Question

Year    Proj Y             Proj Z

    0      ($2,100,000) ($2,100,000)

1          2,000,000        950,000

2          950,000           780,000

3                      —        730,000

4                      —        875,000

The projects provide a necessary service, so whichever one is selected is expected to be repeated into the foreseeable future. Both projects have an 10% cost of capital.

- What is each project’s initial NPV without replication? Which project will you choose?

-What is each project’s equivalent annual annuity? Which project will you choose?

-Now apply the replacement chain approach to determine the shorter project’s extended NPV. Which project should be chosen?

Now assume that the cost to replicate Project Y in 2 years will increase by $750,000 because of inflationary pressures. How should the analysis be handled now, and which project should be chosen?

Answer 1

10% A B с D 1 Year Project Y Project Z WACC 2 0 $ (2,100,000.00) $ (2,100,000.00) 3 1 $ 2,000,000.00 $ 950,000.00 4 2 $ 950,000.00 $ 780,000.00 5 3 $ 730,000.00 6 4 $ 875,000.00 7 a.) 8 Initial NPV $ 503,305.79 $ 554,361.04 9 Choose project Z NPV is higher 10 11 c.) Replacement approach 12 Year Project Y Project Z 13 0 $ (2,100,000.00) $ (2,100,000.00) 14 1 $ 2,000,000.00 $ 950,000.00 15 2 $ (1,150,000.00) $ 780,000.00 added costs 16 3 $ 2,000,000.00 $ 730,000.00 17 4 $ 950,000.00 $ 875,000.00 18 19 NPV with $ 919,260.98 $ 554,361.04 20 Replacement NPV of Project Y is higher so choose Y 21 22 d.) Cost of replicating Y increase by $ (750,000.00) 23 Year Project Y Project Z 24 0 $ (2,100,000.00) $ (2,100,000.00) 25 1 $ 2,000,000.00 $ 950,000.00 26 2 $ (1,900,000.00) $ 780,000.00 added costs 27 3 $ 2,000,000.00 $ 730,000.00 28 4 $ 950,000.00 $ 875,000.00 29 30 NPV 299,426.27 $ 554,361.04 31 Now NPV of Project Y is higher 32 $

For replication we just add the initial cost in the ending cash flows and replicate them till the end and then find the NPV

A B с D E 1 Year WACC 0.1 2 0 31 Project Y -2100000 2000000 950000 Project Z -2100000 950000 780000 730000 875000 4 2 5 3 6 4 7 a.) 8 Initial NPV 9 =C2+NPV($F$1,C3:06) =B2+NPV($F$1,B3:36) Choose project Z NPV is higher Replacement approach Project Y -2100000 2000000 =950000+B13 =B14 =B4 Project Z -2100000 950000 780000 730000 875000 added costs =B13+NPV($F$1,B14:B17) =C13+NPV($F$1,C14:C17) NPV of Project Y is higher so choose 10 11 c.) 12 Year 13 0 14 1 15 2 16 3 174 18 19 NPV with 20 Replacement 21 22 d.) 23 Year 24 0 25 1 26 2 27 3 28 4 29 30 NPV 31 32 -750000 Cost of replicating Y increase by Project Y -2100000 2000000 =950000+B24+D22 =B25 =B17 Project Z -2100000 950000 780000 730000 875000 added costs =C24+NPV($F$1,C25:C28) =B24+NPV($F$1,B25:B28) Now NPV of Project Y is higher

For second part

NPV y = 503305.79

NPV z = 554361.04

EAA y : PV = -503305.79 FV = 0 N = 2 I/Y = 10

Put all the values in the financial calculator and get PMT y= 290000

EAA z: PV = -554361.04 FV = 0 N= 4 I/Y = 10

Put all the values in the financial calculator and get PMT z= 174884.7

So from both the approaches Project Y should be chosen because its EAA is more and also from replication process its NPV is more