Microéconomie, chapter 15 - CEScermsem.univ-paris1.fr/davila/teaching/SBS/Ch15_Pindyck-09.pdf · 1...
Transcript of Microéconomie, chapter 15 - CEScermsem.univ-paris1.fr/davila/teaching/SBS/Ch15_Pindyck-09.pdf · 1...
1 Solvay Business School – Université Libre de Bruxelles
1
Microéconomie, chapter 15
Investment and capital markets
2 Solvay Business School – Université Libre de Bruxelles
2
Points to be discussed Discounted present value
The value of bonds
The net present value as a criterion for investment decisions
Adjusting for risks
Consumers’ investment decisions
Investing in education
How are interest rates determined?
3 Solvay Business School – Université Libre de Bruxelles
3
Introduction
What characterizes capital markets? investments, financial or physical, take time
to produce a return They induce a present, sure cost But they deliver only future, uncertain returns Present sure costs and future uncertain
returns must be compared
4 Solvay Business School – Université Libre de Bruxelles
4
Net present value NPV
How do we compute the value of a flow of future returns? The present value of a future income P is the
investment today necesary to obtain a return P at the same date
The present value of a flow of future incomes is the sum of the present values of each of them
5 Solvay Business School – Université Libre de Bruxelles
5
Net present value NPV
Future value: if the annual return R is constant, then 1 euro invested today delivers 1 + R euros
a year from now x euros invested today deliver (1 + R)x
euros a year from now Value today of y euros a year from now? (1 + R)-1y euros invested today deliver (1 +
R) (1 + R)-1y=y euros a year from now
6 Solvay Business School – Université Libre de Bruxelles
6
Net present value NPV
€
(1+ R)n = value n years from now of 1 euro today
1(1+ R)n
= value today of 1 euro n years fom now
The interest rate R determines the net present value
7 Solvay Business School – Université Libre de Bruxelles
7
Net present value of €1 in the future
R 1 year 5 years 10 years 30 years
1% €0,990 €0,951 €0,905 €0,742
2% €0,980 €0,906 €0,820 €0,552
5% €0,952 €0,784 €0,614 €0,231
10% €0,909 €0,621 €0,386 €0,057
8 Solvay Business School – Université Libre de Bruxelles
8
Assessing flows of future incomes
Flows of future incomes are compared comparing their net present values
Their net present values depend on the assumed rate of return R
9 Solvay Business School – Université Libre de Bruxelles
9
Two flows of income
flow A: €100 €100 €0 flow B: €20 €100 €100
today 1 yr 2 yrs
10 Solvay Business School – Université Libre de Bruxelles
10
€
NPV of flow A =100 +100
(1+ R)
NPV of flow B = 20 +100
(1+ R)+
100(1+ R)2
Two flows of income
11 Solvay Business School – Université Libre de Bruxelles
11
Two flows of income
NPV of flow A: €195,24 €190,90 €186,96 €183,33
NPV of flow B: €205,94 €193,54 €182,57 €172,78
R = 0,05 R = 0,10 R = 0,15 R = 0,20
Which flow of future incomes has a higher neet present value depends of the interest rate R
For small values of R, B’s net present value is higher For big values of R, A’s net present value is higher
12 Solvay Business School – Université Libre de Bruxelles
12
The value of lost revenues
The NPV can be used to compute the value for a household of the lost revenues due to the death of one of the spouses
Example: One of the spouses dies at 52 in 2009 wage: €85.000 Retirement age: 60
13 Solvay Business School – Université Libre de Bruxelles
13
The value of lost revenues
Which is the net present value of the lost revenues for the household? The wage must be adjusted for foreseable
career advancemts (g%) say g=8%
The probability (m) of death at a later date must be taken into account as well It can be obtained from the statistics of mortality
Assume the return on Treasury bills is R=9%
14 Solvay Business School – Université Libre de Bruxelles
14
€
NPV = W0 +W0(1+ g)(1−m1)
(1+ R)
+ W0(1+ g)2(1−m2)(1+ R)2 + ...
+W0(1+ g)7(1−m7)
(1+ R)7
The value of lost revenues
15 Solvay Business School – Université Libre de Bruxelles
15
The value of lost revenues
16 Solvay Business School – Université Libre de Bruxelles
16
The value of lost revenues
The sum of column 4 is the NPV of lost revenues: $650.252
This NPV computations are used to write life insurance contracts, or for litigation for compensation in cases of accidental death
17 Solvay Business School – Université Libre de Bruxelles
17
The value of a bond
A bond is a contract by which the issuer commits to make a flow of payments to the holder, either indefinitely or until a final payment at a fixed date
Example: a corporate bond guarantees a payment of €100 per year (the coupon) for the next 10 years and a final payment of €1000 How much is this bond worth?
18 Solvay Business School – Université Libre de Bruxelles
18
The value of a bond
Payments of the bond: Payments from coupons = €100 per year for
10 years Final payment = €1000 within 10 years
€
NPV = 100(1+ R)
+100
(1+ R)2 +
...+ 100(1+ R)10 +
1000(1+ R)10
19 Solvay Business School – Université Libre de Bruxelles
19
The value of a bond
Interest rate 0,05 0,10 0,15 0,20
NPV
of t
he fl
ow o
f pa
ymen
ts (th
ousa
nds €)
0 0,5
1
1,5
2
The higher the interest rate, the smaller the value
of the bond
20 Solvay Business School – Université Libre de Bruxelles
20
The value of a bond
An perpetual bond pays a fixed income every period indefinitely
The net present value of a perpetual bond is an infinite sum
If the interest rate is R, the net present value of a perpetual bond of €100 is
NPV = €100/R
21 Solvay Business School – Université Libre de Bruxelles
21
The value of a bond
€
NPVn = 100(1+ R)
+100
(1+ R)2 + ...+ 100(1+ R)n
€
NPVn1
(1+ R) = 100
(1+ R)2 +100
(1+ R)3 + ...+ 100(1+ R)n+1
€
NPVn 1− 1(1+ R)
=100 1
(1+ R)−
1(1+ R)n+1
€
NPVn =100
1(1+ R)
−1
(1+ R)n+1
1− 1(1+ R)
€
→NPV =100 1R
22 Solvay Business School – Université Libre de Bruxelles
22
The actuarial return of a bond
Treasury bills and corporate bonds are trade in secondary markets
The price of a bond is then determined by its demand and supply
The market price of a bond determines its implicit return
23 Solvay Business School – Université Libre de Bruxelles
23
The actuarial return of a bond
If P is the market price of a perpetual bond paying C
€
since P =CR
, then R =CP
24 Solvay Business School – Université Libre de Bruxelles
24
The actuarial return of a bond
If the price of a perpetual bond paying €100 is €1000, its actuarial return is
R = €100/ €1000 = 0,10 = 10%
25 Solvay Business School – Université Libre de Bruxelles
25
The actuarial return of a bond
Computing the return of a bond:
€
if P equals the NPV = 100(1+ R)
+100
(1+ R)2 +
...+ 100(1+ R)10 +
1000(1+ R)10
then R can be computed as a function of P
26 Solvay Business School – Université Libre de Bruxelles
26
The actuarial return of a bond
Interest rate 0,05 0,10 0,15 0,20 0
0,5
1
1,5
2 N
PV o
f pay
men
ts (th
ousa
nds €)
The actuarial return is the interest rate that equalizes the NPV of the flow of payments from the bond and its
market price
The actuarial return of a bond is inversely related to its price
27 Solvay Business School – Université Libre de Bruxelles
27
The actuarial return of a bond
The return can vary across bonds Corporate bonds have typically a higher return than
Treasury bills This is a consequence of the different levels of risk of
different bonds Riskier bonds yield higher returns Governments very rarely do not pay Some firms are much less sure bets
28 Solvay Business School – Université Libre de Bruxelles
28
The return of corporate bonds
The return of a bond depends on its nominal value and its coupon
Assume
Nominal value
Annual coupon maturity
firm A €100 €7,5 10 years
firm B €100 €5,5 5 years
29 Solvay Business School – Université Libre de Bruxelles
29
The return of corporate bonds
If the price of a bond A is 120,25, then its return is:
30 Solvay Business School – Université Libre de Bruxelles
30
The return of corporate bonds
If the price of a bond B is 73,50, then its return is:
31 Solvay Business School – Université Libre de Bruxelles
31
The Net Present Value as a guide for investment decisions
Investors compare the present value of the flow of returns from an investment with its cost
The investment is profitable if the present value of the flow of returns exceeds this cost
32 Solvay Business School – Université Libre de Bruxelles
32
The Net Present Value as a guide for investment decisions
€
C = cost of capital π n = profits of year n (n =10)
NPV = -C +π1
(1+ R)+
π 2
(1+ R)2 + ...+ π10
(1+ R)10
R = return of an alternative investment (discount rate, oportunity cost) with a similar risk
the investment is profitable is NPV > 0
33 Solvay Business School – Université Libre de Bruxelles
33
The Net Present Value as a guide for investment decisions
Choice of the discount rate The choice matters It should be the return to a similar investment
It must have the same risk In absence of risk, the opportunity cost is the
return of Treasury bills
34 Solvay Business School – Université Libre de Bruxelles
34
The Net Present Value as a guide to investment decisions Example:
Build a plant costs €10 millions Its output will be 8000 engines each month
for 20 years Cost of producing 1 engine = €42,50 Sale price of 1 engine = €52,50 Profit = €10 per engine, i.e. €80.000 per month Useful life of the plant: 20 years Scrap value of the plant €1 million
Is this investment profitable?
35 Solvay Business School – Université Libre de Bruxelles
35
The Net Present Value for investments
The Net Present Value of the investment is
R*=7,5% is the discount factor such that NPV=0 If the return of Treasury bills is below 7,5%, the NPV
is positive If the return of Treasury bills is above 7,5%, the NPV
is negative
€
NPV = -10 + 0,96(1+ R)
+0,96
(1+ R)2 +
...+ 0,96(1+ R)20 +
1(1+ R)20
R* = 7,5%
36 Solvay Business School – Université Libre de Bruxelles
36
The Net Present Value as a guide to investment decisions
discount factor R 0 0,05 0,10 0,15 0,20
-6
Net
Pre
sent
Val
ue
(€ m
illio
ns)
-4
-2
0
2
4
6
8
10 • The investement is not
profitable if Treasury bills yield more than 7,5%
• The investement is not profitable if Treasury bills yield
less than 7,5%
R*=7,5%
37 Solvay Business School – Université Libre de Bruxelles
37
The Net Present Value as a guide to investment decisions
For investment decisions one must distinguish between real and nominal interest rates The real interest rate discounts the impact of
inflation
38 Solvay Business School – Université Libre de Bruxelles
38
Real and nominal interest rates
Assume prices and costs are given in real terms and that the inflation rate is 5% then nominal prices and costs are
today, P = 52,50 1 year, P = 1,05 x 52,50 = 55,13, 2 years, P = 1,05 x 55,13 = 57,88… today, C = 42,50 1 year, C = 1,05 x 42,50 = 44,63, 2 years, C = 1,05 x 44,63 = 46,86… Profits are 960.000 per year in real terms
39 Solvay Business School – Université Libre de Bruxelles
39
Real and nominal interest rates
If the flow of profits is in real terms, then the discount rate must also be in real terms, for instance R real = R nominal - inflation = 9% - 5% =
4%
40 Solvay Business School – Université Libre de Bruxelles
40
The Net Present Value as a guide for investment decisions
discount rate R 0.10 0.15 0.20 0
-6
Net
Pre
sent
Val
ue
(€ m
illio
ns)
-4
-2
0
2
4
6
8
10
0.04**
If real R = 4%, the NPV is positive. The investment
Is profitable
R*=7,5%
41 Solvay Business School – Université Libre de Bruxelles
41
The Net Present Value as a guide for investment decisions
The present value of some future values may be negative Temporary losses may be caused by, for
instance The time to build a plant High initial costs that decrease progressively
The investment decision must take into account the possibility of temporary losses
42 Solvay Business School – Université Libre de Bruxelles
42
The Net Present Value as a guide to investment decisions
The engine production plant Time to build the plant: 1 year
Cost today €5 millions Cost within a year €5 millions
Expected losses first year €1 million, and €0,5 million the next two years
Profits of €0,96 million per year starting at year 3 for the next 20 years
Scrap value of the plant €1 million
43 Solvay Business School – Université Libre de Bruxelles
43
The Net Present Value as a guide for investment decisions
€
NPV = - 5 - 5(1+ R)
−1
(1+ R)2 −0,5
(1+ R)3
+0,96
(1+ R)4 +0,96
(1+ R)5 + ...
+0,96
(1+ R)20 +1
(1+ R)20
44 Solvay Business School – Université Libre de Bruxelles
44
Adjusting for risk
Under uncertainty any risk can be taken care of adding a risk premium to the riskless interest rate
Recall: the risk premium is the amount that a risk averse individual would be willing to pay to get rid of the risk
45 Solvay Business School – Université Libre de Bruxelles
45
Diversifiable and non diversifiable risks
Diversifiable risks can be eliminated investing in different projects or firms
Non diversifiable risks cannot be aliminated and must be included in the risk premium
46 Solvay Business School – Université Libre de Bruxelles
46
Diversifiable and non diversifiable risks
Diversification spreads the risk thin over several uncorrelated options Investments funds invest in different
unrelated sectors Firms invest in several different unrelated
projects Assets with diversifiable risks do not have a
risk premium – their return is close to the riskless rate
47 Solvay Business School – Université Libre de Bruxelles
47
Diversifiable and non diversifiable risks
Some risks cannot be eliminated Firms profits depend on the business cycle Future growth is uncertain
Investor seek a risk premium for nondiversifiable risks
The discount factor must include a risk premium
48 Solvay Business School – Université Libre de Bruxelles
48
Diversifiable and non diversifiable risks
Capital Asset Pricing Model (CAPM) Explains the risk premium as a function of the
correlation of the return of an asset with the average return in the stock market
49 Solvay Business School – Université Libre de Bruxelles
49
Capital asset pricing model
Consider investing in the stock market through an investmet fund if rm is the expected average return in the market and rf is the riskless return then rm - rf is the risk premium for non diversifiable
risks It is the excess return needed to accept the non
diversifiable risks of the stock market
50 Solvay Business School – Université Libre de Bruxelles
50
Capital asset pricing model
The return of different assets is correlated with that of the stock market The CAPM explains the excess return of
each stock by its correlation with the excess return of the market
€
ri − rf = β(rm − rf ) ri = expected return of the stockβ = beta of the stock
51 Solvay Business School – Université Libre de Bruxelles
51
Capital asset pricing model
β mesures the sensitivity of the asset to non diversifiable risks A beta close to 1 means the stock has the same non
diversifiable risks than the market A beta close to 0 means the only risks of the stock are
diversifiable and hence its return does not exceed the riskless rate
The bigger its beta, the higher the expected return of an asset in excess of the riskless rate
52 Solvay Business School – Université Libre de Bruxelles
52
Capital asset pricing model
Once its beta i known, the appropriate discount factor to compute the Net Present Value of an investement in the stock is
€
discount factor = rf + β(rm − rf )
i.e. the riskless rate plus a risk premium for the non diversifiable risks
53 Solvay Business School – Université Libre de Bruxelles
53
Estimation of beta
For stocks, beta can be estimated statistically For direct investments, beta is more difficult to
estimate Firms typically use the cost of capital for the
frim as nominal discount rate The weighted average of the expected return of its
stocks and the interest rate the firm pays for loans
54 Solvay Business School – Université Libre de Bruxelles
54
Consumer’s investment decisions
Consumers face an investment problem when they buy durable goods They have to compare a flow of future
services to a present purchase price
55 Solvay Business School – Université Libre de Bruxelles
55
Consumer’s investment decisions
Example: costs and benefits of buying a car A car provides transportation services for 5
or 6 years One needs to compare the flow of future
services (transportation less insurance, maintenance and gas) and the purchase price
56 Solvay Business School – Université Libre de Bruxelles
56
Consumer’s investment decisions
Example: costs and benefits of buying a car Let S be the value in euros of the transportation
services provided by the car Let E be the annual operating cost
insurance, maintenance, and gas Let €15.000 be the purchase price Let €3.000 be the scrap value after 6 years
The purchasing decision can be made considering the Net Present Value of the car
57 Solvay Business School – Université Libre de Bruxelles
57
Consumer’s investment decisions
Example: costs and benefits of buying a car
€
NPV = −15.000 + (S − E) +(S − E)(1+ R)
+
(S − E)(1+ R)2 + ...+ (S − E)
(1+ R)6 +3.000
(1+ R)6
58 Solvay Business School – Université Libre de Bruxelles
58
Consumer’s investment decisions
The decisions to buy or not depends on the discount rate If the purchase is financed by a loan, the
interest rate of the loan is the relevant discount factor
59 Solvay Business School – Université Libre de Bruxelles
59
Investing in education
Individuals have to make decisions about their education Going to college or not? Pursuing graduate education, MBA, PhD?
Education improves the individual’s productivity and therefore improves his of her expected longlife income
60 Solvay Business School – Université Libre de Bruxelles
60
Investing in education
Consider the choice between going to college or looking for a job after high school What is the net present value of going to
college?
61 Solvay Business School – Université Libre de Bruxelles
61
Investing in education
Cost of going to college Opportunity cost of wages non earned – say €20.000 per year
Registration fees, housing, etc. – say another €20.000 per year
i.e. €40.000 per year during 4 years
62 Solvay Business School – Université Libre de Bruxelles
62
Investing in education
Benefits from going to college A higher starting wage and better career
prospects On average, €20.000 per year over the wage
earned with a high school degree only Assume the active life is 20 years (!)
What is the net present value of going to college?
63 Solvay Business School – Université Libre de Bruxelles
63
Investing in education
€
NPV = −40 − 40(1+ R)
−40
(1+ R)2−
40(1+ R)3
+20
(1+ R)4+ ...+ 20
(1+ R)23
64 Solvay Business School – Université Libre de Bruxelles
64
Investing in education
Which is the relevant discount rate? Assume there is no inflation, so that we can
use the real discount rate A rate of 5% is a typical opportunity cost for
most households It is the return of alternative investments
The net present value of going to college is approximately €66.000
65 Solvay Business School – Université Libre de Bruxelles
65
Investing in education
66 Solvay Business School – Université Libre de Bruxelles
66
Investing in education
On average, the wage is $30.000 higher per year
Assume this difference persists for 20 years An MBA lasts 2 years and costs around
$45.000 The opportunity cost of the non earned pre-
MBA wage is of $45.000 per year All in all an MBA costs $90.000 per year during
two years
67 Solvay Business School – Université Libre de Bruxelles
67
Investing in education
The net present value of an MBA is
€
NPV = −90 − 90(1+ R)
+30
(1+ R)2+ ...+ 30
(1+ R)21
With a discount rate of 5%, it amounts to $158.000
68 Solvay Business School – Université Libre de Bruxelles
68
How interest rates are determined?
An interest rate is the price payed by a borrower to a lender in exchange for a loan It is determined by the supply and demand of funds to
lend Supply of funds comes from household savings Demand of funds comes from
Households wishing to comsume beyond their current income
Firms intending to make some investments
69 Solvay Business School – Université Libre de Bruxelles
69
How interest rates are determined? For households, the higher the interest rate, the
costlier is consumption They borrow less Households demand decreases with the interest rate
For firms investments become profitable if the corresponding NPV> 0 Higher interest rates imply lower NPVs Firms demand is also decreasing in the interest rate
Total demand, from both households and firms, is therefore decreasing
70 Solvay Business School – Université Libre de Bruxelles
70
How interest rates are determined?
Funds to lend
R Interest
rate
DT
DM
DE
DM and DE , households demad (M) and firms demand (E) are decreasing in the
interest rate
71 Solvay Business School – Université Libre de Bruxelles
71
S
How interest rates are determined?
Funds to lend
R Interest
rate
R*
Q*
The equilibrium interest rate is R*
DT
DM
DE
72 Solvay Business School – Université Libre de Bruxelles
72
How interest rates are determined?
Supply and demand for funds to lend determine the equilibrium interest rate In a recession, the NPV of investments
decrease, firms invest less and demand for funds decreases. Interest rates therefore decrease
On the other hand, government debt increases the demand for funds, pushing interest rates upwards
73 Solvay Business School – Université Libre de Bruxelles
73
Changes in the equilibrium interest rate
S
DT
R*
Q*
During recessions the demand for funds decreases, and so do
interest rates
D’T
Q1
R1
Funds to lend
R Interest
rate
74 Solvay Business School – Université Libre de Bruxelles
74
Changes in the equilibrium interest rate
S
DT
R*
Q*
The government debt pushes interest rates upwards
Q2
R2
D’T
Funds to lend
R Interest
rate
75 Solvay Business School – Université Libre de Bruxelles
75
Changes in the equilibrium interest rate
S
DT
R*
Q*
When the central bank increases the money supply, the supply of
funds to lend increases S’
R1
Q1
Funds to lend
R Interest
rate