Chapter 9 Risk analysis, real options, and capital budgeting (стр. 5 )

Annual cash flow = 10($205,000)

Annual cash flow = $2,050,000

The cash flows from this project are an annuity, so the NPV is:

NPV = –$7,500,000 + $205,000(PVIFA13%,5)

NPV = –$289,675.91

b. The company will abandon the project if unit sales are not revised upward. If the unit sales are revised upward, the aftertax cash flows for the project over the last four years will be:

New annual cash flow = 20($205,000)

New annual cash flow = $4,100,000

The NPV of the project will be the initial cost, plus the expected cash flow in year one based on 10 unit sales projection, plus the expected value of abandonment, plus the expected value of expansion. We need to remember that the abandonment value occurs in year 1, and the present value of the expansion cash flows are in year one, so each of these must be discounted back to today. So, the project NPV under the abandonment or expansion scenario is:

NPV = –$7,500,000 + $2,050,000 / 1.13 + .50($3,500,000) / 1.13

+ [.50($4,100,000)(PVIFA13%,4)] / 1.13

NPV = $1,258,996.65

25. To calculate the unit sales for each scenario, we multiply the market sales times the company’s market share. We can then use the quantity sold to find the revenue each year, and the variable costs each year. After doing these calculations, we will construct the pro forma income statement for each scenario. We can then find the operating cash flow using the bottom up approach, which is net income plus depreciation. Doing so, we find:

		Pessimistic	Expected	Optimistic
	Units per year	23,800	31,500	38,400
	Revenue	$2,451,400	$3,402,000	$4,300,800
	Variable costs	1,142,400	1,449,000	1,689,600
	Fixed costs	950,000	900,000	850,000
	Depreciation	420,000	420,000	420,000
	EBT	–$61,000	$633,000	$1,341,200
	Tax	–24,400	253,200	536,480
	Net income	–$36,600	$379,800	$804,720
	OCF	$383,400	$799,800	$1,224,720

Note that under the pessimistic scenario, the taxable income is negative. We assumed a tax credit in the case. Now we can calculate the NPV under each scenario, which will be:

NPVPessimistic = –$2,100,000 +$383,400(PVIFA13%,5)

NPV = –$751,493.53

NPVExpected = –$2,100,000 +$779,800(PVIFA13%,5)

NPV = $713,081.56

NPVOptimistic = –$2,100,000 +$1,224,720(PVIFA13%,5)

NPV = $2,207,623.47

The NPV under the pessimistic scenario is negative, but the company should probably accept the project.

Challenge

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

OCF = [($234 – 205)(50,000) – $195,000](0.62) + 0.38($2,950,000/5)

OCF = $1,002,300

And the NPV is:

NPV = –$2,950,000 – 450,000 + $1,002,300(PVIFA13%,5)

+ [$450,000 + $500,000(1 – .38)]/1.135

NPV = $537,818.44

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

OCFworst = {[($234)(0.9) – 205](50,000) – $450,000}(0.62) + 0.38(1.1)($2,950,000/5)

OCFworst = $310,530

And the worst-case NPV is:

NPVworst = –$2,950,000(1.15) – $195,000(1.05) + $310,530(PVIFA13%,5) +

[$450,000(1.05) + $500,000(0.85)(1 – .38)]/1.135

NPVworst = –$2,373,322.86

The best-case OCF is:

OCFbest = {[$234(1.1) – 205](50,000) – $450,000}(0.62) + 0.38(0.9)($2,950,000/5)

OCFbest = $1,694,070

And the best-case NPV is:

NPVbest = –$2,950,000(.85) – $195,000(0.95) + $1,694,070(PVIFA13%,5) +

[$450,000(0.95) + $500,000(1.15)(1 – .38)]/1.135

NPVbest = $3,448,959.75

27. To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 51,000. The OCF at this level of sale is:

OCF = [($234 – 205)(51,000) – $195,000](0.62) + 0.38($2,950,000/5)

OCF = $1,020,280

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

DOCF/DQ = ($1,002,300 – 1,020,280)/(50,000 – 51,000)

DOCF/DQ = +$17.98

The NPV at this level of sales is:

NPV = –$2,950,000 – 450,000 + 1,020,280(PVIFA13%,5) + [$450,000 + 500,000(1 – .38)]/1.135

NPV = $601,058.26

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

DNPV/DQ = ($537,818.44 – 601,058.26)/(50,000 – 51,000)

DNPV/DQ = +$63.24

You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes $63.24 for every unit sale, so we can divide the NPV for 50,000 units by the sensitivity to get a change in quantity. Doing so, we get:

$537,818.44 = $63.24(DQ)

DQ = 8,504

If sales decreased by 8,504 units the NPV would be zero, so the minimum quantity is:

QMin = 50,000 – 8,504

QMin = 41,496

28. We will use the bottom up approach to calculate the operating cash flow. Assuming we operate the project for all four years, the cash flows are:

	Year	0	1	2	3	4
	Sales		$6,200,000	$6,200,000	$6,200,000	$6,200,000
	Operating costs		2,700,000	2,700,000	2,700,000	2,700,000
	Depreciation		1,750,000	1,750,000	1,750,000	1,750,000
	EBT		$1,750,000	$1,750,000	$1,750,000	$1,750,000
	Tax		665,000	665,000	665,000	665,000
	Net income		$1,085,000	$1,085,000	$1,085,000	$1,085,000
	+Depreciation		1,750,000	1,750,000	1,750,000	1,750,000
	Operating CF		$2,835,000	$2,835,000	$2,835,000	$2,835,000
	Change in NWC	–$1,800,000	0	0	0	$1,800,000
	Capital spending	–7,000,000	0	0	0	0
	Total cash flow	–$8,800,000	$2,835,000	$2,835,000	$2,835,000	$4,635,000

There is no salvage value for the equipment. The NPV is:

NPV = –$8,800,000 + $2,835,000(PVIFA16%,4) + $1,800,000/1.164

NPV = $126,966.09

The cash flows if we abandon the project after one year are:

	Year	0	1
	Sales		$6,200,000
	Operating costs		2,700,000
	Depreciation		1,750,000
	EBT		$1,750,000
	Tax		665,000
	Net income		$1,085,000
	+Depreciation		1,750,000
	Operating CF		$2,835,000
	Change in NWC	–$1,800,000	$1,800,000
	Capital spending	–7,000,000	$5,219,000
	Total cash flow	–$8,800,000	$9,854,000

The book value of the equipment is:

Book value = $7,000,000 – (1)($7,000,000/4)

Book value = $5,250,000

So the taxes on the salvage value will be:

Taxes = ($5,250,000 – 5,200,000)(.38)

Taxes = $19,000

This makes the aftertax salvage value:

Aftertax salvage value = $5,200,000 + 19,000

Aftertax salvage value = $5,219,000

The NPV if we abandon the project after one year is:

NPV = –$8,800,000 + $9,854,000/1.16

NPV = –$305,172.41

If we abandon the project after two years, the cash flows are:

	Year	0	1	2
	Sales		$6,200,000	$6,200,000
	Operating costs		2,700,000	2,700,000
	Depreciation		1,750,000	1,750,000
	EBT		$1,750,000	$1,750,000
	Tax		665,000	665,000
	Net income		$1,085,000	$1,085,000
	+Depreciation		1,750,000	1,750,000
	Operating CF		$2,835,000	$2,835,000
	Change in NWC	–$1,800,000	0	$1,800,000
	Capital spending	–7,000,000	0	$4,244,000
	Total cash flow	–$8,800,000	$2,835,000	$8,879,000

The book value of the equipment is: