Chapter 9, Problem 6CC

Conch Republic Electronics

Conch Republic Electronics is a midsized electronics manufacturer located in Key West, Florida. The company president is Shelly Couts, who inherited the company. The company originally repaired radios and other household appliances when it was founded more than 70 years ago. Over the years, the company has expanded, and it is now a reputable manufacturer of various specialty electronic items. Jay McCanless, a recent MBA graduate, has been hired by the company in its finance department.

One of the major revenue-producing items manufactured by Conch Republic is a smartphone. Conch Republic currently has one smartphone model on the market and sales have been excellent. The smartphone is a unique item in that it comes in a variety of tropical colors and is preprogrammed to play Jimmy Buffett music. However, as with any electronic item, technology changes rapidly, and the current smartphone has limited features in comparison with newer models. Conch Republic spent $750,000 to develop a prototype for a new smartphone that has all the features of the existing one but adds new features such as wifi tethering. The company has spent a further $200,000 for a marketing study to determine the expected sales figures for the new smartphone.

Conch Republic can manufacture the new smartphone for $205 each in variable costs. Fixed costs for the operation are estimated to run $5.1 million per year. The estimated sales volume is 64,000, 106,000, 87,000, 78,000, and 54,000 per year for the next five years, respectively. The unit price of the new smartphone will be $485. The necessary equipment can be purchased for $34.5 million and will be depreciated on a seven-year MACRS schedule. It is believed the value of the equipment in five years will be $5.5 million.

Net working capital for the smartphones will be 20 percent of sales and will occur with the timing of the cash flows for the year (i.e., there is no initial outlay for NWC). Changes in NWC will thus first occur in Year 1 with the first year’s sales. Conch Republic has a 35 percent corporate tax rate and a required return of 12 percent.

Shelly has asked Jay to prepare a report that answers the following questions:

6.    How sensitive is the NPV to changes in the quantity sold?

Summary Introduction

Case summary:

Company CR is an electronics manufacturing company that is located in the Key West of State F. The president of the company is Person SC, who started the company. The company initially repaired radios and home appliances. Over the years, the company has expanded its operations and is now a reputed manufacturer of many electronic items. The company has hired Person JMC for their finance department, as he has completed his MBA recently.

The smart phone is the major revenue-producing item that is manufactured by the company. The current smart phone model of the company has very good sales on the market.

Characters in the case:

• Company CR
• State F
• Person JMC
• Person SC

Adequate information:

• The company currently manufactures smart phones.
• The net working capital is 20% of the sales and will take place with the timing of cash flow in the year.
• The corporate tax is 35% and the required return is 12%.
• Person JMC prepares an essential report for further calculation.
• The quantity change is 100.

To find: The sensitivity of the net present value to the changes in the quantity sold.

Explanation of Solution

Given information:

The spending made by the company to develop a prototype for smart phone is $750,000. The money spent by the company to study the market is $200,000. The company can manufacture the new smart phones at available cost of $205 each in a variable cost, the estimated fixed cost to run the operation is $5.1 million for a year.

The estimated sales volume (sales unit) is 64,000, 106,000, 87,000, 78,000, and 54,000 for a year and for the next 5 years. The price of a unit for a smart phone is $520. The essential equipment can be bought for $34.5 million and will be depreciated on7-year MACRS depreciation. It is believed that the equipment in the next 5 years will be around 5.5 million dollars. The unit price of the new smart phone is $485.

Explanation:

The computations for the sensitivity changes in the quantity are same as the original flow of cash. The only variation will be the sale quantity of the new smart phone. Thus, the unit sold will be increased by 100 units for a year.

Note: Remember the quantity that is selected is not relevant. The last answer of the sensitivity of the net present value to a unit per year change in the sales will be the same regardless of the quantity that is selected.

Formula to calculate the sales:

$\text{Sales}=\left(\text{Estimated sales}+\text{Quantity change}\right)\text{Price per unit}$

Computation of sales:

$\begin{array}{c}\text{Sales in year 1}=\left(\text{Estimated sales}+\text{Quantity change}\right)\text{Price per unit}\\ \text{=}\left(64,000+100\right)\$485\\ =\$31,088,500\end{array}$

$\begin{array}{c}\text{Sales in year 2}=\left(\text{Estimated sales}+\text{Quantity change}\right)\text{Price per unit}\\ \text{=}\left(106,000+100\right)\$485\\ =\$51,458,500\end{array}$

$\begin{array}{c}\text{Sales in year 3}=\left(\text{Estimated sales}+\text{Quantity change}\right)\text{Price per unit}\\ \text{=}\left(87,000+100\right)\$485\\ =\$42,243,500\end{array}$

$\begin{array}{c}\text{Sales in year 4}=\left(\text{Estimated sales}+\text{Quantity change}\right)\text{Price per unit}\\ \text{=}\left(78,000+100\right)\$485\\ =\$37,878,500\end{array}$

$\begin{array}{c}\text{Sales in year 5}=\left(\text{Estimated sales}+\text{Quantity change}\right)\text{Price per unit}\\ \text{=}\left(54,000+100\right)\$485\\ =\$26,238,500\end{array}$

MACRS depreciation table for 7-Year:

MACRS Depreciation table for seven year
Year	Seven year
1	14.29%
2	24.49%
3	17.49%
4	12.49%
5	8.93%
6	8.92%
7	8.93%
8	4.46%

Projection of the new quantity:

Particulars	Year
Sales	Year 1	Year 2	Year 3	Year 4	Year 5
Sales	$31,088,500	$51,458,500	$42,243,500	$37,878,500	$26,238,500
Variable cost	13,140,500	21,750,500	17,855,500	16,010,500	11,090,500
Fixed costs	5,100,000	5,100,000	5,100,000	5,100,000	5,100,000
Depreciation	4,930,050	8,449,050	6,034,050	4,309,050	3,080,850
Earnings before tax	$7,917,950	$16,158,950	$13,253,950	$12,458,950	$6,967,150
Tax	2,771,283	5,655,633	4,638,883	4,360,633	2,438,503
Net income	$5,146,668	$10,503,318	$8,615,068	$8,098,318	$4,528,648
+ Depreciation	4,930,050	8,449,050	6,034,050	4,309,050	3,080,850
Operating cash flow	$10,076,718	$18,952,368	$14,649,118	$12,407,368	$7,609,498
Net working capital
Beginning	$0	$6,217,700	$10,291,700	$8,448,700	$7,575,700
End	6,217,700	10,291,700	8,448,700	7,575,700	0
Net working capital  Cash flow	$6,217,700	$4,074,000	$1,843,000	$873,000	$7,575,700
Net Cash flow	$3,859,018	$14,878,368	$16,492,118	$13,280,368	$15,185,198

• The variable cost is calculated by adding the sales unit with the quantity change of 100 and then multiplying it with the given variable cost.
• The depreciation is calculated by multiplying the purchase price of the equipment with the MACRS depreciation table of 7-Year based on the years.
• The beginning price in the net working capital is the end price of the next year.
• The end price is calculated by multiplying the sales with the net working capital percentage.
• The net present value that is computed in the previous problem is $13,096,371.21.

Formula to compute the book value of the equipment:

$\text{Book value of the equipment}=\text{New equipment's cost}-\text{Depreciation at each year}$

Computation of the book value of the equipment:

$\begin{array}{c}\text{Book value of the equipment}=\text{New equipment's cost}-\text{Depreciation at each year}\\ =\left[\begin{array}{l}\$34,500,000-4,930,050-8,449,050-\\ 6,034,050-4,309,050-3,080,850\end{array}\right]\\ =\$7,696,950\end{array}$

Hence, the book value of the equipment is $7,696,950.

Formula to compute the taxes on sale of the equipment:

$\text{Taxes on sale of the equipment}=\left(\text{Book value}-\text{Market value}\right)\text{Tax rate}$

Computation of the taxes on sale of the equipment:

$\begin{array}{c}\text{Taxes on sale of the equipment}=\left(\text{Book value}-\text{Market value}\right)\text{Tax rate}\\ \text{=}\left(\$7,696,950-\$5,500,000\right)0.35\\ =\$768,933\end{array}$

Hence, the taxes on the sale of the equipment are $768,933.

Formula to calculate the cash flow on the equipment sales:

$\text{Cash flow on the equipment sales}=\text{Salvage value}+\text{Taxes on the equipment sales}$

Computation of the cash flow on the equipment sales:

$\begin{array}{c}\text{Cash flow on the equipment sales}=\text{Salvage value}+\text{Taxes on the equipment sales}\\ =\$5,500,000+\$768,933\\ =\$6,268,933\end{array}$

Hence, the cash flow on the equipment sales is $6,268,933.

Cash flow of the project:

Time	Cash flow
0	-$34,500,000
1	$3,859,018
2	$14,878,368
3	$16,492,118
4	$13,280,368
5	$21,454,130

Note: In the above table, the cash flow for 5th year is calculated by adding the net cash flow at Year 5 and the cash flow on the equipment sales.

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 under this assumption are calculated as follows.

Computation of the net present value:

$\begin{array}{c}\text{Net present value}=\left(\begin{array}{l}-\text{Present value of cash outflows}+\\ \text{Present value of cash inflows}\end{array}\right)\\ =\left[\begin{array}{l}-\$34,500,000+\frac{\$3,859,018}{1+0.12}+\frac{\$14,878,368}{\left(1+0.122\right)}+\frac{\$16,492,118}{\left(1+0.123\right)}+\\ \frac{\$13,280,368}{\left(1+0.124\right)}+\frac{\$21,454,130}{\left(1+0.125\right)}\end{array}\right]\\ =\$13,158,821.46\end{array}$

Hence, the net present value of the project is $13,158,821.46.

The sensitivity of changes in the net present value to the changes in the quantity is as follows:

$\begin{array}{c}\frac{\Delta \text{NPV}}{\Delta \text{Q}}=\frac{\left(\$13,158,821.46-\$13,096,371.21\right)}{100}\\ =\frac{62,450.25}{100}\\ =\$624.50\end{array}$

Hence, a unit change in the quantity for a year of the sales in the new smart phone, changes the net present value to $624.50 in the same direction.