Question

ABC, Inc is considering launching a new product which incurred $2.5 million in Research and Development expenses over the last year. The company will spend $1.8 million to acquire the equipment necessary for the manufacture of the new product. The equipment will last for 15 years and have a salvage value of $35,000. It will be depreciated to zero over 10 years using straight line depreciation. The company will also have an increase of $250,000 in accounts receivable and a decrease of $75,000 in accounts payable. The company anticipates to produce 100,000 units every year for the next 15 years and sell the units for $4 per unit. The variable costs are $0.25 per unit and the annual fixed costs are projected to be $10,000 per year. The company has a target capital structure of 40% debt and 60% equity. The company’s outstanding bonds have a yield to maturity of 5.5% and the company’s tax rate is 30%. The company has a beta of 1.4, the risk free rate is 2% and the market risk premium is 6%. Please answer the questions below and show all the formulae you used and all the calculations. (show work)

1) What is the project’s cash flow at time 0?

2) What is the after tax operating cash flow in years 1 through 10?

3) What is the after tax operating cash flow in years 11 through 14?

4) What is the after tax cash flow in year 15?

5) What is the company’s cost of equity?

6) What is the company’s WACC?

7) What is the NPV of the project?

8) What is the IRR of the project?

9) What is the profitability index?

10) Should the company launch the new product?

Answer 1

1) Project’s cash flow at time 0:

• R&D is sunk cost and should not for a part of the CF at time 0
• Capex = 1.8 million
• Working capital investment = Increase in A/R + Decrease in A/P as both result in cash outflow or cash flow deferment.
  • 250000+75000 = 325000
• So total cash out flow at time 0 = 1,800,000 + 325,000 = 2125000

2) After tax operating cash flow in years 1 through 10:

• Following is the depreciation schedule:

  • Straight line method
    Year	Opening balance	Investment	Depreciation	Closing balance
    0		$ 18,00,000.00		$   18,00,000.00
    1	$      18,00,000.00		$ 1,80,000.00	$   16,20,000.00
    2	$      16,20,000.00		$ 1,80,000.00	$   14,40,000.00
    3	$      14,40,000.00		$ 1,80,000.00	$   12,60,000.00
    4	$      12,60,000.00		$ 1,80,000.00	$   10,80,000.00
    5	$      10,80,000.00		$ 1,80,000.00	$      9,00,000.00
    6	$        9,00,000.00		$ 1,80,000.00	$      7,20,000.00
    7	$        7,20,000.00		$ 1,80,000.00	$      5,40,000.00
    8	$        5,40,000.00		$ 1,80,000.00	$      3,60,000.00
    9	$        3,60,000.00		$ 1,80,000.00	$      1,80,000.00
    10	$        1,80,000.00		$ 1,80,000.00	$                         -

  • Investment/Life = Depreciation
  • 1800000/10 = 180000
  • Opening balance = previous year's closing balance
  • Closing balance = Opening balance+investment-Depreciation
• OCF for years 1-10 is as follows:

  • Particulars	Remark	Value
    Units sold	Given	100000
    SP	Given	$4.00
    Sales	SP x Units Sold	$ 4,00,000.00
    Vc per unit	Given	$0.25
    Total VC	Vc per unit x units sold	$       25,000.00
    Fixed Cost	Given	$       10,000.00
    EBTDA	Sales-Total VC-Fixed Cost	$    3,65,000.00
    Depreciation	Calculated above	$    1,80,000.00
    EBT	EBTDA-Depreciation	$    1,85,000.00
    Taxes	30% x EBT	$       55,500.00
    EAT	EBT-Taxes	$    1,29,500.00
    Depreciation	Added back as Non cash	$    1,80,000.00
    OCF	EAT+Depreciation	$    3,09,500.00

  • So the required OCF = $ 3,09,500.00

3) After tax operating cash flow in years 11 through 14

• OCF for years 1-10 is as follows:

  • Particulars	Remark	Value
    Units sold	Given	100000
    SP	Given	$               4.00
    Sales	SP x Units Sold	$ 4,00,000.00
    Vc per unit	Given	$               0.25
    Total VC	Vc per unit x units sold	$     25,000.00
    Fixed Cost	Given	$     10,000.00
    EBTDA	Sales-Total VC-Fixed Cost	$ 3,65,000.00
    Depreciation	Calculated above	$                    -
    EBT	EBTDA-Depreciation	$ 3,65,000.00
    Taxes	30% x EBT	$ 1,09,500.00
    EAT	EBT-Taxes	$ 2,55,500.00
    Depreciation	Added back as Non cash	$                    -
    OCF	EAT+Depreciation	$ 2,55,500.00

  • So the required OCF = $ 2,55,500.00

4) After tax cash flow in year 15:

• OCF for years 1-10 is as follows:

  • Particulars	Remark	Value
    Units sold	Given	100000
    SP	Given	$               4.00
    Sales	SP x Units Sold	$ 4,00,000.00
    Vc per unit	Given	$               0.25
    Total VC	Vc per unit x units sold	$     25,000.00
    Fixed Cost	Given	$     10,000.00
    EBTDA	Sales-Total VC-Fixed Cost	$ 3,65,000.00
    Depreciation	Calculated above	$                    -
    EBT	EBTDA-Depreciation	$ 3,65,000.00
    Taxes	30% x EBT	$ 1,09,500.00
    EAT	EBT-Taxes	$ 2,55,500.00
    Depreciation	Added back as Non cash	$                    -
    OCF	EAT+Depreciation	$ 2,55,500.00
    Salvage value	Given	$35,000.00
    Tax on salvage value	30% x salvage value	$-10,500.00
    WCINV recovery	As per convention	$3,25,000.00
    After Tax CF	OCF+Salvage value+Tax +WCINV recovery	$6,05,000.00

  • So the required After tax CF= $ 6,05,000.00
  • As the book value of the equipment was reduced to 0 in year 10 the entire salvage value is a profit and therefore an inflow but there will be a tax on the same which will be an outflow and therefore a negative CF
  • Working capital investment is recovered at the end of the project as per convention

5) Company’s cost of equity calculated as per CAPM approach:

here Ke is cost of equity, RF is risk free rate and RM- RF is market risk premium:

6) Company’s WACC is as follows:

Kd is the cost of debt and as the interest on debt is tax deductible, we reduce it by (1-t) where t is the tax rate

7) NPV of the project is calculated below:

Year	CF	Discount Factor		Discounted CF
0	$   -21,25,000.00	1/(1+0.0778)^0=	1	1*-2125000=	$   -21,25,000.00
1	$       3,09,500.00	1/(1+0.0778)^1=	0.927815921	0.92781592132121*309500=	$       2,87,159.03
2	$       3,09,500.00	1/(1+0.0778)^2=	0.860842384	0.860842383857125*309500=	$       2,66,430.72
3	$       3,09,500.00	1/(1+0.0778)^3=	0.798703269	0.798703269490745*309500=	$       2,47,198.66
4	$       3,09,500.00	1/(1+0.0778)^4=	0.74104961	0.741049609844818*309500=	$       2,29,354.85
5	$       3,09,500.00	1/(1+0.0778)^5=	0.687557627	0.687557626502893*309500=	$       2,12,799.09
6	$       3,09,500.00	1/(1+0.0778)^6=	0.637926913	0.637926912695206*309500=	$       1,97,438.38
7	$       3,09,500.00	1/(1+0.0778)^7=	0.591878746	0.591878746237898*309500=	$       1,83,186.47
8	$       3,09,500.00	1/(1+0.0778)^8=	0.549154524	0.549154524251158*309500=	$       1,69,963.33
9	$       3,09,500.00	1/(1+0.0778)^9=	0.509514311	0.509514310865799*309500=	$       1,57,694.68
10	$       3,09,500.00	1/(1+0.0778)^10=	0.47273549	0.472735489762292*309500=	$       1,46,311.63
11	$       2,55,500.00	1/(1+0.0778)^11=	0.438611514	0.438611513975035*255500=	$       1,12,065.24
12	$       2,55,500.00	1/(1+0.0778)^12=	0.406950746	0.406950745940837*255500=	$       1,03,975.92
13	$       2,55,500.00	1/(1+0.0778)^13=	0.377575381	0.377575381277452*255500=	$           96,470.51
14	$       2,55,500.00	1/(1+0.0778)^14=	0.35032045	0.350320450248146*255500=	$           89,506.88
15	$       6,05,000.00	1/(1+0.0778)^15=	0.325032891	0.325032891304644*605000=	$       1,96,644.90
				NPV = Sum of all Discounted CF	$       5,71,200.28

NPV = 571200.28, which is positive and therefore this project should be invested in.

8) IRR of the project is the rate at which the NPV = 0. It can be calculated by hit an trial or by using a financial calculator or the goalseek function of Excel:

Using Excel we get the IRR as 11.68 rounded to 2 decimal places as shown below:

Year	CF	Discount Factor		Discounted CF
0	$   -21,25,000.00	1/(1+0.118616796256513)^0=	1	1*-2125000=	$   -21,25,000.00
1	$       3,09,500.00	1/(1+0.118616796256513)^1=	0.893961188	0.89396118791219*309500=	$       2,76,680.99
2	$       3,09,500.00	1/(1+0.118616796256513)^2=	0.799166605	0.799166605493373*309500=	$       2,47,342.06
3	$       3,09,500.00	1/(1+0.118616796256513)^3=	0.714423928	0.714423927986608*309500=	$       2,21,114.21
4	$       3,09,500.00	1/(1+0.118616796256513)^4=	0.638667263	0.638667263335801*309500=	$       1,97,667.52
5	$       3,09,500.00	1/(1+0.118616796256513)^5=	0.570943745	0.5709437454123*309500=	$       1,76,707.09
6	$       3,09,500.00	1/(1+0.118616796256513)^6=	0.510401549	0.510401548879814*309500=	$       1,57,969.28
7	$       3,09,500.00	1/(1+0.118616796256513)^7=	0.456279175	0.456279174948821*309500=	$       1,41,218.40
8	$       3,09,500.00	1/(1+0.118616796256513)^8=	0.407895873	0.407895873256841*309500=	$       1,26,243.77
9	$       3,09,500.00	1/(1+0.118616796256513)^9=	0.364643079	0.364643079401166*309500=	$       1,12,857.03
10	$       3,09,500.00	1/(1+0.118616796256513)^10=	0.32597676	0.325976760425425*309500=	$       1,00,889.81
11	$       2,55,500.00	1/(1+0.118616796256513)^11=	0.291410572	0.29141057198168*255500=	$           74,455.40
12	$       2,55,500.00	1/(1+0.118616796256513)^12=	0.260509741	0.260509741098914*255500=	$           66,560.24
13	$       2,55,500.00	1/(1+0.118616796256513)^13=	0.232885598	0.232885597615482*255500=	$           59,502.27
14	$       2,55,500.00	1/(1+0.118616796256513)^14=	0.208190685	0.208190685491976*255500=	$           53,192.72
15	$       6,05,000.00	1/(1+0.118616796256513)^15=	0.186114393	0.18611439251466*605000=	$       1,12,599.21
				NPV = Sum of all Discounted CF	$                      0.00

9) Profitability index = 1+NPV/Initial investment

Profitability index = 1+571200.28/2125000 = 1.27

10) As NPV is positive, the project should be invested in.