Chapter 11:

Chapter 11:

Capital Inputs & Capital Investment

Decisions

Key Topics

1. Capital (general & specific types)

2. Capital markets (i.e. S&D of funds for capital purchases)

3. Investment decisionsa. “percentage” costs and returns

b. “dollar” costs and returns (i.e. present value)

Capital Definition

= Items (man-made inputs) used to produce other goods and services over time

Examples (categories):

1. Tangible capital (nonresidential structures, durable equipment, residential structures, inventories)

Capital Definition

2. Social capital = “infrastructure” (public works like roads, bridges, mass transit systems, sewer & water systems; public services like police, fire protection, schools, city halls, courthouses).

3. Intangible (non physical) capital (good will, patents, worker knowledge/skills)

Capital Stock and Flows

Capital stock =current market value ($) given or measured at point in time

Capital flow =either an increase in the stock of capital (i.e. investment)

or decrease in the stock of capital (i.e. depreciation)

Capital Markets

The supply of and demand for funds to buy capital goods

Household savings = supply of funds (for income in form of interest and/or profits/dividends)

Business investments in capital = demand for (uses of) funds

Interest (rate)

Payment for use of money paid by borrower to lender

Price of money; cost of a loan Types of rates

– Fixed rate is known initially and does not vary over life of the loan

– Variable or adjustable or floating rate may vary over life of the loan

Financial “Instruments” (markets)

= specific mechanisms whereby consumer savings are made available to business firms for capital spending

bonds, business loans, venture capital funds, retained earnings, company stock

purchases

Bonds

A financial contract between a borrower (e.g. bond seller who is a business firm or governmental agency) whereby the borrower agrees to pay back to the lender (consumer or bond buyer) the initial price of the bond plus any additional payments (i.e. interest).

A loan from a consumer to a borrower.

Profit-maximizing quantity of capital(company capital investment decisions)

MRPK = PK

Rate of return (%) = cost of capital (%)

Incremental $ return = incremental $ cost (present value of incremental returns = present value of incremental costs)

Graph of profit-maximizing K (based on interest rates)

r

Pk

MRPK

KK*

Time Value of Money (Basic Concept)

A dollar is worth more (or less) the sooner (later) it is received or paid due to the ability of money to earn interest.

Present value+ interest earned= future value

or Future value

- interest lost= present value

Time Value of Money to aBorrower

PV = present value

= the number of $ you will be able to

borrow presently in order to pay back a given number of $ in the future

FV = future value

= the number of $ you will have to

pay back in the future as a result of

having borrowed a given number of

$ presently

Time Value of Money to a Saver

PV = present value

= the number of $ you will have to save

presently in order to collect a given number

of $ in the future

FV = future value

= the number of $ you will be able to collect

in the future as a result of having saved a

given number of $ presently

Time Value of Money Relationships

FV1 = PV + PV (r )= PV (l + r)

FV2 = FV1 + FV1 (r )

= FV1 (l + r)= PV(l + r)(l + r)= PV (l + r)2

.

.

.

FVn = PV (l + r)n

Time Value Problems

FVn = PV (l + r)n

Given Solve for

PV, r, n FVn = PV (l + r)n = ‘compounding’

FVn, r, n PV = FVn [1/(l + r)n] = ‘discounting’

NOTE: In text, PV = R/(l + r)t. Thus, R = FVn, t=n.

How to compare two different $ amounts, two different time periods?

$X $Y

0t1

t2 t3

Comparing Two Different $ Amounts, Two Different Time Periods—A Summary of Different Ways Using Time Value of Money Concepts

Methods:

1. Discount each ‘back’ to t = 0

2. Discount $Y from t = 2 to t = 1

3. Compound each ‘forward’ to t = 3

4. Compound $X from t = 1 to t = 2

0

$X $Y

t1 t2 t3

What is the present value?

0 1 2 3 4

7 77

r = 7%

Present Value

0 1 2 3 4

7 7 7

r = 7%

PV = 7(1/1.07)1 + 7(1/1.07)2 + 7(1/1.07)3

= 7(.9345) + 7(.8734) + 7(.8163)

= 6.5415 + 6.1138 + 5.7141

= 18.37

Graph of profit-maximizing k (based on $ present value)

PV($)

PV of incremental initial cost

K* K

PV of incremental future profits