Chapter 10, Problem 31QP

Calculating Project NPV [LO1] You have been hired as a consultant for Pristine Urban-Tech Zither, Inc. (PUTZ), manufacturers of fine zithers. The market for zithers is growing quickly. The company bought some land three years ago for $2.1 million in anticipation of using it as a toxic waste dump site but has recently hired another company to handle all toxic materials. Based on a recent appraisal, the company believes it could sell the land for $2.3 million on an aftertax basis. In four years, the land could be sold for $2.4 million after taxes. The company also hired a marketing firm to analyze the zither market, at a cost of $125,000. An excerpt of the marketing report is as follows:

The zither industry will have a rapid expansion in the next four years. With the brand name recognition that PUTZ brings to bear, we feel that the company will be able to sell 3,600, 4,300, 5,200, and 3,900 units each year for the next four years, respectively. Again, capitalizing on the name recognition of PUTZ, we feel that a premium price of $750 can be charged for each zither. Because zithers appear to be a fad, we feel at the end of the four-year period, sales should be discontinued.

PUTZ believes that fixed costs for the project will be $415,000 per y ear, and variable costs are 15 percent of sales. The equipment necessary for production will cost $3.5 million and will be depreciated according to a three-year MACRS schedule. At the end of the project, the equipment can be scrapped for $350,000. Net working capital of $125,000 will be required immediately. PUTZ has a 38 percent tax rate, and the required return on the project is 13 percent. What is the NPV of the project?

Summary Introduction

To find: The net present value of the project

Introduction:

The variation between the present value of the cash outflows and the present value of the cash inflows are known as 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 31QP

The net present value of the project is $1,003,682.32.

Explanation of Solution

Given information:

Person X has been hired for the Company P as a consultant; the company is the manufacturer of fine zithers. The company purchased a land 3 years ago for $2.1 million in anticipation of utilizing it as a toxic waste dump, but in recent times the company has hired another company to take care of the toxic material. Based on the recent appraisal the company assumes that it could sell the land for $2.3 million on the after tax basis.

The company has hired a marketing company to examine Company P’s market at a cost of $125,000. The marketing report of the company is as follows:

• There will be a faster expansion in the upcoming 4 years
• The company will be able to sell 3,600, 4,300, 5,200, and 3,900 units for every year in the upcoming 4 years
• The premium price that is charged by the company is $750
• The year-end sales can be discounted

The company believes that the fixed cost of the project is $415,000 for a year, the variable cost is 15% of sales. The essential equipment for sales is $3.5 million the depreciation is based on the MACRS 3 year depreciation. At the project’s end the scrap value of the equipment is $350,000. The immediate requirement of the net working capital is $125,000. Company P’s tax rate is 38% and required rate of return is 13%.

MACRS depreciation table for three-year:

Year	MACRS 3 year percentage
1	33.33%
2	44.45%
3	14.81%
4	7.41%

Computation of the net present value:

To compute the net present value, first it is necessary to find out the after tax salvage value of the equipment and operating cash flow of the project.

Formula to compute the taxes on the salvage value of the equipment:

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

Computation of the taxes on salvage value of the equipment:

$\begin{array}{c}\text{Taxes on salvage value}=\left(\text{Book value}-\text{Market value}\right)\times \text{Tax rate}\\ =\left(\$0-\$350,000\right)\times 0.38\\ =-\$133,000\end{array}$

Hence, the taxes on the salvage value of the equipment are - $133,000.

Formula to calculate the after tax salvage value of the equipment:

$\text{After tax salvage value = Market price}-\text{Tax on salvage value}$

Computation of the after tax salvage value of the equipment:

$\begin{array}{c}\text{After tax salvage value = Market price}-\text{Tax on salvage value}\\ \text{= \$350,000}-\$133,000\\ =\$217,000\end{array}$

Hence, the after tax salvage value is $217,000.

Computation of the total cash flow of the project:

Total cash flow of the project
	Year 0 Amount in ($)	Year 1 Amount in ($)	Year 2 Amount in ($)	Year 3 Amount in ($)	Year 4 Amount in ($)
Revenues		2700000	3225000	39,00,000	29,25,000
Less: Fixed costs		415000	415000	4,15,000	415000
Variable costs		405000	483750	5,85,000	438750
Depreciation		1166550	1555750	5,18,350	259350
EBT		713450	770500	23,81,650	1811900
Less: Taxes		271111	292790	905027	688522
Net income		442339	477710	1476623	1123378
OCF		1608889	2033460	1994973	1382728
Capital spending	–3,500,000				217000
Land	–2,300,000				2400000
NWC	–125,000				125000
Total cash flow	–$5,925,000	$16,08,889	$20,33,460	$19,94,973	$41,24,728

Calculations that is necessary for the above table:

Computation of the revenue:

$\begin{array}{c}\text{Year 1 revenue}=\text{Sales unit}\times \text{Sale price}\\ =\text{3,600units}\times \text{\$750}\\ =\text{\$2,700,000}\end{array}$

$\begin{array}{c}\text{Year 2 revenue}=\text{Sales unit}\times \text{Sale price}\\ =\text{4,300units}\times \text{\$750}\\ =\text{\$3,225,000}\end{array}$

$\begin{array}{c}\text{Year 3 revenue}=\text{Sales unit}\times \text{Sale price}\\ =\text{5,200units}\times \text{\$750}\\ =\text{\$3,900,000}\end{array}$

$\begin{array}{c}\text{Year 4 revenue}=\text{Sales unit}\times \text{Sale price}\\ =\text{3,900units}\times \text{\$750}\\ =\text{\$2,925,000}\end{array}$

Computation of the variable cost:

$\begin{array}{c}\text{Year 1 Variable costs}=\text{Sales}\times \text{15\%}\\ =\text{\$2,700,000}\times \frac{\text{15}}{100}\\ =\$405,000\end{array}$

$\begin{array}{c}\text{Year 2 Variable costs}=\text{Sales}\times \text{15\%}\\ =\text{\$3,225,000}\times \frac{\text{15}}{100}\\ =\$483,750\end{array}$

$\begin{array}{c}\text{Year 2 Variable costs}=\text{Sales}\times \text{15\%}\\ =\text{\$3,225,000}\times \frac{\text{15}}{100}\\ =\$483,750\end{array}$

$\begin{array}{c}\text{Year 4 Variable costs}=\text{Sales}\times \text{15\%}\\ =\text{\$2,925,000}\times \frac{\text{15}}{100}\\ =\$438,750\end{array}$

Computation of the depreciation based on the MACRS 3 year depreciation:

$\begin{array}{c}\text{Year 1}=\text{Cost of equipment}\times \text{MACRS \%}\\ =\text{\$3,500,000}\times \frac{\text{33}\text{.33}}{100}\\ =\$1,166,550\end{array}$

$\begin{array}{c}\text{Year 2}=\text{Cost of equipment}\times \text{MACRS \%}\\ =\text{\$3,500,000}\times \frac{\text{44}\text{.45}}{100}\\ =\$1,555,750\end{array}$

$\begin{array}{c}\text{Year 3}=\text{Cost of equipment }\times \text{MACRS \%}\\ =\text{\$3,500,000}\times \frac{\text{14}\text{.81}}{100}\\ =\$518,350\end{array}$

$\begin{array}{c}\text{Year 4}=\text{Cost of equipment}\times \text{MACRS \%}\\ =\text{\$3,500,000}\times \frac{\text{7}\text{.41}}{100}\\ =\$259,350\end{array}$

Computation of the taxes:

$\begin{array}{c}\text{Year 1 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$713,450}\times 0.38\\ =\$271,111\end{array}$

$\begin{array}{c}\text{Year 2 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$770,500}\times 0.38\\ =\$292,790\end{array}$

$\begin{array}{c}\text{Year 3 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$2,381,650}\times 0.38\\ =\$905,027\end{array}$

$\begin{array}{c}\text{Year 4 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$1,811,900}\times 0.38\\ =\$688,522\end{array}$

Computation of the operating cash flow:

$\begin{array}{c}\text{Year 1 OCF}=\text{Revenues}-\text{Variable cost}-\text{Fixed costs }\left(1-\text{Tax}\right)+\text{Tax}\left(\text{Depreciation}\right)\\ =\$2,700,000-\$405,000-\$415,000\left(1-0.38\right)+0.38\left(\$1,166,550\right)\\ =\$1,165,600+\$443,289\\ =\$1,608,889\end{array}$

$\begin{array}{c}\text{Year 2 OCF}=\text{}\text{Revenues}-\text{Variable cost}-\text{Fixed costs }\left(1-\text{Tax}\right)+\text{Tax}\left(\text{Depreciation}\right)\\ =\$3,225,000-\$483,750-\$415,000\left(1-0.38\right)+0.38\left(\$1,555,750\right)\\ =\$1,442,275+\$591,185\\ =\$2,033,460\end{array}$

$\begin{array}{c}\text{Year 3 OCF}=\text{}\text{Revenues}-\text{Variable cost}-\text{Fixed costs }\left(1-\text{Tax}\right)+\text{Tax}\left(\text{Depreciation}\right)\\ =\$3,900,000-\$585,000-\$415,000\left(1-0.38\right)+0.38\left(\$518,350\right)\\ =\$1,798,000+\$196,973\\ =\$1,994,973\end{array}$

$\begin{array}{c}\text{Year 4 OCF}=\text{Revenues}-\text{Variable cost}-\text{Fixed costs }\left(1-\text{Tax}\right)+\text{Tax}\left(\text{Depreciation}\right)\\ =\$2,925,000-\$438,750-\$415,000\left(1-0.38\right)+0.38\left(\$259,350\right)\\ =\$1,284,175+\$98,553\\ =\$1,382,728\end{array}$

Formula to calculate the net present value of the project:

$\text{NPV}=-\text{Outflow}+\text{Inflow}$

Computation of the net present value of the project:

$\begin{array}{c}\text{NPV}=-\text{Outflow}+\text{Inflow}\\ =-\text{Year 0 cash flow}+\left(\begin{array}{l}\frac{\text{Year 1 cash flow}}{{\left(1+\text{r}\right)}^1}+\frac{\text{Year 2 cash flow}}{{\left(1+\text{r}\right)}^2}+\\ \frac{\text{Year 3 cash flow}}{{\left(1+\text{r}\right)}^3}+\frac{\text{Year 4 cash flow}}{{\left(1+\text{r}\right)}^4}\end{array}\right)\\ =-\text{\$5,925,000}+\left(\begin{array}{l}\frac{\text{\$1,608,889}}{{\left(1+0.13\right)}^1}+\frac{\text{\$2,033,460}}{{\left(1+0.13\right)}^2}+\\ \frac{\text{\$1,994,973}}{{\left(1+0.13\right)}^3}+\frac{\text{\$4,124,728}}{{\left(1+0.13\right)}^4}\end{array}\right)\\ =-\text{\$5,925,000}+\left(\begin{array}{l}\$1,423,795,575+\$1,592,497.455+\\ \$1,382,616.361+\$2,529,772.929\end{array}\right)\end{array}$

$\begin{array}{c}=-\text{\$5,925,000}+\$6,928,682.32\\ =\text{\$1,003,682}\text{.32}\end{array}$

Hence, the net present value of the project is $1,003,682.32.