Chapter 24, Problem 22QP

Abandonment Decisions [LO5] Consider the following project of Hand Clapper, Inc. The company is considering a four-year project to manufacture clap-command garage door openers. This project requires an initial investment of $12 million that will be depreciated straight-line to zero over the project’s life. An initial investment in net working capital of $900,000 is required to support spare parts inventory; this cost is fully recoverable whenever the project ends. The company believes it can generate $9.1 million in pretax revenues with $3.7 million in total pretax operating costs. The tax rate is 38 percent and the discount rate is 13 percent. The market value of the equipment over the life of the project is as follows:

Year	Market Value (millions)
1	$8.20
2	6.20
3	4.70
4	.00

a. Assuming the company operates this project for four years, what is the NPV?

b. Now compute the project NPV assuming the project is abandoned after only one year, after two years, and after three years. What economic life for this project maximizes its value to the firm? What does this problem tell you about not considering abandonment possibilities when evaluating projects?

Summary Introduction

To find: The net present value

Introduction:

The variations between the present value of the cash outflows and the present value of the cash inflows are the net present value. In capital budgeting the net present value is utilized to analyze the profitability of a project or investment.

Answer to Problem 22QP

The net present value is $1,001,414.16.

Explanation of Solution

Given information:

Company HC considers the following project. The company is considering a 4 year project to produce clap-command garage door openers. The initial investment of the project is $12 million that has a straight line depreciation to zero over the project’s life. The initial investment in the net working capital that is essential to support the spare parts inventory is $900,000 and this cost is recoverable at the project’s end.

The company has a belief that it can generate a pretax revenue of $9.1 million and it will have a pretax operating cost of $3.7 million. The tax rate is 38% and the discount rate is 13%. The market value of the equipments over the life cycle of the project is as follows:

• The first year’s market value is $8.20 million
• The second year’s market value is $6.20 million
• The third year’s market value is $4.70 million
• The fourth market value is $0

Formula to calculate depreciation:

$\text{Depreciation}=\frac{\text{Investment}}{\text{Life}\text{?}\text{of}\text{?}\text{the}\text{?}\text{project}}$

Computation of the depreciation:

It is given that investment is $12,000,000 and life of project is 4years. Depreciation is found using straight-line method.

$\begin{array}{c}\text{Depreciation}=\frac{\text{Investment}}{\text{Life}\text{?}\text{of}\text{?}\text{the}\text{?}\text{project}}\\ =\frac{\$12,000,000}{4}\\ =\$3,000,000\end{array}$

Hence, annual depreciation is $3,000,000.

Computation of the cash flow for the year:

The depreciation is 3,000,000, initial investment is 12,000,000, investment in working capital is $900,000, sales are $9,100,000, tax rate is 38%, and discount rate is 13%.

The cash flow of the project is calculated with the bottom-up approach.

Year	0	1	2	3	4
Sales		$9,100,000	$9,100,000	$9,100,000	$9,100,000
(-) Operating costs		37,00,000	37,00,000	37,00,000	37,00,000
(-) Depreciation		30,00,000	30,00,000	30,00,000	30,00,000
EBT		$2,400,000	$2,400,000	$2,400,000	$2,400,000
(-) Tax (38% of EBT)		9,12,000	9,12,000	9,12,000	9,12,000
Net income		$1,488,000	$1,488,000	$1,488,000	$1,488,000
+Depreciation		30,00,000	30,00,000	30,00,000	30,00,000
Operating CF		$4,488,000	$4,488,000	$4,488,000	$4,488,000
Change in NWC	–$900,000	0	0	0	$900,000
Capital spending (Initial investment)	–$12,000,000	0	0	0	0
Total cash flow	–$12,900,000	$4,488,000	$4,488,000	$4,488,000	$5,388,000

Formula to calculate the net present value:

$\text{Net present value}=\left(\begin{array}{l}-\text{Present value of cash outflows}+\\ \text{Present value of cash inflows}\end{array}\right)$

Note: The net present value is calculated by the above formula and this formula. PVIFA is the present value interest factor of annuity.

Computation of the net present value:

$\begin{array}{c}\text{Net present value}=\left(\begin{array}{l}-\text{Present value of cash outflows}+\\ \text{Present value of cash inflows}\end{array}\right)\\ \text{=}-\$12,900,000+\text{\$4,488,000}\left(\text{13\%, 3years}\right)\text{+}\frac{\$5,388,000}{{\left(1+0.13\right)}^4}\\ \text{=}-\$12,900,000+\text{\$4,488,000}\left(2.3612\right)\text{+}\frac{\$5,388,000}{{\left(1+0.13\right)}^4}\\ =-\$12,900,000+\$10,597,065.6+\left(\frac{\$5,388,000}{1.6305}\right)\end{array}$

$=\$1,001,572$

Note: The value of the PVIFA at 13% for 3 years is 2.3612.

Hence, the net present value is $1,001,572.

Summary Introduction

To find: The net present value of the project if it is abandoned after a year, after two years, and after three years also determine the economic life of the project.

Introduction:

The cash value or the equivalent value that are associated with an asset is the abandonment value and it is also known as the liquidation value. The abandonment value is significant for a firm at the time of analyzing the profitability of a specific project or asset and taking decisions on whether it has to be maintained or abandoned.

Answer to Problem 22QP

The net present value of the project if it abandons within a year is - $606,194.6903, after 2 years is $87,266.0349, and after 3 years $1,130,212.4322.

Explanation of Solution

Given information:

Computation of the net present value of the project if it abandons within a year:

It is given that depreciation is 3,000,000, initial investment is 12,000,000, investment in working capital is $900,000, sales is $9,100,000, tax rate is 38%, and discount rate is 13%.

Year	0	1
Sales		$9,100,000
(-) Operating costs		37,00,000
(-) Depreciation		30,00,000
EBT		$2,400,000
(-) Tax (38% of EBT)		9,12,000
Net income		$1,488,000
+Depreciation		30,00,000
Operating CF		$4,488,000
Change in NWC	–$900,000	$900,000
Capital spending	–$12,000,000	$8,504,000
(Initial investment)
Total cash flow	–$12,900,000	$13,892,000

Note: The capital spending that refers to the initial investment is the value of the equipment after tax (computed below).

Formula to calculate the book value of the equipment:

$\text{Book}\text{?}\text{value}=\text{Initial}\text{?}\text{ investment}-\text{?}\text{Life}\text{?}\text{completed}\left(\frac{\text{Initial}\text{?}\text{ investment}}{\text{Life}\text{?}\text{of}\text{?}\text{the}\text{?}\text{project}}\right)$

Computation of the book value of the equipment:

$\begin{array}{c}\text{Book}\text{?}\text{value}=\text{Initial investment}-\text{?}\text{Life}\text{?}\text{completed}\left(\frac{\text{Initial}\text{?}\text{ investment}}{\text{Life}\text{?}\text{of}\text{?}\text{the}\text{?}\text{project}}\right)\\ =\$12,000,000-\left(1\right)\left(\frac{\$12,000,000}{4}\right)\\ =\$12,000,000-\$3,000,000\\ =\$9,000,000\end{array}$

Hence, book value of equipment is $9,000,000.

Formula to calculate the tax of the equipment:

$\text{Tax on equipment}=\left(\text{Book}\text{?}\text{value}-\text{Market}\text{?}\text{value}\right)\times \text{Tax}\text{?}\text{rate}$

Computation of the tax of the equipment:

It is given that book value of equipment is $9,000,000, market value of equipment is $8,200,000, and tax rate is 38%.

Tax on equipment is book value minus market value multiplied with tax rate.

$\begin{array}{c}\text{Tax on equipment}=\left(\text{Book}\text{?}\text{value}-\text{Market}\text{?}\text{value}\right)\times \text{Tax}\text{?}\text{rate}\\ \text{=}\left(\$9,000,000-\$8,200,000\right)\times 0.38\\ =\$800,000\times 0.38\\ =\$304,000\end{array}$

Hence, tax on equipment after one year is $304,000.

Formula to calculate the value of the equipment after tax:

$\text{Value}\text{?}\text{of}\text{?}\text{equipment}\text{?}\text{after}\text{?}\text{tax}=\text{Market}\text{?}\text{value}\text{?}\text{of}\text{}\text{equipment}+\text{Tax}\text{?}\text{on}\text{?}\text{equipment}$

Computation of the equipment value after tax:

It is given that market value of equipment is $8,200,000 and tax on equipment is $304,000.

Value of equipment after tax is market value of equipment plus tax on equipment.

$\begin{array}{c}\text{Value}\text{?}\text{of}\text{?}\text{equipment}\text{?}\text{after}\text{?}\text{tax}=\text{Market}\text{?}\text{value}\text{?}\text{of}\text{}\text{equipment}+\text{Tax}\text{?}\text{on}\text{?}\text{equipment}\\ \text{=\$8,200,000+304,000}\\ \text{=\$8,504,000}\end{array}$

Hence, value of equipment after tax is $8,504,000.

Formula to calculate the net present value:

$\text{NPV= }-\text{Present}\text{?}\text{value}\text{?}\text{of}\text{?}\text{cash}\text{?}\text{outflow}+\text{}\frac{\text{Cash}\text{?}\text{inflow}}{{\left(1+r\right)}^t}$

Computation of the net present value:

It is given that cash inflow for the first year is $13,892,000, cash outflow is $12,900,000, cost of capital (r) is 13%, and time period (t) is 1year.

$\begin{array}{c}\text{NPV= }\text{}\frac{\text{Cash}\text{?}\text{inflow}}{{\left(1+r\right)}^t}-\text{Present}\text{?}\text{value}\text{?}\text{of}\text{?}\text{cash}\text{?}\text{outflow}\\ \text{=}-\$12,900,000+\frac{\$13,892,000}{{\left(1+0.13\right)}^1}\\ =-\$12,900,000+12,293,805.3097\\ =-\$606,194.6903\end{array}$

Hence, the net present value of the project is - $606,194.6903.

Computation of the net present value of the project if it abandons after 2 years:

It is given that depreciation is $3,000,000, initial investment is $12,000,000, investment in working capital is $900,000, sales is $9,100,000, tax rate is 38%, and discount rate is 13%.

Year	0	1	2
Sales		$9,100,000	$9,100,000
(-) Operating costs		37,00,000	37,00,000
(-) Depreciation		30,00,000	30,00,000
EBT		$2,400,000	$2,400,000
(-) Tax (38% of EBT)		9,12,000	9,12,000
Net income		$1,488,000	$1,488,000
+Depreciation		30,00,000	30,00,000
Operating CF		$4,488,000	$4,488,000
Change in NWC	–$900,000	0	$900,000
Capital spending (Initial investment)	–$12,000,000	0	$6,124,000
Total cash flow	–$12,900,000	$4,488,000	$11,512,000

Note: The capital spending that refers to the initial investment is the value of the equipment after tax (computed below).

Computation of the equipment’s book value:

It is given that initial investment is $12,000,000, life is expected to be completed by the project is 2years, and total life of the project is 4years.

$\begin{array}{c}\text{Book}\text{?}\text{value}=\text{Initial}\text{?}\text{investment}-\text{?}\text{Life}\text{?}\text{completed}\left(\frac{\text{Initial}\text{?}\text{investment}}{\text{Life}\text{?}\text{of}\text{?}\text{the}\text{?}\text{project}}\right)\\ =\$12,000,000-\left(2\right)\left(\frac{\$12,000,000}{4}\right)\\ =\$12,000,000-\$6,000,000\\ =\$6,000,000\end{array}$

Hence, book value of equipment is $6,000,000.

Computation of the tax of the equipment:

It is given that book value of equipment is $6,000,000, market value of equipment is $6,200,000, and tax rate is 38%.

Tax on equipment is book value minus market value multiplied with tax rate.

$\begin{array}{c}\text{Tax on equipment}=\left(\text{Book}\text{?}\text{value}-\text{Market}\text{?}\text{value}\right)\times \text{Tax}\text{?}\text{rate}\\ \text{=}\left(\$6,000,000-\$6,200,000\right)\times 0.38\\ =-\$200,000\times 0.38\\ =-\$76,000\end{array}$

Hence, value of equipment after two years is - $76,000.

Computation of the equipment’s value after tax:

It is given that market value of equipment is $6,200,000 and tax on equipment is $76,000.

Value of equipment after tax is market value of equipment plus tax on equipment

$\begin{array}{c}\text{Value}\text{?}\text{of}\text{?}\text{equipment}\text{?}\text{after}\text{?}\text{tax}=\text{Market}\text{?}\text{value}\text{?}\text{of}\text{}\text{equipment}+\text{Tax}\text{?}\text{on}\text{?}\text{equipment}\\ \text{=\$6,200,000}-\text{76,000}\\ \text{=\$6,124,000}\end{array}$

Hence, value of equipment after tax is $6,124,000.

Computation of the net present value:

It is given that cash inflow for the first year is $4,488,000, for second year is 11,512,000, cash outflow is $12,900,000, cost of capital (r) is 13%, and time period (t) is 1year.

$\begin{array}{c}\text{NPV}=-\text{Present}\text{?}\text{value}\text{?}\text{of}\text{?}\text{cash}\text{?}\text{outflow}+\frac{\text{Cash}\text{?}\text{inflow}}{{\left(1+r\right)}^t}\\ \text{=}-\$12,900,000+\frac{\$4,488,000}{{\left(1+0.13\right)}^1}+\frac{\$11,512,000}{{\left(1+0.13\right)}^2}\\ =-\$12,900,000+\$3,971,681.4159+\$9,015,584.619\\ =\$87,266.0349\end{array}$

Hence, value of equipment after tax is $87,266.0349.

Computation of the net present value if the abandonment of the project takes place after 3 years:

It is given that depreciation is 3,000,000, initial investment is 12,000,000, investment in working capital is $900,000, sales is $9,100,000, tax rate is 38%, and discount rate is 13%.

Year	0	1	2	3
Sales		$9,100,000	$9,100,000	$9,100,000
(-) Operating costs		37,00,000	37,00,000	37,00,000
(-) Depreciation		30,00,000	30,00,000	30,00,000
EBT		$2,400,000	$2,400,000	$2,400,000
(-) Tax (38% of EBT)		9,12,000	9,12,000	9,12,000
Net income		$1,488,000	$1,488,000	$1,488,000
+Depreciation		30,00,000	30,00,000	30,00,000
Operating CF		$4,488,000	$4,488,000	$4,488,000
Change in NWC	–$900,000	0	0	$900,000
Capital spending (Initial investment)	–$12,000,000	0	0	$4,054,000
Total cash flow	–$12,900,000	$4,488,000	$4,488,000	$9,442,000

Note: The capital spending that refers to the initial investment is the value of the equipment after tax (computed below).

Computation of the book value:

It is given that initial investment is $12,000,000, life completed by the project is 3years, and total life of the project is 4years.

$\begin{array}{c}\text{Book}\text{?}\text{value}=\text{Initial}\text{?}\text{investment}-\text{?}\text{Life}\text{?}\text{completed}\left(\frac{\text{Initial}\text{?}\text{investment}}{\text{Life}\text{?}\text{of}\text{?}\text{the}\text{?}\text{project}}\right)\\ =\$12,000,000-\left(3\right)\left(\frac{\$12,000,000}{4}\right)\\ =\$12,000,000-\$9,000,000\\ =\$3,000,000\end{array}$

Hence, book value of equipment is $3,000,000.

Computation of the equipment’s tax:

It is given that book value of equipment is $3,000,000, market value of equipment is $4,700,000, and tax rate is 38%.

Tax on equipment is book value minus market value multiplied with tax rate.

$\begin{array}{c}\text{Tax on equipment}=\left(\text{Book}\text{?}\text{value}-\text{Market}\text{?}\text{value}\right)\times \text{Tax}\text{?}\text{rate}\\ \text{=}\left(\$3,000,000-\$4,700,000\right)\times 0.38\\ =-\$1,700,000\times 0.38\\ =-\$646,000\end{array}$

Hence, tax on equipment after three years is - $646,000.

Computation of the equipment after tax:

It is given that market value of equipment is $4,700,000 and tax on equipment is -$646,000.

Value of equipment after tax is market value of equipment plus tax on equipment

$\begin{array}{c}\text{Value}\text{?}\text{of}\text{?}\text{equipment}\text{?}\text{after}\text{?}\text{tax}=\text{Market}\text{?}\text{value}\text{?}\text{of}\text{}\text{equipment}+\text{Tax}\text{?}\text{on}\text{?}\text{equipment}\\ \text{=\$4,700,000}-\text{646,000}\\ \text{=\$4,054,000}\end{array}$

Hence, value of equipment after tax is $4,054,000.

Computation of the net present value:

It is given that cash inflow for first two years is $4,488,000 and for third year is $9,442,000, cash outflow is $12,900,000, cost of capital (r) is 13%, and period (t) is 1year. The “present value” interest factor annuity (PVIFA_r,t) is 1.6681 with 13% interest for two years.

$\begin{array}{c}\text{NPV}=-\text{Present}\text{?}\text{value}\text{?}\text{of}\text{?}\text{cash}\text{?}\text{outflow}+\text{Cash}\text{?}{\text{inflow(PVIFA}}_{\text{r,t}}\text{)+}\frac{\text{Cash}\text{?}\text{inflow}}{{\left(1+r\right)}^t}\\ \text{=}-\$12,900,000+\text{\$4,488,000}\left(1.6681\right)+\frac{\$9,442,000}{{\left(1+0.13\right)}^3}\\ =-\$12,900,000+7,486,432.8+6,543,779.6322\\ =1,130,212.4322\end{array}$

Hence, the net present value is $1,130,212.4322.