Corporate Finance Full Summary Notes for Exams (NPV, WACC, Capital Structure, Dividend Policy)

Lecture 1 Capital Budgeting (without Leverage)

Capital budgeting (investment appraisal) 资本预算/投资评估
The capital budgeting methods for corporate investment decisions to analyze the
forecasted cash flows:

 Net Present Value (NPV) [the most common one]
Calculating the NPV:
1
---- The present value of a net cash flow in year t: PV ( FCF t )=FCF t ×
(1+r )t
---- The project’s net present value is the sum of the present values of the net
N N
1
cash flows over all years: NPV =∑ PV (FCF ¿¿ t)=∑ FCF t × ¿ ¿ ¿ ¿ ¿
t=0 t =0

Five general rules in applying NPV:
1. Discounted cash flows, not profits.
2. Discounted incremental cash flows.
3. Treat inflation consistently.
4. Separate investment and financing decisions.
5. Remember to deduct taxes.
---- Forecast Earnings
Unlevered Net Income (100% equity and 0% debt):
EBIT × (1−tc )= ( Revenues−COGS−Depreciation ) ×(1−tc)
EBIT – Earnings before interest and tax (Operating Profit)
tc – tax rate
---- From earnings to cash flow
Incremental earnings are the amount by which firm’s earnings are expected change as
a result of the investment decision.
The project’s free cash flow (FCF) in each period:
FCF=Unlevered Net Income+ Depreciation−Capital Expenditures(CapEx)−∆ Net Working Capital (NW
Net working capital (NWC) = Cash + Inventory + Receivables – Payables
∆ NWC=Current year NWC−Last year NWC
Do not need to consider a sunk cost, which is any expenditure that has already been
incurred and cannot be recovered.
Consider opportunity costs & salvage value
--- opportunity cost represents a negative cash flow to the firm
--- salvage value represents a positive cash flow to the firm

 Internal Rate of Return (IRR)
A project’s Internal Rate of Return (IRR) is the discount rate at which the project’s
NPV would be zero.

,The rule is to undertake any project where the IRR is greater than the cost of
capital.
Excel Function: IRR(CF0: CFt)
Pros and Cons of using IRR:
Pros:
1. Easy to understand and communicate.
2. Uses discounting methods and incorporates time value of money.
Cons:
1. Multiple IRRs.
Example: Suppose a publisher offers to pay you £550,000 in advance and £1 million
in four years when the book is published. But you need to invest £500,000 annually in
the next 3 years to get the book published. Should you accept or reject the offer?
500000 500000 500000 1000000
550000− − − + =0
1+r ( 1+r )2 ( 1+r )3 ( 1+r )4
IRR could be either r = 7.16% or r = 33.67%
2. IRR may be inapplicable for unusual cash flow patterns, e.g.Delayed investments
Example: Suppose you are offered to receive £1 million today to write your
autobiography. Writing your autobiography would cost you three years of work, each
of which you could have earned £500,000. What is the NPV, assuming that your
opportunity cost of capital is 10%. What is the IRR?
500000 500000 500000
NPV = 1000000− 1+10 % − − =¿-243426
( 1+10 % ) ( 1+10 % )3
2

IRR = 23.38%
The NPV is negative (REJECT) but the IRR =23.38% (>10%, ACCEPT)
---> when the benefits of investment occur before the costs, the NPV is an increasing

function of the discount rate. 当投资收益出现在成本之前时，NPV 是贴现率的递

增函数
3. Problems specific to mutually exclusive investments.
---Timing problem
Consider two mutually exclusive investment projects A&B
0 1 2 3
Investment A -10000 10000 1000 1000
Investment B -10000 1000 1000 12000
Investment A: NPV (@10%) = 669; IRR= 16.04% ✅
Investment B: NPV (@10%) = 751 ✅; IRR= 12.94%
Crossover IRR: NPVA= NPVB
How to calculate the crossover rate?
1. calculate the differences between the CFs of the two projects
0 1 2 3
Project A-Project B 0 9000 0 -11000
2. calculate the IRR of the differences in two projects’ CFs
Crossover rate = 11% when NPVA= NPVB

, ---> If cost of capital < crossover rate, conflict between IRR and NPV
In this example, the cost of capital (10%) is less than the crossover rate (11%),

IRRA>IRRB, But NPVA<NPVB. (有 conflict，根据 NPV 选)
---> If cost of capital > crossover rate, no conflict between IRR and NPV
--- Scaling problem
0 1 2 IRR NPV( @10%)
Small -90 12 112 18%. 13
Large -1000 120 1120 12%. 35
Difference. 910 -108 -1008. 11%

NPV vs. IRR: the Reinvestment Rate Assumption
The NPV rule assumes that intermediate cash flows on the project get reinvested at
the hurdle rate (which is based upon what projects of comparable risk should earn)
The IRR rule assumes that intermediate cash flows on the project get reinvested at the
IRR.
---> when the IRR is high and the project life is long, the IRR will overstate the true
return on the project.

 Modified IRR (MIRR)
Similar to the regular IRR, except it is calculated based on the assumption that cash
flows are reinvested at the cost of capital (or some other explicit hurdle rate).
Two advantages:
1. It assumes that cash flows are reinvested at the cost of capital (or some other
explicit hurdle rate) rather than at the IRR
2. The MIRR eliminates the multiple IRR problem
Excel Function: MIRR(CFs, finance rate, reinvest rate)

题目如果只有 cost of capital, finance rate & reinvest rate 都填 cost of capital


 Profitability index (PI)
Compares present value of future cash flows with initial investment
Total PV of Future Cash Flows
PI =
Initial Investment
Minimum Acceptance Criteria: Accept if PI >1.
Ranking Criteria: Select alternative with highest PI.
Pros and Cons of the profitability index:
Pros:
1. may be useful when available investment funds are limited
2. easy to understand and communicate
3. correct decision when evaluating independent project
Cons:
1. problems with mutually exclusive investments