Question

3. Analysis of an expansion project

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

Consider the case of Yeatman Co.:

Yeatman 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	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	$12,500	$13,000	$13,220	$13,250

This project will require an investment of $15,000 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. Yeatman 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.

$22,858

$27,430

$26,287

$18,286

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 Yeatman turns it down. How much should Yeatman 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 $400 for each year of the four-year project?

$1,365

$1,055

$1,241

$745

The project will require an initial investment of $15,000, but the project will also be using a company-owned truck that is not currently being used. This truck could be sold for $18,000, after taxes, if the project is rejected. What should Yeatman do to take this information into account?

Increase the amount of the initial investment by $18,000.

Increase the NPV of the project by $18,000.

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

Answer 1

1).NPV = 22,858

Formula	Year (n)	0	1	2	3	4
	Unit sales (u)		3,000	3,250	3,300	3,400
	Sales price per unit (p)		17.25	17.33	17.45	18.24
	Variable cost per unit (vc)		8.88	8.92	9.03	9.06
	Fixed operating costs (FC)		12,500	13,000	13,220	13,250
u*p	Sales (S)		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
100% dep. At the time of purchase	Depreciation (D)	(15,000)	-
S - VC - FC - D	EBIT	(15,000)	12,610	14,333	14,566	17,962
EBIT*(1-Tax rate)	Net income	(11,250)	9,458	10,749	10,925	13,472
	Depreciation	15,000	-
Net income + Depreciation	OCF	3,750	9,458	10,749	10,925	13,472
1/(1+d)^n	Discount factor @ 11%	1.000	0.901	0.812	0.731	0.659
OCF*Discount factor	PV of cash flows	3,750	8,520	8,724	7,988	8,874
Sum of all PVs	Total PV	37,857
	Less: initial investment	15,000
Total PV - Initial investment	NPV	22,857

2). NPV (if straight line depreciation is used) = 13,759

Formula	Year (n)	1	2	3	4
	Unit sales (u)	3,000	3,250	3,300	3,400
	Sales price per unit (p)	17.25	17.33	17.45	18.24
	Variable cost per unit (vc)	8.88	8.92	9.03	9.06
	Fixed operating costs (FC)	12,500	13,000	13,220	13,250
u*p	Sales (S)	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
Cost of equipment/4	Depreciation (D)	3,750	3,750	3,750	3,750
S - VC - FC - D	EBIT	8,860	10,583	10,816	14,212
EBIT*(1-Tax rate)	Net income	6,645	7,937	8,112	10,659
	Depreciation	3,750
Net income + Depreciation	OCF	10,395	7,937	8,112	10,659
1/(1+d)^n	Discount factor @ 11%	0.901	0.812	0.731	0.659
OCF*Discount factor	PV of cash flows	9,365	6,442	5,931	7,021
Sum of all PVs	Total PV	28,759
	Less: initial investment	15,000
Total PV - Initial investment	NPV	13,759

Note: Answers many differ slightly from the given options due to rounding off.

Using the 100% bonus depreciation method will result in the highest NPV for the project. (Reason: Higher depreciation in the earlier years adds more to the discounted cash flows so accelerated depreciation always results in a higher NPV compared to straight line depreciation.)

3). PV of after-tax reduction in cash flow of a division: PMT = 400; N = 4; rate = 11%, CPT PV.

PV = 1,241 (NPV should be reduced by this amount.)

4). After-tax sales price of 18,000 is an opportunity cost which the company incurs when it goes ahead with the project. To account for this, initial investment amount should be increased by 18,000.