Selecting an Interest Rate for SelectingComparing Projects

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Selecting an Interest Rate for Selecting/Comparing
Projects

• Generally specified by management
• MARR Minimum Attractive Rate of Return, defines
  minimum amount you are willing to make on an
  investment
• Assume you can ALWAYS make the interest rate --
  so your project must beat it to be worth the
  investment.
• PW is a measure of worth above the baseline

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Selecting an Interest Rate

• Interest rate represents an opportunity cost for
  funds
• The rate should, at a minimum, define the cost of
  capital -- that is, the cost of funds
• Additional percentage points above cost of
  capital represent desired profit margin

3
Is MARR Important

• Is project selection sensitive to MARR?
• If you change MARR, might you change your mind as
  to which project is better? (yes)
• Sensitivity analysis is always a good idea

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Example
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Sources of Capital

• Loans
• Traditional bank funding
• Assets offered as collateral for possible
  defaults
• Investment capital firm
• Future contracts or company ownership offered
• Bond Issue
• Stock Issue

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Loans

• Financial instrument in which one borrows money
  and pays it back over time according to some
  predefined arrangement.

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Loan Terminology

• Principal Amount borrowed.
• Remaining Balance Remaining principal owed.
• True Cost of Loan Interest rate that equates
  all payments to principal loaned.

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Payment Plan 1 Equal Principal

• Example 10,000 at 10 per year, 5 years

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Payment Plan 1 Equal Principal
10
Plan 2 Equal Total Payments

• Example 10,000 at 10 per year, 5 years

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Payment Plan 2 Equal Total
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Plan 1 versus Plan 2

• Total Principal Paid is the same.
• Equal Principal Payments
• Total Interest Paid 3,000
• Time Zero Value of TP (10) 10,000
• Equal Total Payments
• Total Interest Paid 3,189
• Time Zero Value of TP (10) 10,000

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Plan 3 Specially Designed Plan

• Ex Increasing Principal Payment Plan

n LBn-1 IPn PPn TPn 1 10,000 1,000 1,000 2,00
0 2 9,000 900 2,000 2,900 3 7,000 700 3,000
3,700 4 4,000 400 4,000 4,400
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Plan Statistics

• Total Principal Paid is the same.
• Total Interest Paid 3,000
• Time Zero Value of TP (10) 10,000
• Same as others!
• Why have different plans?
• People have budgets.
• Payments only equate at 10 interest.

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Plan 3 Specially Designed Plan

• Any payment scheme can be completed.
• Must compute true cost of loan. (15.15)

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Bonds

• Financial instrument in which companies borrow
  money from investors. Investors are provided
  coupon payments and returned capital at end.

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Bond Terminology

• Principal Face value of bond.
• Current Yield Interest Payment/Price of Bond
  (Face Value at initial offering)
• Yield to Maturity Interest rate the bond earns
  (payments plus return of face value).

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Bond Example

• If a bond holder wants to sell their bond, they
  can do so on the market.

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Bond Example
IBM 5¼ 09 5.1 4 106.13 0.88
Coupon Rate 5.25 Expires 2009 Current Yield
5.1 Volume 4M Price 106.13 ( of face) Change
0.88
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Bond Example

• Lets assume this is a 10,000 bond.
• The current yield is
• (10,0005.25)/10,613 4.9
• Assume next coupon payment in 6 mos.
• If you buy it, your cash flow diagram is

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Bond Example

• Lets assume this is a 10,000 bond. If you buy
  it, your cash flow diagram is

0
Pay 1.061310,000 for the bond.
10613
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Bond Example

• Lets assume this is a 10,000 bond. If you buy
  it, your cash flow diagram is

A
A
A
A
262.50
A
0
03
04
09
Receive bi-annual payments Coupon Rate
5.25 Payment .0525 10,000 525 Paid every
6-months 525/2 262.50
10613
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Bond Example

• Lets assume this is a 10,000 bond. If you buy
  it, your cash flow diagram is

10000
A
A
A
A
262.50
A
0
03
04
09
Company returns the principal amount (face value)
to you when the bond reaches maturity.
10613
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Bond Example

• Lets assume this is a 10,000 bond. If you buy
  it, your cash flow diagram is

10000
A
A
A
A
262.50
A
0
03
04
09
To calculate Yield to Maturity, find the rate
that equates outflows with inflows
10613
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Bond Example

• Lets assume this is a 10,000 bond. If you buy
  it, your cash flow diagram is

10000
A
A
A
A
262.50
A
0
03
04
09
10613
These roughly equate at isa2.53 which is ia
1.02532-15.12
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Bond Market and Rates

• New 10,000 bonds are issued on the market with a
  current yield of 6.
• One year later, a similar company issues its
  10,000 bond on the market with a yield of 6.5.
• Would you buy the old bond on the market?

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Bond Market and Rates

• New 10,000 bonds are issued on the market with a
  current yield of 6.
• One year later, a similar company issues its
  10,000 bond on the market with a yield of 6.5.
• Would you buy the old bond on the market?

As interest rates increase, prices of bonds with
lower rates drop.
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Bond Market and Rates

• If rates go up, lower interest rate bond values
  drop
• Buy them at discounts.
• If rates go down, higher interest rate bond
  values rise
• Buy them at premiums.

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Other Notes on Bonds

• Many entities sell bonds
• Companies
• Governments
• Municipalities
• Government or Municipal Bonds generally have tax
  breaks
• Interest rates are not only input to price
• Bonds are rated for safety
• AAA versus BBB

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Other Bond Variants

• Zero Coupon Bonds
• Savings Bonds
• Similar in figure to zero coupon, as principal
  and accrued interest paid at end.
• Principal Interest Payment Bonds
• Specialized plans. Like loans.

X
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Stock Issues

• Company issues (sells) stock on the market.
• Company becomes a public entity
• Company must adhere to wishes of shareholders
• Directors relinquish liability

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Stock Issues

• Company often keeps a number of shares when
  issuing stock
• If stock rises, their treasure chest grows
• Can use stock in acquisitions of other companies
  or sell later to raise cash

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Cost of Capital

• Hard to evaluate cost of capital with respect
  to stock issues.
• If company pays a dividend, then the yield can be
  viewed as the cost of capital (or at least a
  lower bound).
• If no dividend, companies use the growth rate of
  the company as a measure of the cost of capital.

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Depreciation

• Definition 1 The allocation of the cost of an
  asset over a period of time for accounting and
  tax purposes.Definition 2 A decline in the
  value of a property due to general wear and tear
  or obsolescence opposite of appreciation

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To calculate depreciation you must know

• How much the asset cost (including all costs
  necessary to make the asset operational),
• How long the asset can reasonably be expected to
  last (its useful life)
• Salvage value (if any) at the end of its useful
  life.
• There are certain conventions for items such as
  computers, vehicles, furniture, buildings, and
  other fixed assets

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Half Year Convention

• Assume half a years depreciation in the year the
  asset was purchased.
• Example
• 5 year asset, Straight Line Depreciation
• Year 1 2 3 4 5 6
• Depr 10 20 20 20 20 10

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MACRS
Modified Accelerated Cost Recovery System
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ATCF Examples

• A 5-year property class asset costs 600,000 and
  has no salvage value after 6 years. The asset is
  expected to produce annual revenues of 1 M with
  annual labor and material expenses of 200K and
  100K respectively. Using an i10 and an
  effective tax rate of 34, compare ATCF
• Alternative SL Depreciation
• MACRS tables Depreciation
• Sell asset after year six for 10K
• Finance 500K of purchase price

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Alternative SL Depreciation
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MACRS Depreciation
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MACRS Depreciation with Gain
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MACRS with Loan (EPP)
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Equal Prin. Payments Loan

• MARR 10
• Loan 5 NPV 1.65 M
• Loan 10 NPV 1.61 M
• Loan 20 NPV 1.53 M

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MACRS with Loan (ETP)
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Equal Total Payments Loan

• MARR 10
• Loan 5 NPV 1.65 M
• Loan 10 NPV 1.61 M
• Loan 20 NPV 1.53 M
• (There are differences, out at the 1,000 level.)

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MACRS with Bond
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Bond Results

• MARR 10
• Yield 5 NPV 1.7 M
• Yield 10 NPV 1.63 M
• Yield 20 NPV 1.51 M