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Finance lecturesLecture 1 and 2
In this course, we build up towards the intrinsic valuation model called ‘Net Present Value (NPV, also
called ‘Discounted Cash Flow’ model).
Book value: historical purchase price, minus all accumulated depreciation, amortisation and any
impairments. Used in e.g. a balance sheet.
Market value: Would you sell off an asset today, this is what the market is expected to pay for it.
Market values typically depend upon market conditions as supply and demand, cost and availability
of capital, etc.
Fair value/Intrinsic value: The present value of the expected cash flows the asset will yield
(discounted at a rate representative for the riskiness of earning these cash flows). Used for some
items in the balance sheet.
What we can take away is that when valuing(part of) a company, its book value need to be
informative. It would be way more interesting to see the market value of assets. The problem is that
the market value is only observed after you have sold the assets, whereas we wish to value them
prior to selling or buying them. This is where the concept of ‘Enterprise value’ (EV) comes in. Also,
ideally the left-hand side of a balance sheet solely shows (current and non-current ) operating assets,
and the right-hand side only their financing. This is where the concepts of the ‘managerial balance
sheet’ comes in.
ROIC = Return On Invested Capital
(1−𝑇𝑐) × 𝐸𝐵𝐼𝑇
ROIC =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
𝐷 𝐸
WACC = (1 – Tc) × rd × 𝐷+𝐸 + re × 𝐷 +𝐸
Future value: You have some money now that you put at a savings account, and wish to know how
much it is worth somewhere in the future.
Present value: You get some money somewhere in the future, and wish to know how much today’s
equivalent would be worth.
Simple interest: you do receive interest on your deposit, but do not get interest on interest.
A (t) = r × P × T + P
A (t) = P × (1 +rT)
P = principal
Compound interest: You receive interest over principal plus interest earned.
A (t) = P × (1 + r)T
,The result of compounded interest depend on three crucial inputs:
1. The level of the monthly payment
2. The level of the interest rate
3. The lifespan of my savings project
When you increase monthly payment with X%, the terminal value also increases with X%.
When you increase interest rate with X%, the terminal value will increase more than X%. So we may
safely state the outcome of the analysis is more sensitive to the interest rate than to the amount of
monthly savings.
Application of future value
1. Estate planning: you need an amount of money in the future, and today you start saving or
investing for it. Examples include:
- Saving on a savings account
- Investing in stocks/bonds/trackers
- Contributing to a pension fund savings plan
Calculating effective annual rates (EAR): the return you effective pay on a loan or receive on a
savings account, adjusted for the compounding frequency.
Calculating annual percentage rate (APR): The annualised simple interest percentage, without any
intra-period (quarterly/monthly/etc.) compounding, and adjusted for any costs/expenses.
EAR
-Imagine you are indebted on your current account. The bank charges you R = 10% per annum
(‘stated annual rate’, or ‘nominal interest rate’) but this is compounded monthly.
-The EAR now tells us what you effectively pay on your annualised basis:
𝑅
EAR = (1 + (𝑚))m – 1
The interest rate depends on the risk for the bank. Therefore, the rate is lower for a mortgage than
for a loan for a car.
Morale: The higher the frequency of compounding, the bigger the difference between the ‘stated
annual rate’ and the effective annual rate.
Continuously interest gives EAR: eR – 1
APR
-The APR is the average yearly cost of a loan over the lifespan of that loan, including any financing
charges and any fees or additional charges associated with the loan:
𝐹𝑒𝑒𝑠 (€)+𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 (€)
APR = (( 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙
𝑁
(€)
) × n ) × 100%
N = total number of compounding periods
n = number of instalments per year
Where:
- Fees are any additional costs
- Interest is total interest paid over the life of the loan
- Principal is the total loan principal
- N is the total number of compounding periods over the loan’s lifespan
- n is the number of compounding periods per annum
-The APR thus quotes a simple interest rate per annum, without the effect of compounding.
,Lecture 3
How to currently value future income?
- In present value (also called ‘discounted cash flow’) analysis we decide between either receiving
some money in the future (and wait for it), or we are happy with some ‘present value equivalent’
today.
- Perhaps it is more intuitive to think of an entrepreneur, who plans to stay in the business for the
next 40 years. He expects to receive income during that period. Imagine somebody comes along, and
makes a takeover bid. The entrepreneur now has to decide whether he either (1) stays in the
business and is entitled to all the future cash flows, or (2) take some amount of cash today.
- In present value analysis, we look for a present value alternative for which you are indifferent.
𝐶𝐹
𝑡
PV(CFt) = (1+𝑟) 𝑡
r is called the ‘discount rate’
For plotting all the present value equivalents as a graphic, we plot two lines.
1. The line with the nominal cash flows.
2. The line with the present value equivalents of these cash flows.
This would become as follows:
- In the present value analysis, we are interested in finding an alternative to receiving money in the
future.
- We calculate a value we makes us equally happy today as we would otherwise be when receiving
money in the future.
- This principle is used in many economic analyses, for example:
- You wish to take over a company. How much are its future cash flows worth today?
- You must decide between multiple investment opportunities. Which one is most profitable?
- You consider replacing some asset (machine, car, etc.). What is the best moment to swap?
In general, if we wish to determine the present value of a series of cash flows, we may write:
𝐶𝐹1 𝐶𝐹2 𝐶𝐹3 𝐶𝐹𝑇
PV = (1+𝑟) 1 + (1+𝑟)2 + (1+𝑟)3 + … + (1+𝑟)𝑇
Which can be written as the sum (∑) of a series from time t = 1, …, T:
𝑇
𝐶𝐹𝑡
∑
(1 + 𝑟)𝑡
𝑡=1
𝐶𝐹
NPV = -Io + ∑𝑇𝑡=1 (1+𝑟)
𝑡
𝑡 (should at least be 0 to invest)
Note that these cash flows CFt may still fluctuate for each time period t (which is most reasonable for
any income stream of a business).
We may consider two special cases:
1. All cash flows are constant -> annuity
2. The lifespan of the constant cash flows is endless -> Perpetuity
, Perpetuity: Perpetual bonds
Though it may seem counterintuitive, some financial securities pay constant amounts of cash for an
(almost) infinite time period. A good example is given by the so-called ‘perpetual bonds’. The most
frequently used example are the so-called ‘consols’, being government bonds issued by the UK
government (in the 18th century). These bonds still constant amounts of interest, and may never be
redeemed. Modern versions of perpetual bonds are (deeply) subordinated bonds.
Imagine an endless series of constant cash flows:
𝐶𝐹 𝐶𝐹 𝐶𝐹 𝐶𝐹
PV = (1+𝑟)1 + (1+𝑟)2 + (1+𝑟)3 + … + (1+𝑟)∞
More concrete, imagine you will earn €2,000 net per month for the next 40 years. In addition,
imagine the relevant annual simple discount rate would be 10%, resulting in 0.8333% per month.
2,000
The present value of the first payout (after one month) equals (1+0.008333)1 = €1,983.47, the PV of
the second payout would be 1,967.08, etc.
In a picture this looks as follows:
𝐶𝐹𝑡 𝐶𝐹
PV∞ = ∑∞
𝑡=1 =
(1+𝑟)𝑡 𝑟
1
𝐶𝐹𝑡 1−
(1+𝑟)𝑡
PVA = ∑𝑇𝑡=1 = CF ×
(1+𝑟)𝑡 𝑟
The ‘time value of money’ logic dictates that since we face opportunity costs (we might have
invested money meanwhile), we care more for income now than in the future. By discounting, we
make this logic explicit, and calculate our indifference between:
1. Receiving some future amount in the future, or
2. Receiving the PV of such future amount right now.
Thus, given the previously made assumptions on monthly income, you should be indifferent between
2,000
receiving €2,000 after 480 months from now, or receiving (1+0.008333)480 = €37.24 right away.
If the PV of €2,000 to be received after 480 months is only €37.24, you may imagine that after some
time period the PV of a cash flow is negligible.
This idea of ignoring the last few fractions is exactly the idea underlying the limit theorem. If we
apply that limit theorem to an infinite series (sum) of constant cash flows, we simplify:
𝐶𝐹 𝐶𝐹 𝐶𝐹 𝐶𝐹 𝐶𝐹
PV = (1+𝑟)1 + (1+𝑟)2 + (1+𝑟)3 + … + (1+𝑟)∞ = 𝑟
We call this awfully simple equation the ‘perpetuity’.
Annuity: term loans
So-called ‘term loans’ are a fine example in which a debtor pays fixed amounts of money per time
period during a finite time horizon.
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