Case study and calculations: Optimization using NPV, Profitability index

By | April 16, 2014

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The given data in the question is shown as following:

JobToday (cost)

 

Expected Sale Price in Year 5
KCC Pearl$3,000,000$18,000,000
Sea View15,000,00075,500,000
Mountain View9,000,00050,000,000
Hill Top3,000,00035,500,000
Bridgetown6,000,00010,000,000
Northern Giant9,000,00046,500,000

 

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

YearCash inflow15%NPV
0-30000001.0000-3,000,000.00
10.86960.00
20.25000.00
30.15300.00
40.40960.00
5180000000.49078,832,190.60
Total5,832,190.60

 

Sea View

YearCash inflow15%NPV
0-150000001.0000-15,000,000.00
10.86960.00
20.25000.00
30.15300.00
40.40960.00
5755000000.490737,046,132.78
Total22,046,132.78

 

Mountain View

YearCash inflow15%NPV
0-90000001.0000-9,000,000.00
10.86960.00
20.25000.00
30.15300.00
40.40960.00
5500000000.490724,533,862.76
Total15,533,862.76

 

Hill Top

YearCash inflow8%NPV
0-60000001.0000-6,000,000.00
10.92590.00
20.25000.00
30.14000.00
40.40960.00
5355000000.519418,438,806.89
Total12,438,806.89

 

Bridgetown

Bridgetown
YearCash inflow8%NPV
0-30000001.0000-3,000,000.00
10.92590.00
20.25000.00
30.14000.00
40.40960.00
5100000000.51945,194,030.11

 

Northern Giant

YearCash inflow8%NPV
0-90000001.0000-9,000,000.00
10.92590.00
20.25000.00
30.14000.00
40.40960.00
5465000000.519424,152,240.01
Total15,152,240.01

 

Calculations – Profitability index

 

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

 

PV of future cash flowInitial investmentProfitability index
KCC Pearl8,832,190.6030000002.94
Sea View37,046,132.78150000002.47
Mountain View24,533,862.7690000002.73
Hill Top18,438,806.8960000003.07
Bridgetown5,194,030.1130000001.73
Northern Giant24,152,240.0190000002.68

 

Recommended choice

 

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

 

OptionsIRRNPVProfitability indexInitial investmentBudgetNPV of the option + unused budget money
KCC Pearl0.435,832,190.602.94$3,000,00018,000,00020832190.6
Sea View0.3822,046,132.782.4715,000,00018,000,00025046132.78
Mountain View0.4115,533,862.762.739,000,00018,000,00024533862.76
Hill Top0.4312,438,806.893.073,000,00018,000,00027438806.89
Bridgetown0.272,194,030.111.736,000,00018,000,00014194030.11
Northern Giant0.3915,152,240.012.689,000,00018,000,00024152240.01

 

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:

OptionsIRRNPVInitial investmentBudgetNPV of the option + unused budget money
KCC Pearl0.435,832,190.60$3,000,00012,000,00014,832,190.6
Mountain View0.4115,533,862.769,000,00012,000,00018,533,862.76
Hill Top0.4312,438,806.893,000,00012,000,00021,438,806.89
Bridgetown0.272,194,030.116,000,00012,000,0008,194,030.11
Northern Giant0.3915,152,240.019,000,00012,000,00018,152,240.01

 

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.