April 3, 2019

CHAPTER 11 B-217

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = $4,005,000 + 3,200,000

OCF = $7,205,000

The NPV at this quantity is:

NPV = –$22,400,000 – $1,250,000 + $7,205,000(PVIFA10%,7) + $1,250,000/1.107

NPV = $12,068,405.23

So, the sensitivity of the NPV to changes in the quantity sold is:

NPV/Q = ($10,841,563.69 – 12,068,405.23)/(51,000 – 52,000)

NPV/Q = $1,226.84

For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by $1,226.84.

23. a. First we need to determine the total additional cost of the hybrid. The hybrid costs more to

purchase and more each year, so the total additional cost is:

Total additional cost = $5,450 + 6($400)

Total additional cost = $7,850

Next, we need to determine the cost per mile for each vehicle. The cost per mile is the cost per

gallon of gasoline divided by the miles per gallon, or:

Cost per mile for traditional = $3.60/23

Cost per mile for traditional = $0.156522

Cost per mile for hybrid = $3.60/25

Cost per mile for hybrid = $0.144000

So, the savings per mile driven for the hybrid will be:

Savings per mile = $0.156522 – 0.144000

Savings per mile = $0.012522

B-218 SOLUTIONS

b. First, we need to determine the total miles driven over the life of either vehicle, which will be:

Total miles driven = 6(15,000)

Total miles driven = 90,000

Since we know the total additional cost of the hybrid from part a, we can determine the necessary

savings per mile to make the hybrid financially attractive. The necessary cost savings per mile will

c. To find the number of miles it is necessary to drive, we need the present value of the costs and

savings to be equal to zero. If we let MDPY equal the miles driven per year, the breakeven

equation for the hybrid car as:

Cost = 0 = –$5,450 – $400(PVIFA10%,6) + $0.012522(MDPY)(PVIFA10%,6)

The savings per mile driven, $0.012522, is the same as we calculated in part a. Solving this

equation for the number of miles driven per year, we find:

$0.012522(MDPY)(PVIFA10%,6) = $7,192.10

MDPY(PVIFA10%,6) = 574,369.44

Miles driven per year = 131,879

To find the cost per gallon of gasoline necessary to make the hybrid break even in a financial

sense, if we let CSPG equal the cost savings per gallon of gas, the cost equation is:

CHAPTER 11 B-219

d. The implicit assumption in the previous analysis is that each car depreciates by the same dollar

amount.

24. a. The cash flow per plane is the initial cost divided by the breakeven number of planes, or:

Cash flow per plane = $13,000,000,000 / 249

determine the annual cash flow necessary to deliver a 20 percent return. Using the perpetuity

equation, we find:

PV = C /R

$13,000,000,000 = C / .20

determine the annual cash flow necessary to deliver a 20 percent return. Using the present value of

an annuity equation, we find:

PV = C(PVIFA20%,10)

$13,000,000,000 = C(PVIFA20%,10)

C = $3,100,795,839

25. a. The tax shield definition of OCF is:

OCF = [(P – v)Q – FC ](1 – tC) + tCD

Rearranging and solving for Q, we find:

B-220 SOLUTIONS

b. The cash breakeven is:

Q

C = $500,000/($40,000 – 20,000)

Q

C = 25

And the accounting breakeven is:

Q

A = {$500,000 + [($700,000 – $700,000(0.38))/0.62]}/($40,000 – 20,000)

Q

A = 60

c. At the accounting break-even point, the net income is zero. This using the bottom up definition of

OCF:

OCF = NI + D

We can see that OCF must be equal to depreciation. So, the accounting breakeven is:

Q

A = {FC + [(D – tCD)/(1 – t)]}/(P – v)

Q

26. The DOL is expressed as:

DOL = %OCF / %Q

DOL = {[(OCF1 – OCF0)/OCF0] / [(Q1 – Q0)/Q0]}

The OCF for the initial period and the first period is:

OCF1 = [(P – v)Q1 – FC](1 – tC) + tCD

OCF0 = [(P – v)Q0 – FC](1 – tC) + tCD

27. a. Using the tax shield approach, the OCF is:

OCF = [($230 – 185)(35,000) – $450,000](0.62) + 0.38($3,200,000/5)

OCF = $940,700

b. In the worst-case, the OCF is:

OCFworst = {[($230)(0.9) – 185](35,000) – $450,000}(0.62) + 0.38($3,680,000/5)

OCFworst = $478,080

And the worst-case NPV is:

NPVworst = –$3,680,000 – $360,000(1.05) + $478,080(PVIFA13%,5) +

[$360,000(1.05) + $500,000(0.85)(1 – .38)]/1.135

28. To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 36,000. The OCF at

this level of sale is:

OCF = [($230 – 185)(36,000) – $450,000](0.62) + 0.38($3,200,000/5)

OCF = $968,600

B-222 SOLUTIONS

The sensitivity of changes in the OCF to quantity sold is:

OCF/Q = ($968,600 – 940,700)/(36,000 – 35,000)

OCF/Q = +$27.90

29. At the cash breakeven, the OCF is zero. Setting the tax shield equation equal to zero and solving for the

quantity, we get:

OCF = 0 = [($230 – 185)QC – $450,000](0.62) + 0.38($3,200,000/5)

Q

C = 1,283

CHAPTER 11 B-223

30. Using the tax shield approach to calculate the OCF, the DOL is:

DOL = 1 + [$450,000(1 – 0.38) – 0.38($3,200,000/5)]/ $940,700

DOL = 1.03806

Thus a 1% rise leads to a 1.03806% rise in OCF. If Q rises to 36,000, then

The percentage change in quantity is: