© 2012 McGraw-Hill Ryerson Limited Chapter 8 -1

The Investment Timing Decision◦ Sometimes you have the ability to defer an

investment and select a time that is more ideal at which to make the investment decision

◦ The decision rule is to choose the investment date that results in the highest NPV today

Example:◦ You can buy a computer system today for $50,000.

Based on the savings it provides to you, the NPV of this investment ~ $20,000

◦ However, you know that these systems are dropping in price every year

◦ When should you purchase the computer?

LO4

© 2012 McGraw-Hill Ryerson Limited Chapter 8 -2

Year of Purchase Cost

PV of Savings

NPV at Year of

PurchaseNPV

Todayt = 0 $50 $70 $20 $20.0t = 1 $45 $70 $25 $22.7t = 2 $40 $70 $30 $24.8t = 3 $36 $70 $34 $25.5t = 4 $33 $70 $37 $25.3t = 5 $31 $70 $39 $24.2

Decision rule for investment timing:Choose the investment date which results

in the highest NPV today

LO4

© 2012 McGraw-Hill Ryerson Limited Chapter 8 -3

Long-Lived vs. Short-Lived Equipment◦Suppose you must choose between buying

two machines with different lives. Machines D and E are designed differently, but have

identical capacity and do the same job. Machine D costs $15,000 and lasts 3 years. It costs

$4,000 per year to operate. Machine E costs $10,000 and lasts 2 years. It costs

$6,000 per year to operate.

◦Which machine should the firm acquire?

LO4

© 2012 McGraw-Hill Ryerson Limited Chapter 8 -4

We cannot compare the PV of costs of assets with different lives

LO4

© 2012 McGraw-Hill Ryerson Limited Chapter 8 -5

For comparing assets with different lives, we need to compare their Equivalent Annual Costs

The Equivalent Annual Cost is the cost per period with the same PV as the cost of the machine

LO4

© 2012 McGraw-Hill Ryerson Limited Chapter 8 -6

An example of calculating equivalent annual cost

Cash Flows in Dollars

Project: C0 C1 C2 C3 PV @ 6%

Machine D 15 4 4 4 $25.69

EquivalentAnnual cost: ? ? ? $25.69

The equivalent annual cost is calculated as follows:

Equivalent Annual Cost= PV of Costs / Annuity Factor

= $25.69 / 3 Year Annuity Factor

= $25.69 / 2.673

= $9.61 per yearLO4

© 2012 McGraw-Hill Ryerson Limited Chapter 8 -7

If mutually exclusive projects have unequal lives, then you should calculate the equivalent annual cost of the projects

Picking the lowest EAC allows you to select the project which will maximize the value of the firm

Cash Flows in Dollars

Project: PV @ 6% Equivalent Annual Cost

D $25.69 $9.61

E $21.00 $11.45

LO4

Replacing an old machine◦ You are operating an old machine that will last

two more years before it gives up the ghost. ◦ It costs $12,000 per year to operate. ◦ You can replace it now with a new machine,

which costs $25,000 but is much more efficient ($8,000 per year in operating costs) and will last for five years.

◦ Should you replace it now or wait a year? ◦ The opportunity cost of capital is 6 percent.

© 2012 McGraw-Hill Ryerson Limited Chapter 8 - 8LO4

Costs, $000sYear: 0 1 2 3 4 5 PV at

6%

New machine -25 8 8 8 8 8 58.70Equivalent 5-year annuity 13.93 13.93 13.93 13.93 13.93 58.70

Cash flow will be $13,930 for new machine Cash flow will be $12,000 for old machine Why replace an old machine with a new one that will

cost $1930 more to run? Wait the two years

© 2012 McGraw-Hill Ryerson Limited Chapter 8 - 9LO4