are then “equally lengthy” i.e. both infinite.
[pic 1]
NPV0 is the project’s standard NPV
NPV∞(BAD) = NPV0 × (1 + k)n/[(1 + k)n –1] = 25.92 × 1.103/(1.103 – 1) = $104.23
NPV∞(SAD) = 11.15 × 1.102/(1.102 – 1) = $64.29
NPV∞(BAD) > NPV∞(SAD) → rank Project BAD ahead of Project SAD
* NPV (LCM) and NPV (Perpetuity) are related by the below formula
[pic 2]
• NPV0 = Standard NPV
• t A = Life of Project A
• t B = Life of Project B
• t AB = t A × t B (t AB is not necessarily the lowest common multiple of A and B)
[pic 3]
* Equivalent Annual Value (EAV)
The annual cash flow from an annuity that has the same life as the project and whose present value is equal to the NPV of the project.
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