7/30/2019 EACADIFL

1/11

0

EAC (Advance) ExampleConsider a Dentists office; he needs an autoclave to sterilize

his instruments. He has an old one that is in use, but themaintenance costs are rising and so is consideringreplacing this indispensable piece of equipment.

New Autoclave

Cost = $3,000 today, Maintenance cost = $20 per year

Resale value after 6 years = $1,200

Total PV of Costof new autoclave (at k = 10%) is $2,409.74

6

6

1 )10.1(200,1$

)10.1(20$000,3$74.409,2$

tt

EACof new autoclave = -$553.29

7/30/2019 EACADIFL

2/11

1

Example

Existing AutoclaveYear 0 1 2 3 4 5

Maintenance 0 200 275 325 450 500

Resale 900 850 775 700 600 500

Total Annual CostTotal Cost for year 1 = (900 1.10850) + 200 = $340340 435Total Cost for year 2 = (850 1.10775) + 275 = $435

478

Total Cost for year 3 = (775 1.10700) + 325 = $478620

Total Cost for year 4 = (700 1.10600) + 450 = $620Total Cost for year 5 = (600 1.10500) + 500 = $660

660

Note that the total cost of keeping an autoclave for the first year includes the $200

maintenance cost as well as the opportuni ty cost of the foregone future value of the

$900 we didnt get from selling it in year 0 less the $850 we have if we still own it at

year 1.

7/30/2019 EACADIFL

3/11

2

New Autoclave

EACof new autoclave = -$553.29

Existing Autoclave

Year 0 1 2 3 4 5

Maintenance 0 200 275 325 450 500

Resale 900 850 775 700 600 500

Total Annual Cost

Example

340 435 478 620 660

We should keep the old autoclave until its cheaper to buy

a new one.

Replace the autoclave at the end of year 3: at that point the

new one will cost $553.29 for the next years autoclaving

and the old one will cost $620 for one more year.

7/30/2019 EACADIFL

4/11

Inflation and Capital Budgeting

Inflation is an important fact of economic lifeand must be considered in capital budgeting.

Consider the relationship between interest rates and inflation,often referred to as the Fisher relationship:

(1 + Nominal Rate) = (1 + Real Rate) (1 + Inflation Rate)

For low rates of inflation, this is often approximated as

Real Rate Nominal Rate Inflation Rate

When considering inflation in capitalbudgeting, one must compare real cash flowsdiscounted at real rates or nominal cash flowsdiscounted at nominal rates.

7/30/2019 EACADIFL

5/11

4

Example of Capital Budgeting underInflation

Sony International has an investment opportunity to produce anew stereo color TV.

The required investment on January 1 of this year is $32million. The firm will depreciate the investment to zero usingthe straight-line method. The firm is in the 34% tax bracket.

The price of the product on January 1 will be $400 per unit.The price will stay constant in real terms.

Labor costs will be $15 per hour on January 1. It will increaseat 2% per year in real terms.

Energy costs will be $5 per TV; they will increase 3% per yearin real terms.

The inflation rate is 5% Revenues are received and costs arepaid at year-end.

7/30/2019 EACADIFL

6/11

5

Example of Capital Budgeting underInflation

The riskless nominal discount rate is 4%.The real discount rate for costs and revenues is 8%.Calculate the NPV.

Year 1 Year 2 Year 3 Year 4

Physical

Production

(units)

100,000 200,000 200,000 150,000

Labor Input(hours)

2,000,000 2,000,000 2,000,000 2,000,000

Energy input,

physical units

200,000 200,000 200,000 200,000

7/30/2019 EACADIFL

7/11

6

Year 1 After-tax Real Risky CashFlows

Risky Real Cash Flows Price: $400 per unit with zero real price increase

Labor: $15 per hour with 2% real wage increase

Energy: $5 per unit with 3% real energy cost increase

Year 1 After-tax Real Risky Cash Flows:After-tax revenues =

$400 100,000 (1 .34) = $26,400,000

After-tax labor costs =

$15 2,000,000 1.02 (1 .34) = $20,196,000After-tax energy costs =

$5 2,00,000 1.03 (1 .34) = $679,800

After-tax net operating CF =

$26,400,000 $20,196,000 $679,800 = $5,524,200

7/30/2019 EACADIFL

8/11

7

Year 2 After-tax Real Risky CashFlows

Risky Real Cash Flows Price: $400 per unit with zero real price increase

Labor: $15 per hour with 2% real wage increase

Energy: $5 per unit with 3% real energy cost increase

Year 1 After-tax Real Risky Cash Flows:After-tax revenues =

$400 100,000 (1 .34) = $26,400,000

After-tax labor costs =

$15 2,000,000 (1.02)2 (1 .34) = $20,599,920

After-tax energy costs =

$5 2,00,000 (1.03)2 (1 .34) = $700,194

After-tax net operating CF =

$26,400,000 $ 20,599,920 $ 700,194 = $ 31,499,886

7/30/2019 EACADIFL

9/11

8

Year 3 After-tax Real Risky CashFlows

Risky Real Cash Flows Price: $400 per unit with zero real price increase

Labor: $15 per hour with 2% real wage increase

Energy: $5 per unit with 3% real energy cost increase

Year 1 After-tax Real Risky Cash Flows:After-tax revenues =$400 100,000 (1 .34) = $26,400,000

After-tax labor costs =

$15 2,000,000 (1.02)3 (1 .34) = $21,011.92

After-tax energy costs =

$5 2,00,000 (1.03)3 (1 .34) = $721,199.82

After-tax net operating CF =

$26,400,000 $ 21,011.92 $ 721,199.82 = $31,066,882

7/30/2019 EACADIFL

10/11

9

Year 4 After-tax Real Risky CashFlows

Risky Real Cash Flows Price: $400 per unit with zero real price increase

Labor: $15 per hour with 2% real wage increase

Energy: $5 per unit with 3% real energy cost increase

Year 1 After-tax Real Risky Cash Flows:After-tax revenues =$400 100,000 (1 .34) = $26,400,000

After-tax labor costs =

$15 2,000,000 (1.02)4 (1 .34) = $21,432.16

After-tax energy costs =

$5 2,00,000 (1.03)4 (1 .34) = $742,835.82

After-tax net operating CF =

$26,400,000 $21,432.16 $742,835.82 = $17,425,007

7/30/2019 EACADIFL

11/11

10

Example of Capital Budgetingunder Inflation

The project NPV can now be computed asthe sum of the PVof the cost, the PVof therisky cash flows discounted at the risky

rate and the PVof the risk-free cash flowsdiscounted at the risk-free discount rate.

NPV=$32,000,000 + $69,590,868 + $9,873,315 =

$47,464,183