Investment Analysis (Chapter 17)

1
Investment Analysis(Chapter 17)
2
Objectives

• Explain the time value of money and its use in
  decision making and investment analysis.
• Illustrate the process of determining the future
  value or present value of a sum of money or a
  series of payments.
• Discuss the payback period, simple rate of
  return, net present value, and internal rate of
  return.
• Introduce how income taxes, inflation, and risk
  affect investment analysis.

3
Investment in Capital Assets

• Capital assets are long-lasting assets.
• Investment decisions are made less frequently.
• Large initial expense.
• Expenses and returns spread over a number of
  future time periods.
• Note that time is a critical element!
• Cannot make such decisions and ignore the time
  element!

4
Time Value of Money

• Would you rather have a dollar today or at some
  time in the future?
• A dollar received today can be invested to earn
  interest.
• Interest represents the opportunity cost of using
  money today.

5
Why is interest charged?

• Consumption
• We would prefer to have the dollar now so we
  could spend it and enjoy the new item.
• Risk
• Unforeseen circumstance could prevent us from
  collecting the dollar in the future.
• Inflation
• The general increase in the cost of goods and
  services may diminish what the dollar can buy in
  the future compared to today.
• Now time for some new terminology

6
Future Value(FV)

• The amount of money to be received at some future
  time.
• OR
• The amount a present dollar value will become at
  some future date when invested at a given
  interest rate.

7
Present Value(PV)

• The amount of money available or invested at the
  current time
• Easy to determine.
• The current value of some amount(s) to be
  received in the future
• More difficult, since interest plays a role.
• Need to discount back to the present!

8
Payment(PMT)

• The amount of money to be paid or received at the
  end of each of a number of time periods.

9
Interest Rate(i)

• Also called the discount rate.
• The interest rate used to find present and future
  values.
• Often equal to the opportunity cost of capital.
• What is appropriate interest rate??
• If borrowing money?
• If using own money?

10
Time Periods(n)

• The number of time periods to be used for
  computing present and future values
• 1 year or several years.
• 1 month on several months.
• The annual interest rate i must be adjusted to
  the length of the time periods
• The standard is annual (one year), so no
  adjustment necessary.
• A monthly rate must be used if the time periods
  are months (1/12 of the annual rate).
• A quarterly rate must be used if the time periods
  are quarters (1/4 of the annual rate).

11
Annuity

• A series of equal periodic payments.
• Receipts
• Expenditures
• Now lets look more carefully at the concepts of
  future and present value.

12
Future Value of a Present Amount

• The value of a current investment at a specific
  date in the future.
• What will a given amount of money today be worth
  at some date in the future?
• This value depends on
• PV amount.
• Interest rate.
• Length of time.

13
Future Value of a Present Amount

• Assumptions
• Investment earns interest.
• Interest is reinvested.
• The future value includes
• The original investment and the interest it has
  earned.
• The interest on the accumulated interest
  (compounding).

14
Future Value of a Present Amount(1,000
invested for 3 years at 8 interest)

• FV PV (1 i)n
• Year 1 FV 1000 (1 0.08)1 1000 (1.080)
  1080.00
• Year 2 FV 1000 (1 0.08)2 1000 (1.1664)
  1166.40
• Year 3 FV 1000 (1 0.08)3 1000 (1.2597)
  1259.70

15
Future Value of a Present Amount

• FV PV (1 i)n
• Appendix Table 2 (text page 420).
• Calculates (1i)n for a range of i and n.
• - based on 1, so must multiply by PV.
• Look under i 8 for 1, 2, and 3 years.
• What is FV of 100 invested for 10 years
  at 5.0?
• Answer

16
Rule of 72

• To find the approximate time it takes for an
  investment to double divide 72 by the interest
  rate.
• Example
• An investment at 8 interest will double in
  approximately 9 years 72 8 9
• Check this approximation with the table value?
• Table value is 1.999 (look under 8 and 9 years)

17
Future Value of an Annuity

• What is the future value of a number of payments
  made at the end of each year for a given number
  of years?
• Each payment will earn interest from the time it
  is invested until the last payment is made.

18
Future Value of an Annuity(1000 at the end of
each year for 3 years at 8)

• First payment 1,000
  1,000(1 0.08)2 1,166.40
• Second payment 1,000 1,000(1
  0.08)1 1,080.00
• Third payment 1,000 1,000(1
  0.08)0 1,000.00
• Future value 3,246.40
• FV PMT (1 i)n - 1
• i
• Appendix Table 3
• 1000 (3.2464) 3,246.40

19
FV for a Present Sum and for an Annuity
FV for a single payment FV of
an annuity
20
Present Value

• The value today of a sum of money to be received
  or paid in the future.
• A sum to be received in the future is worth less
  than the same amount available today.
• The future value is discounted back to the
  present.

21
Present Value

• The sum of money that would have to be invested
  now at the certain interest rate to equal a given
  future value on the same date.
• Interest rate is called the discount rate.
• Compounding and discounting are opposite
  procedures.

22
Relationship Between Compounding Discounting
Compounding (FV)
Discounting (PV)
23
Present Valueof a Future Amount

• The future value is known.
• The problem is to find the present value of that
  amount.
• The PV of a FV depends on
• Interest rate.
• Length of time
• High interest rates long time periods will
  reduce the PV.
• Low interest rates short time periods will
  increase the PV.

24
Present Value of a Single Future Payment

• PV FV OR FV 1/(1i)n
• (1 i)n
• Example A payment of 1,000 to be received in 5
  years using an interest rate of 8 has a PV of
  680.58 (1000/1.4693).
• An investor should not pay more than 680.58 for
  an investment that will return 1,000 in 5 years
  if the appropriate interest rate is 8.

25
Present Value of a Single Future Payment

• PV FV OR FV 1/(1i)n
• (1 i)n
• Appendix Table 4
• 5 years at 8 is
• 0.68058
• Note gives 1/(1i)n so multiply!
• 1,000 (0.68058) 680.58

26
Powerball Choices

• You won the 25 million jackpot
• 1. Can take the discounted value
• 14,275,000.00 (current payout).
• 2. Take the 25-year payout
• 1,000,000 per year for 25 years.
• How to approach (personal or economic)?
• What is implied discount rate for the present
  value (14,275,000) of this 1,000,000 annuity?
• 14,275,000 1,000,000 14.275 (table value)
• implied i of between 4.5 and 5.

27
Present Value of an Annuity(1,000 at the end of
the year for 3 years at 8)

• PV PMT 1 (1 i)-n
• 
  i
• Appendix Table 5
• (1,000 X 2.5771) 2,577.10

28
PV for a Future Sum and for an Annuity
PV for a single payment
PV for an annuity
29
Some Points about PVs FVs

• PVs are more useful than FVs when analyzing
  investments
• Not all investments have the same
• Useful lives.
• Pattern of net cash flows.
• FVs are not directly comparable
• Different years.
• Different amounts.
• FVs are comparable after they have been
  discounted to a common point in time
• The present!

30
Investment Analysis

• Determining if the investment is profitable.
• Comparing the profitability of two or more
  investments.
• Must know
• Initial cost.
• Annual net cash revenues.
• Terminal or salvage value.
• Interest or discount rate to be used.

31
Investment Analysis

• Payback Period
• Simple Rate of Return
• Net Present Value
• Internal Rate of Return

32
Investment Analysis

• Payback Period (P)
• The number of years it would take an investment
  to return its original cost through the annual
  net cash revenues it generates
• Used to rank investments.
• Establish a minimum payback period.
• If net cash returns are equal
• P Cost/Net cash revenue per year.
• If net cash returns are unequal
• Sum annual cash revenue year by year until total
  revenue is equal to initial cost and identify the
  years necessary to reach that point.

33
Investment Analysis

• Payback Period (P)
• Example 1
• Cost of investment 10,000.
• Net cash revenue 2,500 year for 6 years.
• P 10,000/2,500 4.
• Example 2
• Cost 10,000.
• Net cash revenue year 1 of 500 year 2 of
  1,500
• year 3 of
  2,500 year 4 of 5,500
• year 5 of
  6,000 year 6 of 5,000.
• P 500 1,500 2,500 5,500 4.

34
Investment Analysis

• Payback Period
• Advantages
• Easy to use.
• Identifies investments with the most immediate
  cash returns.
• Weaknesses
• Ignores cash flows after the payback period.
• Ignores timing of cash flows.
• Can lead to poor investment decisions (liquidity
  focus).

35
Investment Analysis

• Simple Rate of Return (RR)
• Expresses the average annual net revenue as a
  percent return on the investment.
• Simple rate of return Average annual net
  revenue
• 
  Initial Cost
• Multiply times 100 to convert to return.
• Net revenue is the average annual net cash
  revenue minus the average annual depreciation.

36
Investment Analysis

• Simple Rate of Return (RR)
• Example 1
• Cost of investment 10,000.
• Net revenue 2,500 year for 6 years
• Depreciation 1,000/year.
• RR (1,500/10,000) 0.15 x 100 15.
• Example 2
• Cost 10,000 (depreciation 1,000/year).
• Net cash revenue year 1 of -500 year 2 of
  1,500
• year 3 of
  2,500 year 4 of 5,500
• year 5 of
  5,000 year 6 of 1,000.
• RR (- 1500 500 1,500 4,500 4,000
  0)/6 1,500 1,500/10,000 0.15 x
  100 15.

37
Investment Analysis

• Simple Rate of Return (RR)
• Strength
• Considers an investments earnings over its
  entire life.
• Weakness
• Ignores the size and timing of earnings.

38
Investment Analysis

• Net Present Value (NPV)
• The sum of the present values for each years net
  cash flow, minus the initial cost of the
  investment
• NPV P1 P2 . . . Pn -
  C
• (1i)1 (1i)2
  (1i)n

39
Investment Analysis

• Payback Period
• Simple Rate of Return
• Net Present Value
• Internal Rate of Return

40
Investment Analysis

• Net Present Value (NPV)
• Example 1
• Cost of investment 10,000.
• Net cash revenue 2,500 year for 6 years
• Discount rate 8.
• Table 4
• Year Payment PV Factor Present
  Value
• 1 2,500 0.92593
  2,314.83
• 2 2,500 0.85734
  2,143.35
• 3 2,500 0.79383
  1,984.58
• 4 2,500 0.73503
  1,837.58
• 5 2,500 0.68058
  1,701.45
• 6 2,500 0.63017
  1,575.43
• 
  Total 11,557.72
• NPV 11,557.72 10,000.00 1,557.72

41
Investment Analysis

• Net Present Value (NPV)
• Example 1 (NPV 11,557.72 10,000)
• Two Issues
• 1. Since constant net cash revenue each year, is
  there an easier way?
• Is a 6 year constant annuity of 2,500.
• PV 2,500 x (Table 5 value of 4.6229)
  11,557.25.
• 2. What about residual value of investment?
• Depreciation 1,000/year or 6,000.
• Residual 4,000 at end of year 6!
• PV 4,000 (0.63017) 2,520.68
• Add to NPV of 1,557.72.
• NPV (including residual value) 4,078.40.
  

42
Investment Analysis

• Net Present Value (NPV)
• Considers the time value of money and the size of
  the stream of cash flows over the entire life of
  the investment.
• A positive NPV indicates that the rate of return
  on the investment is greater than the discount
  rate.
• Accept investments with a positive NPV.
• Reject investments with a negative NPV.

43
Investment Analysis

• Internal Rate of Return (IRR)
• The actual rate of return on an investment, with
  proper accounting for the time value of money.
• The discount rate that makes the NPV just equal
  to zero
• When the NPV is positive, the IRR is greater than
  the discount rate.
• When the NPV is negative, the IRR is less than
  the discount rate.

44
Estimation of IRR
Example from textbook

•  

45
Investment Analysis

• IRR Drawbacks
• Difficult to calculate (is IRR function in
  excel).
• Assumes the annual net returns from the
  investment can be reinvested each period to earn
  a return equal to the IRR.
• Ignores the size of the investment.

46
Financial Feasibility

• Final step in investment analysis.
• Is the investment financially feasible?
• Will the investment generate sufficient cash
  flows at the right time to meet the required cash
  outflows, including loan payments?

47
Financial Feasibility

•  

NPV 1,370
NPV 1,272 IRR 15.2
IRR
13.8 Assumes 10,000 borrowed at 8 percent with 5
principal payments of 2,000 interest.
48
Financial Feasibility

• Taking care of negative cash flows (investment B)
• Use equity capital for part or all of the initial
  cost of the investment.
• Lengthen the payment schedule of the loan to make
  the debt payments smaller
• Smaller payments with a balloon payment at the
  end.
• Interest-only payments for the first few years.
• Use excess cash from other parts of the business
  or from savings.

49
Income Taxes

• Investment analysis didnt consider the effects
  of income taxes on net cash revenues.
• Investments generate
• Taxable income.
• Deductible expenses.
• Different investments may affect income taxes
  differently
• Compare them on an after-tax basis

50
Inflation

• A general increase in price levels over time.
• Inflation affects
• Net cash revenues.
• Terminal value.
• Discount rate.
• Two parts of a discount rate
• Real interest rate
• - interest rate without inflation
• 2. Adjustment for inflation.

51
Inflation

• Two ways to treat inflation in capital budgeting
• Estimate net cash revenues for each year and the
  terminal value, using current prices, then
  discount these values using a real (nominal rate
  - inflation rate) discount rate.
• Increase the net cash revenues for each year and
  the terminal value to reflect the expected
  inflation rate, and then use a nominal discount
  rate.
• For comparing investments, inflation may not
  matter unless they are impacted differently by
  inflation.

52
Risk

• Unexpected changes can make a potentially
  profitable investment unprofitable
• Net cash revenues.
• Terminal value.
• Future production.
• Prices.
• Costs.
• Add a risk premium to the discount rate
• Investments with greater risk would have a higher
  risk premium.
• Margin for error.

53
Sensitivity Analysis

• Asking What if? questions.
• What if the net cash revenues were higher or
  lower?
• What if the timing of net cash revenues was
  different?
• What if the discount rate was higher or lower?
• Change one or more values and recalculate the NPV
  or IRR.

54
Summary

• The future value of a sum of money is greater
  than the present value because of the interest it
  can earn over time.
• Future values are found through compounding.
• Present values are found through discounting.

55
Summary

• Investments can be analyzed by one or more
  methods
• Payback period
• Simple rate of return each has
  advantages
• Net present value and
  disadvantages
• Internal rate of return
• The net cash revenues and the discount rate
  should be on an after-tax basis.
• The discount rate may need to be adjusted for
  risk and inflation.
• Financial feasibility analysis is the final step
  in analyzing an investment.