Question

PMP– Project Management

You have to evaluate an Infrastructure Investment project in the P.R. of China. To make a solid recommendation you have to calculate the NPV, Payback Period, and the IRR as we discussed in class.

You have two scenarios you need to evaluate before making your final recommendation.

Alternative 1

The first option includes an initial investment of 19,500,000 and an annual maintenance fee of 500,000 at the end of each year. The rate of return i = 0.1 (10%). The revenue is shown below.

Calendar year    Year Cash Outflow Ao Cash inflow Ft  

2011 0. 19,500,000   

2012 1. 500,000. 3,950,000

2013. 2. 500,000. 6,010,000

2014. 3. 500,000. 7,925,000

2015. 4. 500,000. 10,300,000

2016. 5. 500,000. 12,000,000

Alternative 2

The second option includes an initial investment of 19,500,000 as well, but does not require a maintenance fee at the end of each year. The rate of return i = 0.1 (10%). However, the revenue is fixed at 6,755,000 for each of the five years.

Calendar year    Year Cash Outflow Ao Cash inflow Ft  

2011 0. 19,500,000   

2012 1.     6,755,000

2013. 2. 6,755,000

2014. 3. 6,755,000

2015. 4. 6,755,000

2016. 5. 6,755,000

           

1. a) After you calculate the NPV, Payback Period, and the IRR for each option, make a recommendation regarding which option you would recommend and why.

2. b) Your chief economist is telling you that an inflation rate of 5% should be expected. What is the impact on your analysis?

3. c) Perform a sensitivity analysis to test your conclusions. Would that change your opinion or not?

Answer 1

A) NOTE - WILL BE EXCLUDING THREE ZERO'S FOR CALCULATION

NPV AND IRR (IN THE IMAGE UPLOADED)

025 B с D E F G H I K L o M N P 0 R A OPTION 1 J OPTION 1 1 NPV IRR YR 0 1 2 3 4 5 nmin 00 -19500 YR NET CASHFLOW D RATE (10%) PV 0 -19500 1 -19500 1 3450 0.909 3136.364 2 5510 0.826 4553.719 3 7425 0.751 5578.512 4 9800 0.683 6693.532 5 11500 0.621 7140.595 3950 6010 7925 10300 12000 -500 -500 -500 -500 -500 3450 5510 7425 9800 11500 0.909 0.826 0.751 0.683 0.621 3136.363636 4553.719008 5578.512397 6693.531863 7140.595215 D RATE (22 %) PV 1 -19500 0.820 2827.869 0.672 3701.962 0.551 4088.999 0.451 4423.711 0.370 4254.991 -19500 1 -19500 NPV 7602.722 -202.468 7602.722 IRR 21.68872 5 INITIAL INV 6 CASH INFLOW 7 CASH OUTFLOW 8 NET CASHFLOW 9 D FACTOR (10%) 10 PRESENT VALUE 11 12 NPV 13 14 OPTION 2 15 16 YR 17 18 INITIAL INV 19 CASH INFLOW 20 CASH OUTFLOW 21 NET CASHFLOW 22 D FACTOR (10%) 23 PRESENT VALUE 24 25 NPV 26 0 1 2 3 4 5 -19500 OPTION 2 YR NET CASHFLOW D RATE (10%) PV D RATE (22%) PV 0 -19500 1 -19500 1 -19500 1 6755 0.909 6140.909 0.820 5536.885 2 6755 0.826 5582.645 0.672 4538.431 3 6755 0.751 5075.131 0.551 3720.025 4 6755 0.683 4613.756 0.451 3049.201 5 6755 0.621 4194.324 0.370 2499.345 6755 6755 6755 6755 6755 -19500 1 -19500 6755 6755 0.909 0.826 6140.909091 5582.644628 6755 6755 6755 0.751 0.683 0.621 5075.13148 4613.755891 4194.323537 NPV 6106.765 -156.113 6106.765 IRR 21.70087 27 28 29

IRR FORMULA (UPLOADED IMAGE)

usl chey yordat ith maximisation FORMULA FOR IRR IRR LR + (HK - LR) NOV (LR) [NPV (ER) - NPV (HR LR - Lower Discount Rate HR Higher Discount Rate 7 To find - IRC of option IRR 10% + 7602.722 ( 22% - 10%) (7602.722 - - 202.468 11 10% t 91232.664 7602-722 + 202.468 5 10% + 91232.644 Rovato 7805.19 10% + 11. 69% 21. 69%

PAYBACK PERIOD

OPTION 1

YR	NET CASHFLOW	BALANCE
0	-19500	-19500
1	3450	-16050 ie; (19500-3450)
2	5510	-10540
3	7425	-3115
4	9800	0

SO IT WILL BE BETWEEN YEAR 3 AND 4;

= 3+(3115/9800)

=3.318 YEARS OR 3 YEARS AND 4 MONTHS .

OPTION 2

YR	NET CASHFLOW	BALANCE
0	-19500	-19500
1	6755	-12745
2	6755	-5990
3	6755

IT WILL BE BETWEEN YEAR 2 AND 3

= 2+(5990/6755)

=2.886 YEARS OR 2 YEARS AND 11 MONTHS .

RESULTS SHOWS

OPTION 1 IS HAVING NPV OF 7602000, IRR OF 21.69 % AND PAYBACK PERIOD OF 3.32 YRS.

OPTION 2 IS HAVING NPV OF 6107000, IRR OF 21.7% AND PAYBACK PERIOD OF 2.89 YRS.

BOTH OPTION SHOWS POSITIVE NPV ,SIMILAR IRR , BUT OPTION 2 IS HAVING A SHORTER PAYBACK PERIOD WHICH MEANS ,WE CAN COVER INVESTMENT COST MORE FASTER THAN OPTION 1.

C) SENSITIVITY ANALYSIS

ON SALES REVENUE

OPTION 1

YR	D FACTOR (10%)	SALES	PV
1	0.909	3950	3590
2	0.826	6010	4964
3	0.751	7925	5952
4	0.683	10300	7035
5	0.621	12000	7452
TOTAL			28993

SENSITIVITY = NPV / PV OF SALES REVENUE

= 7602/28993

=26.22%

IF CASH INFLOW IS DECREASED BY BY 26.22% ; NPV BECOMES ZERO

OPTION 2

SINCE SALES REVENUE IS SAME FOR EVERY YEAR WE CAN FIND PV OF SALES REVENUE USING ANNUITY FACTOR ( 10 % FOR 5 YEARS IN THE ANNUITY TABLE)

PV OF SALES REVENUE = 6755 * 3.791 = 25608

SENSITIVITY = 6107/25608 =23.8%

IF CASH INFLOW IS DECREASED BY BY 23.8% ; NPV BECOMES ZERO

SO OPTION 2 IS MORE SENSITIVE OR CRITICAL.

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