Chapter 10, Problem 2M

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 repairs the radios and home appliances at first when it was started. Over the years, the firm has expanded its operations and is now a reputed producer of many electronic items. The company for the finance department selects Person JMC as he has recently completed his MBA.

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.
• If the company does not introduce the new smart phones, then the sales of company would be 80,000 and 60,000 units in the next 2 years.
• The existing smart phone’s price is $310 for a unit, fixed cost is $1.8 million, and the variable cost is $125.
• If the company introduces the new smart phone, there will be a fall in the existing phone by 15,000 units and the price will be reduced to $275.
• 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.

To calculate: The project’s profitability index.

Explanation of Solution

Given information:

The spending made by the company to develop a prototype for the 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 a variable cost of $185 and the estimated fixed cost to run the operation is $5.3 million for a year.

The projected sales volume (sales unit) is 74,000, 95,000, 125,000, 105,000, and 80,000 for a year and for the next 5 years. The price of a unit for a smart phone is $480. The essential equipment can be bought for $38.5 and will be depreciated on a 7 year MACRS depreciation. It is believed that the equipment in the next 5 years will be around to 5.4 million dollar.

The initial cash outlay at the time 0 is the new equipment’s cost which is $38,500,000. The sale for every year is the combination of the new smart phone’s sales, the lost in revenue, and the lost in sales. In the above case, the lost sales are 15,000 units of the old smart phone every year for 2 years at a price of $310 each. The firm will be forced to decrease the old smart phone’s unit price that will be sold in the next 2 years.

Formula to calculate the total change in sales:

$\text{Sales}=\text{New sales}-\text{Lost sales}-\text{Lost revenue}$

$\text{New sales}=\text{Estimated sales volume}\times \text{Unit price of the new smart phone}$

$\text{Lost sales}=\text{Lost sales of the old smart phone}\times \text{Unit price of the existing smart phone}$

$\text{Lost revenue}=\left(\begin{array}{c}\left[\begin{array}{l}\text{Sales unit if the company does not }\\ \text{introduce the new smart phone}-\text{Lost in sales of the}\\ \text{ old smart phone}\end{array}\right]\times \\ \left[\begin{array}{l}\text{Unit price of the existing smart phone}-\\ \text{Lowered price of the existing units}\end{array}\right]\end{array}\right)$

Computation of the sales:

$\begin{array}{c}\text{Year 1}=\left[\begin{array}{l}\left(74,000\times \$480\right)-\left(15,000-\$310\right)\\ -\left[\left(80,000-15,000\right)\times \left(\$310-275\right)\right]\end{array}\right]\\ =\$28,595,000\end{array}$

Hence, the sale at Year 1 is $28,595,000.

$\begin{array}{c}\text{Year 2}=\left[\begin{array}{l}\left(95,000\times \$480\right)-\left(15,000-\$310\right)\\ -\left[\left(60,000-15,000\right)\times \left(\$310-275\right)\right]\end{array}\right]\\ =\$39,375,000\end{array}$

Hence, the sale at Year 2 is $39,375,000.

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%

Computations of the operating cash flow and net cash flow:

Particulars	Year
Sales	Year 1	Year 2	Year 3	Year 4	Year 5
New	$35,520,000	$45,600,000	$60,000,000	$50,400,000	$38,400,000
Lost sales	(4,650,000)	(4,650,000)
Lost revenue	(2,275,000)	(1,575,000)
Net sales	$28,595,000	$39,375,000	$60,000,000	$50,400,000	$38,400,000
Variable cost
New variable cost	$13,690,000	$17,575,000	$23,125,000	$19,425,000	$14,800,000
Lost sales	(1,875,000)	(1,875,000)
Variable cost	$11,815,000	$15,700,000	$23,125,000	$19,425,000	$14,800,000
Sales	$28,595,000	$39,375,000	$60,000,000	$50,400,000	$38,400,000
Variable cost	11,815,000	15,700,000	23,125,000	19,425,000	14,800,000
Fixed costs	5,300,000	5,300,000	5,300,000	5,300,000	5,300,000
Depreciation	5,501,650	9,428,650	6,733,650	4,808,650	3,438,050
Earnings before tax	$5,978,350	$8,946,350	$24,841,350	$20,866,350	$14,861,950
Tax	2,092,423	3,131,223	8,694,473	7,303,223	5,201,683
Net income	$3,885,928	$5,815,128	$16,146,878	$13,563,128	$9,660,268
+ Depreciation	5,501,650	9,428,650	6,733,650	4,808,650	3,438,050
Operating cash flow	$9,387,578	$15,243,778	$22,880,528	$18,371,778	$13,098,318
Net working capital
Beginning	$0	$5,719,000	$7,875,000	$12,000,000	$10,080,000
End	5,719,000	7,875,000	12,000,000	10,080,000	0
Net working capital  Cash flow	($5,719,000)	($2,156,000)	($4,125,000)	$1,920,000	$10,080,000
Net Cash flow	$3,668,578	$13,087,778	$18,755,528	$20,291,778	$23,178,318

Note:

• The new variable cost is calculated by multiplying the sales unit with the given variable cost.
• The lost in sales under the variable cost is computed by multiplying the variable cost of old phone and the lost in sales (15,000 units).
• The depreciation is calculated by multiplying the purchase price of the equipment with the MACRS depreciation table of 7 Year according to 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 net sales with the net working capital percentage.

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:

$\begin{array}{c}\text{Book value of the equipment}=\text{New equipment's cost}-\text{Depreciation at each year}\\ =\left[\begin{array}{l}\$38,500,000-5,501,650-9,428,650-\\ 6,733,650-4,808,650-3,438,050\end{array}\right]\\ =\$8,589,350\end{array}$

Hence, the book value of the equipment is $8,589,350.

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:

$\begin{array}{c}\text{Taxes on sale of the equipment}=\left(\text{Book value}-\text{Market value}\right)\text{Tax rate}\\ \text{=}\left(\$8,589,350-\$5,400,000\right)0.35\\ =\$1,116,273\end{array}$

Hence, the taxes on the sale of the equipment are $1,116,273.

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:

$\begin{array}{c}\text{Cash flow on the equipment sales}=\text{Salvage value}+\text{Taxes on the equipment sales}\\ =\$8,589,350+\$1,116,273\\ =\$9,705,623\end{array}$

Hence, the cash flow on the equipment sales is $9,705,623.

Cash flow of the project:

Time	Cash Flow
0	$ (38,500,000)
1	3,668,578
2	13,087,778
3	18,755,528
4	20,291,778
5	32,883,941

Note: In the above table the cash flow for the 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 profitability index:

$\text{Profitability index}=\frac{\text{Present value of the cash inflows}}{\text{Present value of the cash outflows}}$

Computation of the profitability index:

$\begin{array}{c}\text{Profitability index}=\frac{\text{Present value of the cash inflows}}{\text{Present value of the cash outflows}}\\ =\left[\frac{\begin{array}{l}\frac{\$3,668,578}{1+0.12}+\frac{\$13,087,778}{{\left(1+0.12\right)}^2}+\frac{\$18,755,528}{{\left(1+0.12\right)}^3}+\\ \frac{\$20,291,778}{{\left(1+0.12\right)}^4}+\frac{\$32,883,941}{{\left(1+0.12\right)}^5}\end{array}}{\$38,500,000}\right]\\ =1.522\end{array}$

Hence, the profitability index is 1.522.