Question

Companies invest in expansion projects with the expectation of increasing the earnings of its business.

Consider the case of Fox Co.:

Fox Co. 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	4,800	5,100	5,000	5,120
Sales price	$22.33	$23.45	$23.85	$24.45
Variable cost per unit	$9.45	$10.85	$11.95	$12.00
Fixed operating costs	$32,500	$33,450	$34,950	$34,875

This project will require an investment of $25,000 in new equipment. Under the new tax law, the equipment is eligible for 100% bonus deprecation at t = 0, so it will be fully depreciated at the time of purchase. The equipment will have no salvage value at the end of the project’s four-year life. Fox pays a constant tax rate of 25%, and it has a weighted average cost of capital (WACC) of 11%. Determine what the project’s net present value (NPV) would be under the new tax law.

Determine what the project’s net present value (NPV) would be under the new tax law.

$38,036

$54,677

$42,791

$47,545

Now determine what the project’s NPV would be when using straight-line depreciation.     

Using the      depreciation method will result in the highest NPV for the project.

No other firm would take on this project if Fox turns it down. How much should Fox 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 $500 for each year of the four-year project?

$1,551

$931

$1,318

$1,163

The project will require an initial investment of $25,000, 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 Fox do to take this information into account?

Answer 1

		Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^t)
		i=discount rate=WACC=11%=0.11
		N=Year   of Cash Flow
	t	Year	0	1	2	3	4
		INITIAL CASH FLOW
	a	Equipment	-$25,000
	b	100% bonus depreciation at time t=0	$25,000
	c=b*25%	Depreciation tax shield	$6,250
	I=a+c	Net Initial Cash Flow	-$18,750
		ANNUAL CASH FLOW
	e	Unit Sales		4,800	5,100	5,000	5,120
	f	Sales Price		$22.33	$23.45	$23.85	$24.45
	g	Unit Variable Cost		$9.45	$10.85	$11.95	$12.00
	h=f-g	Unit Contribution Margin		$12.88	$12.60	$11.90	$12.45
	i=h*e	Total Contribution Margin		$61,824	$64,260	$59,500	$63,744
	j	Fixed Operating Costs		$32,500	$33,450	$34,950	$34,875
	k=i-j	Before Tax Profit		$29,324	$30,810	$24,550	$28,869
	X=k*(1-0.25)	Annual After tax Cash Flow		$21,993	$23,108	$18,413	$21,652
	CF=I+X	Net Cash Flow	-$18,750	$21,993	$23,108	$18,413	$21,652	SUM
	PV=CF/(1.11^N)	Present Valure	-$18,750	$19,814	$18,755	$13,463	$14,263	$47,545
	NPV =Sum of PV	Net Present Value(NPV)	$47,545
		ANSWER:$47,545
		NPV with Straight Line Depreciation:
	t	Year	0	1	2	3	4
		INITIAL CASH FLOW
	I	Equipment	-$25,000
		ANNUAL CASH FLOW
	e	Unit Sales		4,800	5,100	5,000	5,120
	f	Sales Price		$22.33	$23.45	$23.85	$24.45
	g	Unit Variable Cost		$9.45	$10.85	$11.95	$12.00
	h=f-g	Unit Contribution Margin		$12.88	$12.60	$11.90	$12.45
	i=h*e	Total Contribution Margin		$61,824	$64,260	$59,500	$63,744
	j	Fixed Operating Costs		$32,500	$33,450	$34,950	$34,875
	k	Annual Depreciation =25000/4		$6,250	$6,250	$6,250	$6,250
	l=i-j-k	Before Tax Profit		$23,074	$24,560	$18,300	$22,619
	m=l*(1-0.25)	Annual After tax profit		$17,306	$18,420	$13,725	$16,964
	n	Add: Depreciation (non cash expense)		$6,250	$6,250	$6,250	$6,250
	X=m+n	Annual Operating Cash Flow		$23,556	$24,670	$19,975	$23,214
	CF=I+X	Net Cash Flow	-$25,000	$23,556	$24,670	$19,975	$23,214	SUM
	PV=CF/(1.11^N)	Present Valure	-$25,000	$21,221	$20,023	$14,606	$15,292	$46,141
	NPV =Sum of PV	Net Present Value(NPV)	$46,141
	R	Reduction in Cash Flow in each year		$500	$500	$500	$500	SUM
	PVR=R/(1.11^N)	Present Value of reduction		$450	$406	$366	$329	$1,551
		Amount of Reduction Required	$1,551
		ANSWER: $1,551
		If this project is rejected, The Truck should be sold