Question

Companies invest in expansion projects with the expectation of increasing the earnings of its business. Consider the case of Happy Dog Soap: Happy Dog Soap is considering an investment that will have the following sales, variable costs, and fixed operating costs: Year 1 Year 2 Year 3 Year 4 Unit sales (units) 3,000 3,250 3,300 3,400 Sales price $17.25 $17.33 $17.45 $18.24 Variable cost per unit $8.88 $8.92 $9.03 $9.06 Fixed operating costs except depreciation $12,500 $13,000 $13,220 $13,250 Accelerated depreciation rate 33% 45% 15% 7% This project will require an investment of $10,000 in new equipment. The equipment will have no salvage value at the end of the project’s four-year life. Happy Dog Soap pays a constant tax rate of 40%, and it has a required rate of return of 11%. When using accelerated depreciation, the project’s net present value (NPV) is . (Hint: Round each element in your computation—including the project’s net present value—to the nearest whole dollar.) When using straight-line depreciation, the project’s NPV is . (Hint: Again, round each element in your computation—including the project’s net present value—to the nearest whole dollar.) Using the straight-line depreciation method will result in the greater NPV for the project. No other firm would take on this project if Happy Dog Soap turns it down. How much should Happy Dog Soap reduce the NPV of this project if it discovered that this project would reduce one of its division’s net after-tax cash flows by $300 for each year of the four-year project? $791 $931 $698 $559 The project will require an initial investment of $10,000, but the project will also be using a company-owned truck that is not currently being used. This truck could be sold for $14,000, after taxes, if the project is rejected. What should Happy Dog Soap do to take this information into account? Increase the amount of the initial investment by $14,000. Increase the NPV of the project by $14,000. The company does not need to do anything with the value of the truck because the truck is a sunk cost.

Answer 1

1).

Formula	Year (n)	1	2	3	4
	Sales (units) (U)	3,000	3,250	3,300	3,400
	Price/unit (p)	17.25	17.33	17.45	18.24
	Variable cost/unit (vc)	8.88	8.92	9.03	9.06
(U*p)	Revenue ('R)	51,750	56,323	57,585	62,016
(U*vc)	Variable cost (VC)	26,640	28,990	29,799	30,804
	Fixed cost (FC)	12,500	13,000	13,220	13,250
	Depreciation rate	33%	45%	15%	7%
(Dep.rate*10,000)	Depreciation (D)	3,300	4,500	1,500	700
(R-VC-FC-D)	Op.profit (EBIT)	9,310	9,832	13,066	17,262
40% of EBIT	Less: tax @40%	3,724	3,933	5,226	6,905
(EBIT-Tax)	Net income (NI)	5,586	5,900	7,840	10,357
	Add: Dep. (D)	3,300	4,500	1,500	700
(NI - D)	Operating Cash Flow (OCF)	8,886	10,400	9,340	11,057

Formula	Year (n)	0	1	2	3	4
	Cash flow (CF)	-10,000	8,886	10,400	9,340	11,057
1/(1+d)^n	Discount factor @11%	1.000	0.901	0.812	0.731	0.659
(CF*Discount factor)	PV of CF	-10,000	8,005	8,440	6,829	7,284
Sum of all PVs	NPV	20,559

NPV when using accelerated dep. = $20,559

2).

Formula	Year (n)	1	2	3	4
	Sales (units) (U)	3,000	3,250	3,300	3,400
	Price/unit (p)	17.25	17.33	17.45	18.24
	Variable cost/unit (vc)	8.88	8.92	9.03	9.06
(U*p)	Revenue ('R)	51,750	56,323	57,585	62,016
(U*vc)	Variable cost (VC)	26,640	28,990	29,799	30,804
	Fixed cost (FC)	12,500	13,000	13,220	13,250
Straight line dep.	Depreciation rate	25%	25%	25%	25%
(Dep.rate*10,000)	Depreciation (D)	2,500	2,500	2,500	2,500
(R-VC-FC-D)	Op.profit (EBIT)	10,110	11,833	12,066	15,462
40% of EBIT	Less: tax @40%	4,044	4,733	4,826	6,185
(EBIT-Tax)	Net income (NI)	6,066	7,100	7,240	9,277
	Add: Dep. (D)	2,500	2,500	2,500	2,500
(NI - D)	Operating Cash Flow (OCF)	8,566	9,600	9,740	11,777

Formula	Year (n)	0	1	2	3	4
	Cash flow (CF)	-10,000	8,566	9,600	9,740	11,777
1/(1+d)^n	Discount factor @11%	1.000	0.901	0.812	0.731	0.659
(CF*Discount factor)	PV of CF	-10,000	7,717	7,791	7,122	7,758
Sum of all PVs	NPV	20,388

NPV when using SL dep. = $20,388

NPV when using SL depreciation is greater than NPV when using accelerated dep. - False

3). If $300/year is reduced from cash flows (year 1 to year 4) as calculated in part (1), the new NPV will be:

Formula	Year (n)	0	1	2	3	4
	Cash flow (CF)	-10,000	8,586	10,100	9,040	10,757
1/(1+d)^n	Discount factor @11%	1.000	0.901	0.812	0.731	0.659
(CF*Discount factor)	PV of CF	-10,000	7,735	8,197	6,610	7,086
Sum of all PVs	NPV	19,628

NPV will have to be reduced by 20,599 - 19,628 = $931

4). The company does not need to do anything with the value of the truck because the truck is a sunk cost.