Question

  PLEASE ANWSER B!! THANK YOU :)

You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 100 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. Ignore the half-year rule for accounting for depreciation.          (18 marks total)

a. Calculate the following six numbers for this project. Round your answers to two decimal places.

(i) NPV

                                                                                       

Sales	$1,900,000
Variable costs	$1,400,000
Gross profit	$500,000
Fixed costs	$150,000
Depreciation	$170,000
EBIT	$180,000
Taxes 35%	$63,000
Net Income	$117,000

OCF = EBIT + depreciation – taxes
= 180000 + 170000 – 63000
= 287,000

PVAF= (1 – (1 / (1 + r)^N)) / r
= (1-(1/(1+.15)^4))/.15
= 2.854978363

PV of cash inflow
= 287,000 * 2.854978363
= 819,398.7901

NPV = 819,398.7901 – 680000
= 139,398.79

(ii) Profitability Index (PI)                                                       (1 mark)

= PV of cash inflow/initial investment
= 1.20

(iii) Payback period (in years)                                                 (1 mark)

Initial investment/ cash flow
= 680000/287000
= 2.37 years

(iv) Discounted payback period (in years)                                 (1 mark)

3.15 years

(v) Internal Rate of Return (IRR in %)                                      (1 mark)

CF0 = -680,000
CF1 = 287,000
CF2= 287,000
CF3= 287,000
CF4 = 287,000
COMP I/Y
IRR = 24.82

(vi) Average Accounting Return (AAR in %)                             

     Hint: Net Income = {[(Price – variable cost)*Quantity Sold] – Fixed Costs – Depreciation} * (1 – Tax rate)

     Average annual profit/initial investment

     117,000/680,000
= 0.17205
= 17.21%

b. Evaluate the sensitivity of the NPV, PI, Payback period, Discounted payback period, AAR, and IRR to a ±10% variation in the number of units sold per year. Ensure that you interpret your answers in words.

Hint #1: For example, for the NPV, increase the quantity sold by 10% and re-calculate the NPV. Then calculate the percentage change of this new NPV over the base case NPV from part (a). Repeat the process for a 10% decrease in quantity sold.

Hint #2: You must perform the process in Hint #1 for each of the six items in part (a). Note that IRR and AAR are already rates of returns. You do not have to calculate the percentage changes over the base case numbers for IRR and AAR. Instead, simply calculate the difference between the new numbers and the base case numbers for IRR and AAR.

Hint #3: It may be easier to perform these calculations in a spreadsheet. If you opt to do these calculations in a spreadsheet, ensure that you copy and paste the spreadsheet into your Word document.      

Answer 1

Sensitivity of NPV:

When Units sold is 10% greater, the new NPV is:

When Units sold is 10% lower, the new NPV is:

So Percentage change in NPV with 10% increase in units sold is 66.57% increase and that when NPV with 10% decrease in units sold is 66.57% decrease so for every 1% change in units sold, the NPV changes by 6.657% in the same direction

Sensitivity of PI:

• 1+ 2,32,165.59/680000 = 1.34
  • PI when Units increased by 10% 1.34, which is a percentage change by 11.32%
• 1+  46,591.99/680000 = 1.07
  • PI when Units decreased by 10% 1.07, which is a percentage change by 11.32%
• So for every 1% change in units sold, the PI changes by 1.132% in the same direction

Sensitivity of Payback period:

When units sold decreases by 10%

Year	Opening Balance	CF	Closing Balance
1	$        6,80,000.00	$                2,54,500.00	$      4,25,500.00
2	$        4,25,500.00	$                2,54,500.00	$      1,71,000.00
3	$        1,71,000.00	$                2,54,500.00	$        -83,500.00
4	$          -83,500.00	$                2,54,500.00	$    -3,38,000.00

• Opening balance of year 1= Cost
• Opening balance = previous year's closing balance for all years after year 1
• Closing balance = Opening balance - CF
• The closing balance of year 2 was 171000 and the CF for year 3 was 254500 so the portion of year during which the 171000 is recovered is 171000/254500= 0.67
• So the payback period is 2.67 years
• Which is an increase by 12.66%
• So for 1% decrease the payback period increases by 1.266%

When units sold increases by 10%

Year	Opening Balance	CF	Closing Balance
1	$        6,80,000.00	$                3,19,500.00	$      3,60,500.00
2	$        3,60,500.00	$                3,19,500.00	$         41,000.00
3	$            41,000.00	$                3,19,500.00	$    -2,78,500.00
4	$       -2,78,500.00	$                3,19,500.00	$    -5,98,000.00

• The closing balance of year 2 was 41000 and the CF for year 3 was 319500 so the portion of year during which the 41000 is recovered is 41000/319500= 0.13
• So the payback period is 2.13 years
• Which is a decrease by 10.13%
• So for 1% increase the payback period decreases by 1.013%

Sensitivity of Discounted Payback period:

When units sold increases by 10%

Year	Opening Balance	DCF	Closing Balance
1	$        6,80,000.00	$                2,77,826.09	$      4,02,173.91
2	$        4,02,173.91	$                2,41,587.90	$      1,60,586.01
3	$        1,60,586.01	$                2,10,076.44	$        -49,490.42
4	$          -49,490.42	$                1,82,675.16	$    -2,32,165.59

• The closing balance of year 2 was 160586.01 and the CF for year 3 was 210076.44 so the portion of year during which the 160586.01 is recovered is 160586.01 /210076.44 = 0.76
• So the payback period is 2.76 years
• Which is an decrease by 12.38%
• So for 1% increase the discounted payback period decreases by 1.238%

When units sold decreases by 10%

Year	Opening Balance	DCF	Closing Balance
1	$        6,80,000.00	$                2,21,304.35	$      4,58,695.65
2	$        4,58,695.65	$                1,92,438.56	$      2,66,257.09
3	$        2,66,257.09	$                1,67,337.88	$         98,919.21
4	$            98,919.21	$                1,45,511.20	$        -46,591.99

• The closing balance of year 3 was 98,919.21 and the CF for year 4 was 1,45,511.20 so the portion of year during which the 98,919.21 is recovered is 98,919.21/1,45,511.20= 0.68
• So the payback period is 3.68 years
• Which is a increasesby 16.83%
• So for 1% decrease the discounted payback period increases by 1.683%

Sensitivity of IRR:

When units sold decreases by 10%

CF0 = $6,80,000.00
CF1 = $2,21,304.35
CF2 = $1,92,438.56
CF3 = $1,67,337.88
CF4 =  $1,45,511.20

IRR = 18.35%

So IRR decreased by 24.82-18.35 = 6.47%

When units sold increase by 10%

CF0 = $6,80,000.00
CF1 = $2,69,964.18
CF2 = $2,28,108.47
CF3 = $1,92,742.15
CF4 =  $1,62,859.08  

IRR = 31.06%

So IRR increased by 31.06-24.82= 6.24%

Sensitivity of AAR:

When units sold decreases by 10%

AAR = 84500/680000 x 100 = 12.43%

Sensitivity = 17.21% -12.43% = 4.78% (decrease)

When units sold increases by 10%

AAR = 149500/680000x 100 = 21.99%

Sensitivity = 21.99% - 17.21% = 4.78% (increase)