Investment and capital markets

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1 Investment and capital markets Microéconomie, chapter 15 1

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? 2

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 3

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 4

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) -1 y euros invested today deliver (1 + R) (1 + R) -1 y=y euros a year from now 5

6 Net present value NPV (1+ R) n = value n years from now of 1 euro today 1 = value today of 1 euro n years fom now n (1+ R) The interest rate R determines the net present value 6

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 7

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 8

9 Two flows of income today 1 yr 2 yrs flow A: flow B:

10 Two flows of income NPV of flow A = (1+ R) NPV of flow B = (1+ R) (1+ R) 2 10

11 Two flows of income R = 0,05 R = 0,10 R = 0,15 R = 0,20 NPV of flow A: 195,24 190,90 186,96 183,33 NPV of flow B: 205,94 193,54 182,57 172,78 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 11

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: Retirement age: 60 12

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% 13

14 The value of lost revenues NPV = W 0 + W 0 (1+ g)(1 m 1 ) (1+ R) + W 0(1+ g) 2 (1 m 2 ) (1+ R) W 0 (1+ g)7 (1 m 7 ) (1+ R) 7 14

15 The value of lost revenues 15

16 The value of lost revenues The sum of column 4 is the NPV of lost revenues: $ This NPV computations are used to write life insurance contracts, or for litigation for compensation in cases of accidental death 16

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? 17

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) (1+ R) (1+ R) (1+ R) 10 18

19 The value of a bond NPV of the flow of payments (thousands ) 2 1,5 1 The higher the interest rate, the smaller the value of the bond 0,5 0 0,05 0,10 0,15 0,20 Interest rate 19

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 20

21 NPV n = The value of a bond NPV n 1 (1+ R) NPV n (1+ R) (1+ R) (1+ R) n = 100 (1+ R) (1+ R) (1+ R) n +1 1 =100 (1+ R) 1 (1+ R) 1 (1+ R) n +1 NPV n =100 1 (1+ R) 1 (1+ R) n (1+ R) NPV =100 1 R 21

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 22

23 The actuarial return of a bond If P is the market price of a perpetual bond paying C since P = C R, then R = C P 23

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% 24

25 The actuarial return of a bond Computing the return of a bond: if P equals the NPV = 100 (1+ R) (1+ R) (1+ R) (1+ R) 10 then R can be computed as a function of P 25

26 The actuarial return of a bond NPV of payments (thousands ) 2 1,5 1 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 0,5 0 0,05 0,10 0,15 0,20 Interest rate 26

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 27

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 28

29 The return of corporate bonds If the price of a bond A is 120,25, then its return is: 29

30 The return of corporate bonds If the price of a bond B is 73,50, then its return is: 30

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 31

32 The Net Present Value as a guide for investment decisions C = cost of capital π n = profits of year n (n =10) π NPV = - C + 1 (1+ R) + π 2 (1+ R) π 10 2 (1+ R) 10 R = return of an alternative investment (discount rate, oportunity cost) with a similar risk the investment is profitable is NPV > 0 32

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 33

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 per month Useful life of the plant: 20 years Scrap value of the plant 1 million Is this investment profitable? 34

35 The Net Present Value for investments The Net Present Value of the investment is NPV = 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 0,96 (1+ R) + 0,96 (1+ R) ,96 (1+ R) (1+ R) 20 R* = 7,5% 35

36 The Net Present Value as a guide to investment decisions Net Present Value ( millions) 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% ,05 R*=7,5% 0,10 0,15 0,20 discount factor R 36

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 37

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 per year in real terms 38

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% 39

40 The Net Present Value as a guide for investment decisions 10 8 If real R = 4%, the NPV is positive. The investment Is profitable Net Present Value ( millions) ** discount rate R R*=7,5% 40

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 41

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 42

43 The Net Present Value as a guide for investment decisions NPV = (1+ R) 1 (1+ R) 0,5 2 (1+ R) 3 + 0,96 (1+ R) 4 + 0,96 (1+ R) ,96 (1+ R) (1+ R) 20 43

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 44

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 45

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 46

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 47

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 48

49 Capital asset pricing model Consider investing in the stock market through an investmet fund if r m is the expected average return in the market and r f is the riskless return then r m - r f is the risk premium for non diversifiable risks It is the excess return needed to accept the non diversifiable risks of the stock market 49

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 r i r f = β(r m r f ) r i = expected return of the stock β = beta of the stock 50

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 51

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 = r f + β(r m r f ) i.e. the riskless rate plus a risk premium for the non diversifiable risks 52

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 53

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 54

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 55

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 be the purchase price Let be the scrap value after 6 years The purchasing decision can be made considering the Net Present Value of the car 56

57 Consumer s investment decisions Example: costs and benefits of buying a car (S E) NPV = (S E) + (1+ R) + (S E) (S E) (1+ R) (1+ R) (1+ R) 6 57

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 58

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 59

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? 60

61 Investing in education Cost of going to college Opportunity cost of wages non earned say per year Registration fees, housing, etc. say another per year i.e per year during 4 years 61

62 Investing in education Benefits from going to college A higher starting wage and better career prospects On average, 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? 62

63 Investing in education NPV = (1+ R) 40 (1+ R) 2 40 (1+ R) (1+ R) (1+ R) 23 63

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

65 Investing in education 65

66 Investing in education On average, the wage is $ higher per year Assume this difference persists for 20 years An MBA lasts 2 years and costs around $ The opportunity cost of the non earned pre- MBA wage is of $ per year All in all an MBA costs $ per year during two years 66

67 Investing in education The net present value of an MBA is NPV = (1+ R) + 30 (1+ R) (1+ R) 21 With a discount rate of 5%, it amounts to $

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 68

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 69

70 How interest rates are determined? R Interest rate D M and D E, households demad (M) and firms demand (E) are decreasing in the interest rate D T D E D M Funds to lend 70

71 How interest rates are determined? R Interest rate S The equilibrium interest rate is R* R* D T D E D M Q* Funds to lend 71

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 72

73 Changes in the equilibrium interest rate R Interest rate S R* During recessions the demand for funds decreases, and so do interest rates R 1 D T Q 1 Q* D T Funds to lend 73

74 Changes in the equilibrium interest rate R Interest rate S The government debt pushes interest rates upwards R 2 R* D T D T Q* Q 2 Funds to lend 74

75 Changes in the equilibrium interest rate R Interest rate S S When the central bank increases the money supply, the supply of funds to lend increases R* R 1 D T Q* Q 1 Funds to lend 75

Investment, Time, and Capital Markets

C H A P T E R 15 Investment, Time, and Capital Markets Prepared by: Fernando & Yvonn Quijano CHAPTER 15 OUTLINE 15.1 Stocks versus Flows 15.2 Present Discounted Value 15.3 The Value of a Bond 15.4 The