Morris Tapestry Analytics (MTA)has prepared the following Income and cash flow s

Question

Morris Tapestry Analytics (MTA)has prepared the following Income and cash flow statements for planning purposes concerning a new product. Management has approved these statements so if there are errors or oversights, that is their problem, not yours.   a Determine the sensitivity of the present worth to changes in the Quantity Sold from 40,000 units to 60,000 units in intervals of 5,000 units. What does this suggest? b Determine the unit Price that would have to be charged to attain the MARR (PW = 0), when the cost of goods sold is $21.00 and the quantity sold is 45,000. Explain how you determined this. c A committee suggested four possible outcomes (Original estimate plus 3 alternatives) shown below. Determine the expected present worth of these four scenarios if all are considered equally likely to occur. Original A B C C14 Investment $2,500,000 $3,000,000 $3,000,000 $2,500,000 C16 Price each $49.00 $49.00 $49.00 $55.00 C17 Quantity Sold 45,000 50,000 45,000 40,000 C18 COGS per unit sold $21.00 $19.00 $21.00 $21.00 C19 SG&A $1,000,000 $1,000,000 $900,000 $1,000,000 Original Values Investment $2,500,000 Year 0 only $2,500,000 Salvage $350,000 Year 5 only $350,000 Price each $49.00 All years $49.00 Quantity Sold 50,000 All years 50,000 COGS per unit sold $19.50 All years $19.50 SG&A $1,000,000 All years $1,000,000 Income tax rate 30% All years 30% Capital Gains Tax rate 15% All years 15% Working capital no change All years no change MARR 15% 15% Depreciation MACRS 5 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% Depreciation $500,000 $800,000 $480,000 $288,000 $288,000 $144,000 Book value $2,000,000 $1,200,000 $720,000 $432,000 $144,000 $0 Income Statement 0 1 2 3 4 5 Sales revenue $2,450,000 $2,695,000 $2,964,500 $3,260,950 $3,587,045 Cost of goods sold ($975,000) ($926,250) ($879,938) ($835,941) ($794,144) Gross Margin $1,475,000 $1,768,750 $2,084,563 $2,425,009 $2,792,901 General, Sales and Admin. ($1,000,000) ($1,030,000) ($1,060,900) ($1,092,727) ($1,125,509) Depreciation ($500,000) ($800,000) ($480,000) ($288,000) ($288,000) EBIT ($25,000) ($61,250) $543,663 $1,044,282 $1,379,393 Income tax $7,500 $18,375 ($163,099) ($313,285) ($413,818) Net income ($17,500) ($42,875) $380,564 $730,998 $965,575 Cash Flow Statement Operations Activities Net Income ($17,500) ($42,875) $380,564 $730,998 $965,575 Add depreciation $500,000 $800,000 $480,000 $288,000 $288,000 Total $482,500 $757,125 $860,564 $1,018,998 $1,253,575 Capital Activities Investment -2,500,000             Salvage $350,000 Salvage $350,000 Book value $144,000 Tax on gain ($30,900) Gain $206,000 Total -2,500,000 0 0 0 0 319,100 Tax ($30,900) Cash flow ($2,500,000) $482,500 $757,125 $860,564 $1,018,998 $1,572,675 Present Worth = $422,408 Morris Tapestry Analytics (MTA)has prepared the following Income and cash flow statements for planning purposes concerning a new product. Management has approved these statements so if there are errors or oversights, that is their problem, not yours.   a Determine the sensitivity of the present worth to changes in the Quantity Sold from 40,000 units to 60,000 units in intervals of 5,000 units. What does this suggest? b Determine the unit Price that would have to be charged to attain the MARR (PW = 0), when the cost of goods sold is $21.00 and the quantity sold is 45,000. Explain how you determined this. c A committee suggested four possible outcomes (Original estimate plus 3 alternatives) shown below. Determine the expected present worth of these four scenarios if all are considered equally likely to occur. Original A B C C14 Investment $2,500,000 $3,000,000 $3,000,000 $2,500,000 C16 Price each $49.00 $49.00 $49.00 $55.00 C17 Quantity Sold 45,000 50,000 45,000 40,000 C18 COGS per unit sold $21.00 $19.00 $21.00 $21.00 C19 SG&A $1,000,000 $1,000,000 $900,000 $1,000,000 Original Values Investment $2,500,000 Year 0 only $2,500,000 Salvage $350,000 Year 5 only $350,000 Price each $49.00 All years $49.00 Quantity Sold 50,000 All years 50,000 COGS per unit sold $19.50 All years $19.50 SG&A $1,000,000 All years $1,000,000 Income tax rate 30% All years 30% Capital Gains Tax rate 15% All years 15% Working capital no change All years no change MARR 15% 15% Depreciation MACRS 5 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% Depreciation $500,000 $800,000 $480,000 $288,000 $288,000 $144,000 Book value $2,000,000 $1,200,000 $720,000 $432,000 $144,000 $0 Income Statement 0 1 2 3 4 5 Sales revenue $2,450,000 $2,695,000 $2,964,500 $3,260,950 $3,587,045 Cost of goods sold ($975,000) ($926,250) ($879,938) ($835,941) ($794,144) Gross Margin $1,475,000 $1,768,750 $2,084,563 $2,425,009 $2,792,901 General, Sales and Admin. ($1,000,000) ($1,030,000) ($1,060,900) ($1,092,727) ($1,125,509) Depreciation ($500,000) ($800,000) ($480,000) ($288,000) ($288,000) EBIT ($25,000) ($61,250) $543,663 $1,044,282 $1,379,393 Income tax $7,500 $18,375 ($163,099) ($313,285) ($413,818) Net income ($17,500) ($42,875) $380,564 $730,998 $965,575 Cash Flow Statement Operations Activities Net Income ($17,500) ($42,875) $380,564 $730,998 $965,575 Add depreciation $500,000 $800,000 $480,000 $288,000 $288,000 Total $482,500 $757,125 $860,564 $1,018,998 $1,253,575 Capital Activities Investment -2,500,000             Salvage $350,000 Salvage $350,000 Book value $144,000 Tax on gain ($30,900) Gain $206,000 Total -2,500,000 0 0 0 0 319,100 Tax ($30,900) Cash flow ($2,500,000) $482,500 $757,125 $860,564 $1,018,998 $1,572,675 Present Worth = $422,408

Explanation / Answer

Question 1: Sensitivity of the present net worth by changing the quantity sold from 40,000 to 60,000 in units of 5000 each.

For this, we have identified how the present worth is obtained. The present worth is calculated as follows:

Present Value of Future cash flows – Initial investment

This will be:

[482,500/(1+r)] + [757,125/(1+r)^2] + [860,564/(1+r)^3] + [1,018,998/(1+r)^4] +[ 1,572,675/(1+r)^5]

-2,500,000 = 422,408

where “r” will be the cost of capital(COC).

Therefore upon calculation r will be 15%

Therefore COC r=15%

Observations

From this the sensitivity of the Present value is shown in the below table

Number of Units

Sensitivity in Present Value

40,000

($524,796)

45,000

($51,194)

50,000

$422,408

55,000

$896,010

60,000

$1,369,612

Question 2: Unit price when Present Worth (PW =0) and units sold is 45,000 and COGS is $21.

By holding the observations in the 1st Question, We can see that for a unit price of $50.5655, the present worth becomes zero.

Therefore, the unit price should be $50.57 to maintain the MARR (PW=0)

Explantion:

Original Values

Investment

$2,500,000

Year 0 only

$2,500,000

Salvage

$350,000

Year 5 only

$350,000

Price each

$50.5655

All years

$49.00

Quantity Sold

45,000

All years

50,000

COGS per unit sold

$21

All years

$19.50

SG&A

$1,000,000

All years

$1,000,000

Income tax rate

30%

All years

30%

Capital Gains Tax rate

15%

All years

15%

Working capital

no change

All years

no change

MARR

15%

15%

Depreciation MACRS

5

20.00%

32.00%

19.20%

11.52%

11.52%

5.76%

Depreciation

$500,000

$800,000

$480,000

$288,000

$288,000

$144,000

Book value

$2,000,000

$1,200,000

$720,000

$432,000

$144,000

$0

Income Statement

0

1

2

3

4

5

Sales revenue

22,75,449

25,02,994

27,53,293

30,28,623

33,31,485

Cost of goods sold

-9,45,000

-8,97,750

-8,52,863

-8,10,219

-7,69,708

Gross Margin

13,30,449

16,05,244

19,00,431

22,18,403

25,61,776

General, Sales and Admin.

-10,00,000

-10,30,000

-10,60,900

-10,92,727

-11,25,509

Depreciation

-5,00,000

-8,00,000

-4,80,000

-2,88,000

-2,88,000

EBIT

-1,69,551

-2,24,756

3,59,531

8,37,676

11,48,268

Income tax

50,865

67,427

-1,07,859

-2,51,303

-3,44,480

Net income

-1,18,686

-1,57,329

2,51,672

5,86,373

8,03,787

Cash Flow Statement

Operations Activities

Net Income

-1,18,686

-1,57,329

2,51,672

5,86,373

8,03,787

Add depreciation

5,00,000

8,00,000

4,80,000

2,88,000

2,88,000

Total

3,81,314

6,42,671

7,31,672

8,74,373

10,91,787

Capital Activities

Investment

-25,00,000

  

  

  

  

Salvage

$350,000

Salvage

$350,000

Book value

$144,000

Tax on gain

($30,900)

Gain

$206,000

Total

-25,00,000

0

0

0

0

3,19,100

Tax

($30,900)

Cash flow

-25,00,000

3,81,314

6,42,671

7,31,672

8,74,373

14,10,887

Present Worth =

1

Question 3: Present Worth of all four scenarios:

Original

A

B

C

Investment

$2,500,000

$3,000,000

$3,000,000

$2,500,000

Price each

$49.00

$49.00

$49.00

$55.00

Quantity Sold

45,000

50,000

45,000

40,000

COGS per unit sold

$21.00

$19.00

$21.00

$21.00

SG&A

$1,000,000

$1,000,000

$900,000

$1,000,000

Present Worth

($196,558)

($23,754)

($696,558)

$15,613

Number of Units

Sensitivity in Present Value

40,000

($524,796)

45,000

($51,194)

50,000

$422,408

55,000

$896,010

60,000

$1,369,612

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