# Calculation Of Project IRR, NPV, And Sensitivity Analysis

## Calculation of Project IRR

Calculation of project IRR:

Initial Cash Flow: \$3,000,000.00

Discounted Net Cash Flows at 19%

 Year Cash Flows PVF(@19 % PV 1 \$1,100,000.00 0.840336134 \$924,369.75 2 \$1,450,000.00 0.706164819 \$1,023,938.99 3 \$1,300,000.00 0.593415814 \$771,440.56 4 \$950,000.00 0.498668751 \$473,735.31 \$3,193,484.61

Discounted Net Cash Flows at 24 %

 Year Cash Flows PVF(@24% PV 1 \$1,100,000.00 0.806451613 \$887,096.77 2 \$1,450,000.00 0.650364204 \$943,028.10 3 \$1,300,000.00 0.524487261 \$681,833.44 4 \$950,000.00 0.422973598 \$401,824.92 \$2,913,783.23

IRR=

IRR = 22.46 %

Calculation of NPV

 Year Cash Flows PVF(@15% PV 1 \$1,100,000.00 0.869565217 \$956,521.74 2 \$1,450,000.00 0.756143667 \$1,096,408.32 3 \$1,300,000.00 0.657516232 \$854,771.10 4 \$950,000.00 0.571753246 \$543,165.58 \$3,450,866.74

Initial Investment = \$ 3,000,000.00

NPV = \$3,450,866.74 – = \$ 3,000,000.00

= \$450,866.74

The Company should accept this project as the NPV of the project is positive. The NPV in this case is \$ 450,866.00. Also, the IRR is higher than the required rate of return.

The depreciation is the expense that occurs every year to write off the plant and machinery. Basically, depreciation does not affect the cash flows, but in case of tax implication, the amount of depreciation is subtracted from the cash flow before subtracting the tax. Therefore, depreciation provides the tax benefits, which ultimately increases the amount of the cash flow (Peterson & Fabozzi, 2004).

Sunk Cost = Sunk cost refers to that part of the project costs, which have been incurred and there is no chance to recover them. Sunk cost is just opposite to the variable cost, because it does not change with the change in the proposed course of action. This cost does not take part in decision making process as there is no relevance in taking this cost and if taken, then it does not affect the decision. Examples of sunk cost are the research cost that has been incurred before the starting the project, staff training cost, advertising cost, etc. In the present case of Air Jet Best Parts Inc., the cost that has been incurred before purchasing the machine is regarded as the Sunk cost and it does affect the decision for purchasing the machine (Bierman & Smidt, 2007).

Opportunity cost: Opportunity cost refers to the benefit that is foregone, when another course of alternative is chosen. In simple words, when an alternative is chosen over other alternative, then the cost of choosing that alternative is called as opportunity cost. Example of opportunity cost in the present case is when the company accepts another proposal whose NPV is greater than the recent alternative having NPV of \$450,866.74 and the benefit that the company will loose for not accepting the recent project is regarded as the opportunity cost (Bierman & Smidt, 2007).

Sensitivity analysis of the project

In the present case, sensitivity analysis of the project has been done for different rates of returns. For this purpose 14%, 16% and 18% rates have been selected.

NPV at 14 %

 Year Cash Flows PVF(@14% PV 1 \$1,100,000.00 0.877192982 \$964,912.28 2 \$1,450,000.00 0.769467528 \$1,115,727.92 3 \$1,300,000.00 0.674971516 \$877,462.97 4 \$950,000.00 0.592080277 \$562,476.26 \$3,520,579.43

NPV (14%) = \$520,579.43

NPV at 16 %

 Year Cash Flows PVF(@16% PV 1 \$1,100,000.00 0.862068966 \$948,275.86 2 \$1,450,000.00 0.743162901 \$1,077,586.21 3 \$1,300,000.00 0.640657674 \$832,854.98 4 \$950,000.00 0.552291098 \$524,676.54 \$3,383,393.59

NPV (16%) = \$383,393.59

NVP at 18 %

 Year Cash Flows PVF(@18% PV 1 \$1,100,000.00 0.847457627 \$932,203.39 2 \$1,450,000.00 0.71818443 \$1,041,367.42 3 \$1,300,000.00 0.608630873 \$791,220.13 4 \$950,000.00 0.515788875 \$489,999.43 \$3,254,790.38

NPV (18%) = \$254,790.38

Following graph represent the relationship between r and NPV.

For analyzing the scenario, three possible cases of cash flows have been selected – most likely, moderate and worst. In all cases, the probability of the cash flow is given below:

 Year Cash Flows Most Likely PVF(@15% PV 1 \$1,100,000.00 \$990,000.00 0.869565217 \$860,869.57 2 \$1,450,000.00 \$1,305,000.00 0.756143667 \$986,767.49 3 \$1,300,000.00 \$1,170,000.00 0.657516232 \$769,293.99 4 \$950,000.00 \$855,000.00 0.571753246 \$488,849.02 \$3,105,780.07
 Year Cash Flows Moderate PVF(@15% PV 1 \$1,100,000.00 \$880,000.00 0.869565217 \$765,217.39 2 \$1,450,000.00 \$1,160,000.00 0.756143667 \$877,126.65 3 \$1,300,000.00 \$1,040,000.00 0.657516232 \$683,816.88 4 \$950,000.00 \$760,000.00 0.571753246 \$434,532.47 \$2,760,693.39
 Year Cash Flows Worst PVF(@15% PV 1 \$1,100,000.00 \$770,000.00 0.869565217 \$669,565.22 2 \$1,450,000.00 \$1,015,000.00 0.756143667 \$767,485.82 3 \$1,300,000.00 \$910,000.00 0.657516232 \$598,339.77 4 \$950,000.00 \$665,000.00 0.571753246 \$380,215.91 \$2,415,606.72

On analyzing the scenario in different conditions it can be concluded that in case of most likely situation there is total NPV of \$ 105780.07 whereas in case of worst situation the NPV is – \$ 584,393.28. The NPV in this scenario is computed below:

## Calculation of NPV

Situation

Probability

NPV

Total

Most likely

0.25

\$3,105,780.07

\$776,445.02

Moderate

0.50

\$2,760,693.39

\$1,380,346.70

Worst

0.25

\$2,415,606.72

\$603,901.68

\$2,760,693.39

There are many risks associated with the project, like market risk and specific risk. Market risk is the risk that arises with the change in the market prices. Examples of market risk are inflation in market, downfall in US dollar value and some other government intervention that leads to close the project. There are also some specified risks associated with this project, like if the expected cash flows are not generated according to the desired level and when whole project fails due to no demand in the market (Baker & English, 2011).

The competitor chosen is Raytheon INC. that has issued “Raytheon 7.2%” having maturity date 15 august, 2027 and YTM of 4.16 % (Morning Star 2013). Let assumed that AirJet Best Parts Inc. has issued the bond having face value of \$100.00 and coupon rate 7.2%. Therefore cost of debt is 4.16 %.

Cost of debt (Bonds) = Current YTM of Bonds x (1-t)

= 4.16 (1-.034)

= 2.74 %

Other method for calculation of cost of debt is as follows: (Pratt, 2003).

Cost of Debt (Kd) = (Amount of Interest / Amount of debt) X 100

Also when there is premium or discount the cost of debt is as follows

Cost of Debt (Kd) = Interest amount/ (Amount of debenture + Amount of premium) X 100

Cost of Debt (Kd) = Interest Amount/ (Amount of Debenture – Amount of Discount) X 100

The coupon rate (based on the face value of the bond) determines the interest payment, but not necessary reflect the actual cost of the corporation’s debt. As the required return changes the price of the debt issue price also changes so that the actual interest payments and anticipated payments at the end gives the investors their revised required return (Pratt, 2003).

Betas of the three competitors are as follows

Competitors

Beta

Raytheon Co.

0.63

Lockheed Martin Corporation

0.6

Northrop Grumman Corporation

1.03

Source: Yahoo Finance

Average of beta: (0.63+ 0.60 + 1.03)/3 = 0.75

Risk free return = 3%, Market return = 4 %

Using CAPM model

Expected return = 3 % + 0.75(4%-3%)

= 3.75%

• It is one the easiest method to calculate the expected return of the equity.
• It considers only systematic risk that reflect that it assume real factors in computing the expected return.

• It assumes that market is stable.
• It also assumes individuals can borrow and lend freely at a risk less rate of return.

Dividend growth model cannot be applied where company does declare any dividend or whose dividend per share is growing at a rate higher than cost of equity (Ke). This method also fails to deal with risk directly. On the contrary CAPM model has a wider approach as it deals with some restrictive assumptions. The main condition for using this model is that company’s share is quoted on the stock exchange and all the variables in this model are market determined.

Current value of stock = \$ 50.00

Dividend paid = \$ 2.93

Face Value (assumed) = \$ 10.00

n = 10 years (assumed)

Cost of preferred stock:

= 23 %

The other method for calculating the cost of preferred stock is as follows

Kp = Amount of preference dividend/ Preference share capital

In adjustment case cost of preferred capital will change and can be calculated by following way:-

Kp = D/ NP

D = Annual preference dividend,

NP = Net proceed = Par value of Pref. share capital – discount – cost of floatation Or NP = Par value of pref. share capital + Premium

WACC = (0.3 x 2.74 %) + (0.6 x 3.75%) + (0.10 x 23 %).

= 5.372 %

Yes, company should use WACC for all the projects because of the following reasons: (Besley & Brigham, 2008)

This method is easy to use as compare to other methods.

• Same rate can be used for all the projects.
• No separate calculation is required to calculate the other project cost of capital as it cover all the capital invested in the business.

 Year Cash Flows PVF(@5.37% PV 1 \$1,100,000.00 0.949036728 \$1,043,940.40 2 \$1,450,000.00 0.900670711 \$1,305,972.53 3 \$1,300,000.00 0.854769584 \$1,111,200.46 4 \$950,000.00 0.811207729 \$770,647.34 \$4,231,760.73

Yes, company should accept the project as the in this case the NPV of the project is \$ \$1,231,760.73 which is mush higher than the actual earning (Besley & Brigham, 2008).

References

Baker, H. K., & English, P. (2011). Capital Budgeting Valuation: Financial Analysis for Today’s Investment Projects. John Wiley & Sons

Besley, S. & Brigham, E. F. (2008). Essentials of Managerial Finance. Cengage Learning.

Bierman, H., & Smidt, S. (2007). The Capital Budgeting Decision, Ninth Edition: Economic Analysis of Investment Projects. Routledge

Morning Star. (2013). Raytheon Company RTN. Retrieved 15 June 2013 from

Peterson, P. P., & Fabozzi, F. J. (2004). Capital Budgeting: Theory and Practice. John Wiley & Sons.

Pratt, S. P. (2003). Cost of Capital: Estimation and Applications. John Wiley & Sons.

Yahoo Finance. (2013). All data retrieved 15 June 2013 from

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