# Case study and calculations: Optimization using NPV, Profitability index

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The given data in the question is shown as following:

 Job Today (cost) Expected Sale Price in Year 5 KCC Pearl \$3,000,000 \$18,000,000 Sea View 15,000,000 75,500,000 Mountain View 9,000,000 50,000,000 Hill Top 3,000,000 35,500,000 Bridgetown 6,000,000 10,000,000 Northern Giant 9,000,000 46,500,000

Relevant terms

Mutually exclusive investment

The term mutually exclusive investment usually involves several competing mutually exclusive projects which refer to those which compete with other projects in such a way that the acceptance of one will automatically exclude the possibility of accepting other alternatives at the same time (Khan 2004, p. 10).  For example, if the company chooses the first investment option, the KCC Pearl, then it at the same time it means that the company could not choose other investment options.

Time value of money

The term time value refers to the belief that a dollar in hand today is worth more than a dollar promised at some future time (Magoon & Vasishth 2007). And because of the time value, people believe that at the future money need to be discounted according to how far it is expected. For example, KCC Pearl’s residual value is \$18,000,000 in the year 5, then the current value of this salvage value should be discounted to present.

Discount rate

Discount rate is the rate of return used to convert future values to present values (Bygrave & Zacharakis 2004, p. 458). In this case, the calculation of the present value for projects, KCC Pearl, Sea View and Mountain View will adopts the discount rate of 15% while the rest will use 8% instead.

Calculations

Calculations – Internal rate of return (IRR)

Because the Internal rate of return (IRR) makes the net present value of all cash flows from a particular project equal to zero, therefore, the calculation is as following:

KCC Pearl

0=-3000000+(18000000)*1/((1+IRR)^5)

3000000=18000000*1/((1+IRR)^5)

3000000/18000000=1/((1+IRR)^5)

18000000/3000000=(1+IRR)^5

(18000000/3000000)^(1/5)=(1+IRR)

1.43=1+IRR

IRR=0.43

Sea View

(75500000/15000000)^(1/5)=(1+IRR)

1.38=1+IRR

IRR=0.38

Mountain View

(50,000,000/9,000,000)^(1/5)=(1+IRR)

1.41=1+IRR

IRR=0.41

Hill Top

(35500000/6000000)^(1/5)=(1+IRR)

1.43=1+IRR

IRR=0.43

Bridgetown

(10000000/3000000)^(1/5)=(1+IRR)

1.27=1+IRR

IRR=0.27

Northern Giant

(46500000/9000000)^(1/5)=(1+IRR)

1.39=1+IRR

IRR=0.39

Calculations – Net present value (NPV)

KCC Pearl

 Year Cash inflow 15% NPV 0 -3000000 1.0000 -3,000,000.00 1 0.8696 0.00 2 0.2500 0.00 3 0.1530 0.00 4 0.4096 0.00 5 18000000 0.4907 8,832,190.60 Total 5,832,190.60

Sea View

 Year Cash inflow 15% NPV 0 -15000000 1.0000 -15,000,000.00 1 0.8696 0.00 2 0.2500 0.00 3 0.1530 0.00 4 0.4096 0.00 5 75500000 0.4907 37,046,132.78 Total 22,046,132.78

Mountain View

 Year Cash inflow 15% NPV 0 -9000000 1.0000 -9,000,000.00 1 0.8696 0.00 2 0.2500 0.00 3 0.1530 0.00 4 0.4096 0.00 5 50000000 0.4907 24,533,862.76 Total 15,533,862.76

Hill Top

 Year Cash inflow 8% NPV 0 -6000000 1.0000 -6,000,000.00 1 0.9259 0.00 2 0.2500 0.00 3 0.1400 0.00 4 0.4096 0.00 5 35500000 0.5194 18,438,806.89 Total 12,438,806.89

Bridgetown

 Bridgetown Year Cash inflow 8% NPV 0 -3000000 1.0000 -3,000,000.00 1 0.9259 0.00 2 0.2500 0.00 3 0.1400 0.00 4 0.4096 0.00 5 10000000 0.5194 5,194,030.11

Northern Giant

 Year Cash inflow 8% NPV 0 -9000000 1.0000 -9,000,000.00 1 0.9259 0.00 2 0.2500 0.00 3 0.1400 0.00 4 0.4096 0.00 5 46500000 0.5194 24,152,240.01 Total 15,152,240.01

Calculations – Profitability index

We use this formula: Profitability index = PV of future cash flow / Initial investment

 PV of future cash flow Initial investment Profitability index KCC Pearl 8,832,190.60 3000000 2.94 Sea View 37,046,132.78 15000000 2.47 Mountain View 24,533,862.76 9000000 2.73 Hill Top 18,438,806.89 6000000 3.07 Bridgetown 5,194,030.11 3000000 1.73 Northern Giant 24,152,240.01 9000000 2.68

Recommended choice

Let’s review the results of the above three kind of calculations:

 Options IRR NPV Profitability index Initial investment Budget NPV of the option + unused budget money KCC Pearl 0.43 5,832,190.60 2.94 \$3,000,000 18,000,000 20832190.6 Sea View 0.38 22,046,132.78 2.47 15,000,000 18,000,000 25046132.78 Mountain View 0.41 15,533,862.76 2.73 9,000,000 18,000,000 24533862.76 Hill Top 0.43 12,438,806.89 3.07 3,000,000 18,000,000 27438806.89 Bridgetown 0.27 2,194,030.11 1.73 6,000,000 18,000,000 14194030.11 Northern Giant 0.39 15,152,240.01 2.68 9,000,000 18,000,000 24152240.01

I will recommend option “sea view” because of the largest NPV which is much higher than those of the rest, suggesting that this option bring in more present value than others after taking into consideration of the time value. Also the IRR is not the lowest and the Profitability index is fair as well. Another important reason that I will recommend this option is that it takes up \$15,000,000 out of the budget \$ 18,000,000 indicating that this project has a better use of the budget if these six options are mutually exclusive investments which means that KP could only choose one of these options and give up the others. But one uncertainty that that we have not taken into account is the unused budget money which could still be used in other purposes or at least could be put in the banks. Therefore, we calculate again the NPV of the option plus unused budget money, Sea View is among the top two scores, therefore, I will insist the Sea view options as it makes a better use of the budget and provides the maximized NPV.

Changed budget

If the budget is only \$12,000,000 instead, then option “sea view” will be excluded while the rest options are still available. But the profitability index method could not longer be used in this evaluation process as a good indicator because the profitability index does not take investment amount into consideration and therefore can not be used when the investment amount is limited.

In this case, let’s review the rest calculations:

 Options IRR NPV Initial investment Budget NPV of the option + unused budget money KCC Pearl 0.43 5,832,190.60 \$3,000,000 12,000,000 14,832,190.6 Mountain View 0.41 15,533,862.76 9,000,000 12,000,000 18,533,862.76 Hill Top 0.43 12,438,806.89 3,000,000 12,000,000 21,438,806.89 Bridgetown 0.27 2,194,030.11 6,000,000 12,000,000 8,194,030.11 Northern Giant 0.39 15,152,240.01 9,000,000 12,000,000 18,152,240.01

Under the changed conditions, I will recommend the Hill Top option which has the highest IRR suggesting that the project has a good growth rate and also the Initial investment is low providing more cash in hand for KP strengthening its financial health though the disadvantage is that its NPV is lower than those of Mountain View Northern Giant, it is still fare. Hence, I will recommend the Hill Top option.