Capital and Financial Market Present Value

1
Capital and Financial MarketPresent Value
Future Value

• Hall and Lieberman, 3rd edition, Thomson
  South-Western, Chapter 13

2
Overview

• Investment
• Capital
• Human capital
• General human capital
• Specific human capital
• Future value
• Present value

3
Capital and Financial Markets

• Events occur every day dealing with money
• A decision makerconsciously or unconsciouslyis
  putting a value on money to be received in the
  future
• Focus on decisions about
• Investing in productive capital
• factory buildings, equipment, or skills and
  training
• Purchasing financial assets, such as stocks and
  bonds

4
Investment Decision

• Investment
• Capital purchase over some period of time
• Human capital investment
• Firms goal is still to maximize its profit
• However it is not appropriate to apply marginal
  approach to profits
• Capital is not always rented
• Capital will not last forever
• Length of time that capital lasts matters when
  deciding whether to buy it

5
Consider

• Furnace Advertisement
• Furnace costs 2,000
• Energy Savings 200/year
• Claim The furnace will pay for itself in 10
  years

Is this true?
6
Consider

• 1626, Peter Minuit bought Manhattan from the
  Man-a-hat-a Indians for goods valued at 24
• The 12800 acres are now valued at 627
  million/acre or 8 trillion unimproved
• This was a heck a deal for the Dutch

Is this true?
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The Value of Future Dollars

• Always preferable to receive a given sum of money
  earlier rather than later
• Because present dollars can earn interest and
• Because borrowing dollars requires payment of
  interest
• 1 one year from now is not equal to 1 today
• Mechanism (r rate of interest)
• Opportunity cost of spending 1 today
• (1 r)1 (1 r)
• at r 0.1 opportunity cost is 1.10 next period

8
Future Value

• Future Value the value in dollars at a future
  point in time of a sum of money today.
• Compounding successive application of interest
  payments to generate future values.
• Period 0 Period 1 Period 2
• 1 (1r)1 (1r)(1r)1
• (1r)21

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Future Value

• Generally, 1 today is worth (1r)t t years from
  now
• At r 0.1
• Period 0 1
• Period 1 (1 0.1) 1.10
• Period 2 (1 0.1)2 1.21
• Period 3 (1 0.1)3 1.33
• Period 40 (1 0.1)40 45.26

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Future Value Man-a-hat-a Indians

• How much is 24 in 1626 worth today if they just
  collected interest?
• 1 in 1626 is worth (1r)T in 2006,
• T 2006-1626 380
• At r 0.1 24(1r)380 1,286,564 trillion
• At r 0.08 24(1r)380 120.6 trillion
• At r 0.07 24(1r)380 35.2 trillion
• At r 0.06 24(1r)380 99.2 billion
• At r 0.05 24(1r)380 2.7 billion

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Example Investment for Retirement

• Suppose you want to be a millionaire when you
  retire. How much should you start putting away
• FV 1 million
• A annual amount invested
• FV A((rT1 1)/r)
• See handout for derivation

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Example Investment for Retirement

• Suppose you want to be a millionaire when you
  retire. How much should you start putting away
• FV A((rT1 1)/r)
• Current age 18 Millionaire by 40? 50? 60?

13
Present Value

• Present value (PV) of a future payment is the
  value of that future payment in todays dollars
• Value of any asset is sum of present values of
  all future benefits it generates
• Discounting
• Converting a future value into its present-day
  equivalent
• Discount rate
• Interest rate used in computing present values
• Period 0 Period 1
• 1 (1r)1
• 1/(1r) 1

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Present Value

• Suppose that the annual interest rate is r, PV of
  Y to be received T years in the future is equal
  to
• Present value of a future payment is smaller if
• Size of the payment is smaller
• Interest rate is larger
• Payment is received later

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Present Value

• Generally
• Period 0 Period T
• 1 (1r)T1
• 1/(1r)T 1
• At r 0.1 compute present value of 1 in Period
  X
• Period Present Value
• 1 1/(1 .1) 0.91
• 2 1/(1 .1)2 0.83
• 3 1/(1 .1)3 0.75
• 40 1/(1 .1)40 0.02

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Example Furnace

• 200 T periods in the future will be worth
  200/(1r)T now
• At r 0.1
• Year Present Value
• 1 200/(1 .1) 181.82
• 2 200/(1 .1)2 165.29
• 3 200/(1 .1)3 150.26
• 200/(1 .1)10 77.11
• ADD UP THESE RETURNS
• Present Value 1,429
• It would take 24 years to break even at r 0.1

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Conclusions Regarding Present Future Value

• General Formula
• PV Present Value
• FV Future Value
• FVT (1r)T PV0 (Compounding)
• PV0 FVT / (1r)T (Discounting)

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Figure 1 The Investment Curve

• A rise in interest rate causes a decrease in
  investment expenditures

A
10
B
5
D
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What Happens When Things Change The Investment
Curve

• At high interest rates, firms end up buying less
  of all different kinds of capital
• Thus, as interest rate rises, each firm will
  place a lower value on additional capital and
  decide to purchase less of it
• Lower interest rates increase firms investment
  in physical capital
• Causing capital stock to be larger, and overall
  standard of living to be higher

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Investment in Human Capital

• Who pays for workers to acquire human capital
  employees or employers?
• If paid by individual, how does he make the
  decision?
• 2 types of human capital
• General human capital
• Knowledge, education, or training that is
  valuable at many different firms
• Specific human capital
• Knowledge, education, or training that is
  valuable only at a specific firm

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General Versus Specific Human Capital

• Employers will provide specific human capital
  (SHC) at the firms expense
• Workers have limited incentive to pay for SHC
  because it increases their value to only one
  firm, and that firm will capture the benefits
• Workers will acquire general human capital (GHC)
  on their own
• Employers have limited incentive to provide GHC
  because it increases workers value to many firms
  and workers will capture benefits in the form of
  a higher wage

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The Decision to Invest in General Human Capital

• Human capital the worker possesses is an asset
  that generates higher income in the future
• Benefit of any given human capital investment
  equals total present value of additional future
  income
• Investment in human capital is inversely related
  to interest rate
• Lower interest rates
• encourage individuals to invest in general human
  capital
• increase total amount of human capitaland
  overall standard