Chapter 5 Review in Class

Chapter 5Examplepg. 111

Sell price of microprocessor $20 Facility A

Fixed Costs ($) 8 milVariable Costs ($) 4 per unit

5.1 Measuring Project RiskinessProject just breaks evenTotal Revenue = Total Cost

P x Q = F + V x QP sales price per unitQ unit volumeF fixed costsV unit variable cost

5.2 rearrange the terms to get the breakeven quantityF

Q = (P - V)

Facility A8 8

20 - 4 16

Facility B4 4

20 - 10 10

To see which facility is best, solve where A's profits = B's profits.Profit for A = Revenue - Cost = Profit B = Revenue - CostP x Q - F

A - V

A x Q = P x Q - F

B - V

B x Q

20Q - 8 mil - 4Q = 20Q - 4 mil - 10Q16Q - 8 mil = 10Q - 4 mil6Q = 4 mil

666,667 = Q

Sensitivity analysis: change one variable, and see what happens to NPV; see how sensitive that variable can be on the project

5.2 Sensitivity AnalysisBox 5.1 page 120Year 0 1Initial Investment (100,000,000)SalesTons sold 90,000 Price 660 Revenue $59,400,000 CostsVariable costs (90,000 x $140) 12,600,000 Fixed Costs 12,000,000 Depreciation 10,000,000 Total Costs 34,600,000 Net Income 24,800,000 Taxes (@50%) 12,400,000 After tax income 12,400,000 Depreciation 10,000,000 NCF 22,400,000

PVIFA15,10 5.0188 result 112,421,120

Less: initial investment (100,000,000)NPV = $12,421,120

Now, suppose Fixed costs increase to $15 million, all else remains constantWhat happens to NPV?

Year 0 1Initial Investment (100,000,000)SalesTons sold 90,000 Price 660 Revenue $59,400,000 CostsVariable costs (90,000 x $140) 12,600,000 Fixed Costs 15,000,000 Depreciation 10,000,000 Total Costs 37,600,000 Net Income 21,800,000 Taxes (@50%) 10,900,000 After tax income 10,900,000 Depreciation 10,000,000 NCF 20,900,000

PVIFA15,10 5.0188 result 104,892,920


Page 122What happens to NPV? If only 80,000 tons sold, all else remains constantYear 0 1Initial Investment (100,000,000)SalesTons sold 80,000 Price 660 Revenue $52,800,000 CostsVariable costs (90,000 x $140) 11,200,000 Fixed Costs 12,000,000 Depreciation 10,000,000

Total Costs 33,200,000 Net Income 19,600,000 Taxes (@50%) 9,800,000 After tax income 9,800,000 Depreciation 10,000,000 NCF 19,800,000

PVIFA15,10 5.0188 result 99,372,240

Less: initial investment (100,000,000)NPV = $(627,760)

What happens to NPV? If only 100,000 tons sold, all else remains constantYear 0 1Initial Investment (100,000,000)SalesTons sold 100,000 Price 660 Revenue $66,000,000 CostsVariable costs (90,000 x $140) 14,000,000 Fixed Costs 12,000,000 Depreciation 10,000,000 Total Costs 36,000,000 Net Income 30,000,000 Taxes (@50%) 15,000,000 After tax income 15,000,000 Depreciation 10,000,000 NCF 25,000,000

PVIFA15,10 5.0188 result 125,470,000


Break-even Analysispage 123Exhibit 5.3 discount rate 10%Starship ProjectInitial Investment $250,000,000 10 yr lifePV of investment tax benefits 120,000,000 givenInitial Investment-net 130,000,000 Price/plane 2,700,000 Variable Costs per plane 1,500,000 Fixed Costs 15,000,000

Exhibit 5.4 Breakeven Analysis for Starship Project

Annual Plane Sales (units) 0 50Revenue - 135,000,000 VC - 75,000,000 Fixed cost 15,000,000 15,000,000 Net Income (15,000,000) 45,000,000 Taxes @ 50% (7,500,000) 22,500,000 After tax income (7,500,000) 22,500,000 PV @ 10% (46,084,500) 138,253,500 Initial Investment 130,000,000 130,000,000 Project NPV @ 10% (176,084,500) 8,253,500

The point at which the project NPV is just -0- is slightly fewer than 50 planes annually

To calculate the actual breakeven point:

+

Q=

Initial Investment 250.00 D PV of Depr w/o & ITC 120.00 Q annual salesP unit sales price 2.70

I0 - D

PVIFAr,n

(P-V)(1-t)

I0

V unit variable cost 1.50 F annual fixed cost 15.00 t tax rate 50%

n project life 10.00 r discount rate 10%

130 +3.68676

35.2613134568

Facility B4 mil

10 per unit

Measuring Project Riskiness

0.50 500,000 breakeven point

0.40 400,000 breakeven point

Sensitivity analysis: change one variable, and see what happens to NPV; see how sensitive that variable can be on the project

Tax rate 50% Discount rate 15%Life 10 yr

2 3 4 5 6

Now, suppose Fixed costs increase to $15 million, all else remains constant

the only item that changed

If only 80,000 tons sold, all else remains constant

NPV negative

If only 100,000 tons sold, all else remains constant

75 202,500,000 112,500,000

15,000,000 75,000,000 37,500,000 37,500,000

230,422,500 PVIFA 10, 10 6.1446 130,000,000 100,422,500

The point at which the project NPV is just -0- is slightly fewer than 50 planes annually

F

P - V

15.00 1.20 12.5 48 breakeven quantity

PVIFA Calculator

Interest rate per period:

Number of period:

PVIFA Result

5.0188PVIFA15,10 5.0188

7 8 9 10

%

Chapter 5Risk Analysis in Capital BudgetingSample Problem 1page 1371). Calculate the NPV of an investment with the following characteristics:Units sold per year 55,000 Price per unit $800 Variable cost per unit $720 Fixed Costs 0Initial cost $20,000,000 Life of the project 10 yearsDiscount rate 10%Depreciation SLTax Rate 34%

- PV (cost)+ PV(depreciation tax shield)+ PV(operating CF's)= NPV

PV (cost) $20,000,000 Initial cost

PV(depreciation tax shield) 2,000,000 depreciation/year34% Tax Rate

$680,000 6.1446 PVIFA

PV(depreciation tax shield) $4,178,328

PV(operating CF's)price $800

(Price-Cost)(units)(1-tax rate)PVIFA10,10

cost (720)

price-cost $80

# of units 55,000 (Price-Cost)(units) 4,400,000 1 minus the tax rate 0.66PVIFA 6.1446

4.055436PV(operating CF's) $17,843,918

a). Suppose an add'l investment of $5 mil would reduce the variable cost per unit to $700Calc the NPV for this alternative

- PV (cost)+ PV(depreciation tax shield)+ PV(operating CF's)= NPV

PV (cost) $25,000,000 PV(operating CF's)

PV(depreciation tax shield) 2,500,000 depreciation/year34% Calc the NPV for this alternative

$850,000 6.1446 PVIFA

PV(depreciation tax shield) $5,222,910

PV(operating CF's)price $800 cost $(700) reduced variable costprice-cost $100

(1-tax rate)PVIFA10,10

(Price-Cost)(units)(1-tax rate)PVIFA10,10

# of units $55,000 (Price-Cost)(units) $5,500,000

0.66 1-tax rate6.1446 PVIFA

4.055436PV(operating CF's) $22,304,898

b). What is the breakeven (NPV) number of units for the 2 alternatives?Breakeven occurs when: PV(operating CF's) = PV (cost) - PV (depreciation tax shield)case 1 (800-720)(X)(.66)(6.1446)PV (cost) $20,000,000

PV(depreciation tax shield) $4,178,328 $15,821,672

80 48,767 units4.055436

324.43488

Part a (800-700)(X)(.66)(6.1446)0 $25,000,000

# of units $5,222,910 $19,777,090

100 48,767 units4.055436405.5436

(1-tax rate)PVIFA10,10

1). Calculate the NPV of an investment with the following characteristics:

see below for individual calc's $(20,000,000)

$4,178,328 $17,843,918

$2,022,246 answer

depreciation/year

10 yrs, 10% discount rate

PVIFA Calculator

%

Number of period:

http://www.miniwebtool.com/pvifa-calculator/?r=10&n=7



PVIFA Result

6.1446

a). Suppose an add'l investment of $5 mil would reduce the variable cost per unit to $700

see below for individual calc's $(25,000,000)

$5,222,910 $22,304,898

$2,527,808

PV(operating CF's) added 5 mil to initial investment

depreciation/yearCalc the NPV for this alternative


reduced variable cost




b). What is the breakeven (NPV) number of units for the 2 alternatives?Breakeven occurs when: PV(operating CF's) = PV (cost) - PV (depreciation tax shield)

The break-even quatities are the same for case 1 & part a

Chapter 5Risk Analysis in Capital BudgetingSample Problem 2page 138

Multifoods, a retail grocery chain4 parameters, can take on 1 of 2 possible values5 year lifeTax rate 35%Cost of capital 12%Initail Investment $150,000

Parameter Pos Value 1 Pos Value 2 42

Revenue/year 100,000 125,000 8Fixed cost/year 20,000 15,000 Vaiable cost/year 10,000 5,000 Depreciation/year 10,000 10,000

Selection is independent of each parameter value, & has 50% probability

a). Construct a probability distribution Since each parameter has a probability of .5, then 8 scenarios

Scenario 1 2 3 4

Revenue 100,000 100,000 100,000 100,000 -fixed cost (20,000) (15,000) (20,000) (15,000)-variable cost (10,000) (10,000) (5,000) (5,000)-depreciation (10,000) (10,000) (10,000) (10,000)=taxable income 60,000 65,000 65,000 70,000 -tax (21,000) (22,750) (22,750) (24,500)=after tax income 39,000 42,250 42,250 45,500 +depreciation 10,000 10,000 10,000 10,000 =CF 49,000 52,250 52,250 55,500

3.6048 3.6048 3.6048 3.6048

176,635 188,351 188,351 200,066 -investment (150,000) (150,000) (150,000) (150,000)

=NPV 26,635 38,351 38,351 50,066 std dev 30.44

The expected NPV given these 8 scenarios, with equal probability of being realized, equals:take average 67.64 8 scenarios, equal probability

xPVIFA12,5 factor

xPVIFA12,5 result

parameterspossible valuesscenarios

Selection is independent of each parameter value, & has 50% probability

Since each parameter has a probability of .5, then 8 scenarios

5 6 7 8

125,000 125,000 125,000 125,000 (20,000) (15,000) (20,000) (15,000)(10,000) (10,000) (5,000) (5,000)(10,000) (10,000) (10,000) (10,000)85,000 90,000 90,000 95,000

(29,750) (31,500) (31,500) (33,250)55,250 58,500 58,500 61,750 10,000 10,000 10,000 10,000 65,250 68,500 68,500 71,750

3.6048 3.6048 3.6048 3.6048

235,213 246,929 246,929 258,644 (150,000) (150,000) (150,000) (150,000)

85,213 96,929 96,929 108,644

Number of period:The expected NPV given these 8 scenarios, with equal probability of being realized, equals:

PVIFA Result

3.6048

PVIFA Calculator


%

Documents

Chapter 5 Review in Class