**Chapter 7** by Jerry Wu

37)

The key here is recognizing the cash flows in nominal terms by converting all the cash flows in respect the the inflation rate given. r=0.06= 6%

Revenue and costs in real terms:

Revenues= 150,000/1.06=141509.43

Labor cost (this is a variable cost)= 80,000/1.06=75,471.70

Other costs 40,000/1.06=37,735.85

Lease payment in real terms 20,000/1.06=18,867.92

Then we calculate the PV using the equation **PV= C/r-g** since they anticipate the business will continue into perpetuity. In this instance the r is the required rate of return which is 10%= 0.10

PV revenue 141,509.43/ (0.10-0.05)=2,830,188.68

PV Labor cost 75471.70/(0.10-0.03)=1,078,167.12

Pv other costs 37,735.85/(0.10-(-0.01))=343,053.17 note 0.01 is in negative value to represent a decrease by 1 percent a year.

** Lease payments are constant in nominal terms, therefore declining in real terms by the inflation rate.

Inflation rate is causing negative growth of -0.06/year= -6%/year

PV lease payment 18867.92/((0.10-(-0.06))=117,924.53

**NPV of the project (after tax) is equal to**:

NPV= PV revenue- PV Labor cost- PV other costs- PV lease payments X (1- Tax rate)

(2830188.68-1078167.12-343053.17-117924.53) x (1-0.34)=852,088.95

38)

Required investment = -32000000

Depreciateion per year= 8000000

Tax rate =0.34

Price of product per unit= 400

Labor cost for year 1=15.30 (15.30x 200000=Total cost 30600000), year 2= 15.30(1.02)=15.606, year 3=15.606 (1.02)=15.918, year 4=15.918(1.02)=16.236

Energy cost for year 1=5.15, year 2=5.15(1.03)=5.305, year 3= 5.464, year 4 =5.627

Based on the information above, we can calculate the depreciation per year in real terms as follows:

8000000/(1.05)=7,619,047.62

8000000/(1.05)^2=7,256,253.83

8000000/(1.05)^3=6,910,700.79

8000000/(1.05)^4=6,581,619.80

NPV is always express in terms of cash flow. In order to find out the OCF (operating cash flow) of the project for each year, we calculate the revenues, labor cost , Energy cost, depreciation, taxes for each year in real terms with respect to their output quantities. refer to Pg 211

**EBIT(Earnings before interest and taxes)= Sales-Costs-Depreciation**

**Taxes= EBIT x Tc**

**OCF= EBIT+Depreciation- Taxes**

With Discount rate 8%=0.08

NPV= -32000000+ 8114676.19/1.08+33967006.18/(1.08)^2+33416520.05/(1.08)^3+19662758.15/1.08^4

NPV=45,614,647.30

Chapter 8

25) Pretty straight forward, please refer to solution book. This is a series of application of converting the values in real terms and then calculate the OCF using the mentioned functions above OCF= EBIT + Depreciation- Taxes.

30) First step is to calculate the salvage value of the old harvester

Depreciation (old)=45000/15=3000

3000/year x 5 years= 15000, therefore there is only 30000 left for the book value.

Aftertax salvage value= Market value +tc (Book value-Market value)

20000 +0.34 (30000-20000)=23400

Secondly, we calculate the incremental depreciation.

-the depreciation tax shield on the old harvester is:

3000x 0.34=1020

-the incremental depreciation tax shield is then: (P/10)(0.34)-1020

where 10 represents the lifetime of the New harvester being depreciated by straight line method of 10 years.

PV depreciation tax shield= (p/10)(0.34)(PVIFA15%^10)-1020(PVIFA15%^10)

PV savings= C(1-tax rate)(PVIFA15%^10)= 10000(1-0.34)(PVIFA15%^10)=**33123.87**

NPV will be zero when the firm is at break even point.

Thus, based on the formula NPV=-P+Salvage value old+ PV depreciation tax shield + PV savings,

**0=-P +23400 + (P/10)(0.34)(PVIFA15%^10)-3000(0.34)(PVIFA15%^10)+33123.37**

Solve for P:

P[1-(1/100)(0.34)(PVIFA15%^10)=51404.73

P=61,981.06