978-0077861704 Chapter 11 Solutions Manual Part 3

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22. To calculate the sensitivity of the NPV to changes in the price of the new club, we simply need to

We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs

and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new

project will be:

Sales

New clubs $725  75,000 = $54,375,000

For the variable costs, we must include the units gained or lost from the existing clubs. Note that the

variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will

save these variable costs, which is an inflow. So:

Var. costs

New clubs –$385  75,000 = –$28,875,000

The pro forma income statement will be:

Sales $47,975,000

Variable costs 25,015,000

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = $5,556,000 + 4,300,000

CHAPTER 11 – 2

And the NPV is:

NPV = –$30,100,000 – 1,400,000 + $9,856,000(PVIFA10%,7) + 1,400,000/1.107

So, the sensitivity of the NPV to changes in the price of the new club is:

For every dollar increase (decrease) in the price of the clubs, the NPV increases (decreases) by

To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we simply

need to change the quantity sold. We will choose 76,000 units, but the choice is irrelevant as the

sensitivity will be the same no matter what quantity we choose.

We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs

and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new

project will be:

Sales

New clubs $715  76,000 = $54,340,000

For the variable costs, we must include the units gained or lost from the existing clubs. Note that the

variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will

save these variable costs, which is an inflow. So:

Var. costs

New clubs –$385  76,000 = –$29,260,000

The pro forma income statement will be:

Sales $47,940,000

Variable costs 25,400,000

CHAPTER 11 – 3

Using the bottom up OCF calculation, we get:

The NPV at this quantity is:

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

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:

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:

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

We can now determine the breakeven point by dividing the total additional cost by the savings

per mile, which is:

So, the miles you would need to drive per year is the total breakeven miles divided by the

number of years of ownership, or:

CHAPTER 11 – 4

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

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 be:

Now we can find the price per gallon for the miles driven. If we let P be the price per gallon,

the necessary price per gallon will be:

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 is:

The savings per mile driven, $.023325, is the same as we calculated in part a. Solving this

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

$.023325(MDPY)(PVIFA10%,6) = $14,932.10

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:

Solving this equation for the cost savings per gallon of gas necessary for the hybrid to break

even from a financial sense, we find:

CSPG(15,000)(PVIFA10%,6) = $6,871.58

Now we can find the price per gallon for the miles driven. If we let P be the price per gallon,

the necessary price per gallon will be:

CHAPTER 11 – 5

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

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

b. In this case the cash flows are a perpetuity. Since we know the cash flow per plane, we need to

PV = C / R

This is the total cash flow, so the number of planes that must be sold is the total cash flow

divided by the cash flow per plane, or:

c. In this case the cash flows are an annuity. Since we know the cash flow per plane, we need to

PV = C(PVIFA20%,10)

This is the total cash flow, so the number of planes that must be sold is the total cash flow

divided by the cash flow per plane, or:

Challenge

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

Rearranging and solving for Q, we find:

CHAPTER 11 – 6

b. The cash breakeven is:

And the accounting breakeven is:

The financial breakeven is the point at which the NPV is zero, so:

So:

QF = [FC + (OCF – TCD)/(1 – TC)]/(P – v)

c. At the accounting breakeven point, the net income is zero. Thus 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:

The tax rate has cancelled out in this case.

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:

The difference between these two cash flows is:

CHAPTER 11 – 7

Dividing both sides by the initial OCF we get:

Rearranging we get:

[(OCF1 – OCF0) / OCF0] / [(Q1 – Q0) / Q0] = [(P – v)(1 – TC)Q0] / OCF0 =

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

And the NPV is:

NPV = –$5,200,000 – 410,000 + $1,846,000(PVIFA13%,5)

And the worst-case NPV is:

NPVworst = –$5,200,000(1.15) – $410,000(1.05) + $1,297,680(PVIFA13%,5) +

The best-case OCF is:

And the best-case NPV is:

NPVbest = –$5,200,000(.85) – $410,000(.95) + $2,394,320(PVIFA13%,5) +

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

OCF at this level of sales is:

CHAPTER 11 – 8

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

The NPV at this level of sales is:

And the sensitivity of NPV to changes in the quantity sold is:

You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV

changes $207.16 for every ton sold, so we can divide the NPV for 35,000 units by the sensitivity to

get a change in quantity. Doing so, we get:

For a zero NPV, we need to decrease sales by 6,148 units, so the minimum quantity is:

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

the quantity, we get:

The accounting breakeven is:

From Problem 28, we know the financial breakeven is 28,852 tons.

CHAPTER 11 – 9

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

Thus a 1 percent rise in Q leads to a 1.12 percent rise in OCF. If Q rises to 36,000, then

the percentage change in quantity is:

So, the percentage change in OCF is:

From Problem 28:

In general, if Q rises by 1,000 tons, OCF rises by 3.19%.