Chapter 9 Risk analysis, real options, and capital budgeting (стр. 3 )

OCF = $5,280,000

So, the payback period is:

Payback period = 3 + $3,935,000/$5,280,000

Payback period = 3.745 years

The NPV is:

NPV = –$18,900,000 – 875,000 + $5,280,000(PVIFA14%,7) + $875,000/1.147

NPV = $3,216,932.21

And the IRR is:

IRR = –$18,900,000 – 875,000 + $5,280,000(PVIFAIRR%,7) + $875,000/IRR7

IRR = 19.09%

15. The upper and lower bounds for the variables are:

Base Case Lower Bound Upper Bound

Unit sales (new) 48,000 43,200 52,800

Price (new) $750 $675 $825

VC (new) $360 $324 $396

Fixed costs $7,500,000 $6,750,000 $8,250,000

Sales lost (expensive) 13,000 11,700 14,300

Sales gained (cheap) 10,000 9,000 11,000

Best-case

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	$825 ´ 52,800 = $43,560,000
	Exp. clubs	$1,200 ´ (–11,700) = – 14,040,000
	Cheap clubs	$420 ´ 11,000 = 4,620,000
		$34,140,000

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 any more, we will save these variable costs, which is an inflow. So:

	Var. costs
	New clubs	$324 ´ 52,800 = $17,107,200
	Exp. clubs	$710 ´ (–11,700) = – 8,307,000
	Cheap clubs	$205 ´ 11,000 = 2,255,000
		$11,055,200

The pro forma income statement will be:

	Sales	$34,140,000
	Variable costs	11,055,200
	Costs	6,750,000
	Depreciation	2,700,000
	EBT	13,634,800
	Taxes	5,453,920
	Net income	$8,180,880

Using the bottom up OCF calculation, we get:

OCF = Net income + Depreciation = $8,180,880 + 2,700,000

OCF = $10,880,880

And the best-case NPV is:

NPV = –$18,900,000 – 875,000 + $10,880,880(PVIFA14%,7) + 875,000/1.147

NPV = $27,235,213.01

Worst-case

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	$675 ´ 43,200 = $29,160,000
	Exp. clubs	$1,200 ´ (– 14,300) = – 17,160,000
	Cheap clubs	$420 ´ 9,000 = 3,780,000
		$15,1780,000

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 any more, we will save these variable costs, which is an inflow. So:

	Var. costs
	New clubs	$396 ´ 43,200 = $17,424,000
	Exp. clubs	$710 ´ (– 14,300) = –10,153,000
	Cheap clubs	$205 ´ 9,000 = 1,845,000
		$8,799,200

The pro forma income statement will be:

	Sales	$15,780,000
	Variable costs	8,799,200
	Costs	8,250,000
	Depreciation	2,700,000
	EBT	– 3,969,200
	Taxes	1,587,680	*assumes a tax credit
	Net income	–$2,381,250

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = –$2,381,250 + 2,700,000

OCF = $318,480

And the worst-case NPV is:

NPV = –$18,900,000 – 875,000 + $318,480(PVIFA14%,7) + 875,000/1.147

NPV = –$18,059,578.02

16. To calculate the sensitivity of the NPV to changes in the price of the new club, we simply need to change the price of the new club. We will choose $760, but the choice is irrelevant as the sensitivity will be the same no matter what price 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	$760 ´ 48,000 = $36,480,000
	Exp. clubs	$1,200 ´ (– 13,000) = –15,600,000
	Cheap clubs	$420 ´ 10,000 = 4,200,000
		$25,080,000

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 any more, we will save these variable costs, which is an inflow. So:

	Var. costs
	New clubs	$360 ´ 48,000 = $17,280,000
	Exp. clubs	$710 ´ (–13,000) = –9,230,000
	Cheap clubs	$205 ´ 10,000 = 2,050, ,000
		$10,100,000

The pro forma income statement will be:

	Sales	$25,080,000
	Variable costs	10,100,000
	Costs	7,500,000
	Depreciation	2,700,000
	EBT	4,780,000
	Taxes	1,912,000
	Net income	$ 2,868,000

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = $2,868,000 + 2,700,000

OCF = $5,568,000

And the NPV is:

NPV = –$18,900,000 – 875,000 + $5,568,000(PVIFA14%,7) + 875,000/1.147

NPV = $4,451,964.00

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

DNPV/DP = ($3,216,932.21 – 4,451,964.00)/($750 – 760)

DNPV/DP = $123,503.18

For every dollar increase (decrease) in the price of the clubs, the NPV increases (decreases) by $123,503.18.

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 50,000 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	$750 ´ 50,000 = $37,500,000
	Exp. Clubs	$1,200 ´ (– 13,000) = –15,600,000
	Cheap clubs	$420 ´ 10,000 = 4,200,000
		$26,100,000

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 any more, we will save these variable costs, which is an inflow. So:

	Var. costs
	New clubs	$360 ´ 60,000 = $18,000,000
	Exp. clubs	$710 ´ (–13,000) = –9,230,000
	Cheap clubs	$205 ´ 10,000 = 2,050,000
		$10,820,000

The pro forma income statement will be:

	Sales	$26,100,000
	Variable costs	10,820,000
	Costs	7,500,000
	Depreciation	2,700,000
	EBT	5,080,000
	Taxes	2,032,000
	Net income	$ 3,048,000

Using the bottom up OCF calculation, we get: