Question

In: Finance

We are working on a project. Two companies have bid on the project and we are...

We are working on a project.

Two companies have bid on the project and we are choosing from two machines.

This is a mutually exclusive project, we must pick one machine or the other but cannot pick both.

Machine A has an initial cost of $19,500 and a salvage value of $7500 (today's value) at the end of its 12 year life.

Machine B has an initial cost of $17,900 and a salvage value of $2300 (today's value) at the end of it's 6 year life.

Inflation is 3.9%

Don’t forget, we will need to increase the costs and salvage values by inflation for any transaction other than year 0.   

The company uses a MARR rate of 14%

Benefits for machine A in year 1 are $5,250 and increase by 5.5% per year.   

Benefits for machine B in year 1 are $5,400 and increase by 5.5% per year.   

Costs for each machine start at $800 and increase with the inflation rate

B. What is the NPW, the EUAW and the IRR for both of these machines?

C. Calculate the delta IRR for these two machines.   

D. Create a graph for the NPW versus rate for these machines. Label clearly the IRR for machine a, the IRR for Machine B and the Delta IRR.

E. Create a MARR decision table based on the graph.

Solutions

Expert Solution

B.

The salvage value is calculated by multiplying the PV of salvage value with (1.14)^No. of years

Benefits and costs are inflated with inflation rate= 3.9%

Machine A
Year Benefits Costs Salvage value Net cash-flow
0 -19500 -19500
1 5250 -844 4406
2 5538.75 -890.42 4648.33
3 5843.38125 -939.3931 4903.98815
4 6164.767219 -991.0597205 5173.707498
5 6503.829416 -1045.568005 5458.261411
6 6861.540034 -1103.074245 5758.465788
7 7238.924735 -1163.743329 6075.181407
8 7637.065596 -1227.749212 6409.316384
9 8057.104204 -1295.275419 6761.828785
10 8500.244935 -1366.515567 7133.729368
11 8967.758406 -1441.673923 7526.084484
12 9460.985119 -1520.965989 $11,869.92 19809.94028
Machine B
Year Benefits Costs Salvage value Net cash-flow
0 -17900 -17900
1 5400 -844 4556
2 5697 -890.42 4806.58
3 6010.335 -939.3931 5070.9419
4 6340.903425 -991.059721 5349.843705
5 6689.653113 -1045.56801 5644.085108
6 7057.584035 -1103.07425 2893.484241 8847.99403

NPV and IRR value are calculated using 'NPV' and 'IRR' functions in excel

Hence,

NPV of Machine A=$14.344.13

IRR of Machine A= 26.24%

EUAW of Machine A= $2534.17

NPV of Machine B=$3347.66

IRR of Machine B= 19.96%

EUAW of Machine B= $860.88

C.

Delta IRR or incremental IRR is calculated by calculating the net cash-flows of Machine A and Machine B

Year 0 1 2 3 4 5 6 7 8 9 10 11 12
Machine A -19500 4406 4648.33 4903.98815 5173.707 5458.261 5758.466 6075.181 6409.316 6761.829 7133.729 7526.084 19809.94
Machine B -17900 4556 4806.58 5070.9419 5349.844 5644.085 8847.994 0 0 0 0 0 0
Net -1600 -150 -158.25 -166.95375 -176.136 -185.824 -3089.53 6075.181 6409.316 6761.829 7133.729 7526.084 19809.94
Delta IRR 38% IRR(S7:AE7)

D.

Here, Machine A NPW = NPV(Rate, Cash flows array from year 1 to 12) - Initial Investment

Machine B NPW = NPV(Rate,Cash flows array from year 1 to 6) - Initial Investment

Rate Machine A NPW Machine B NPW
1% 58320.92646 15091.02731
2% 52687.54318 13876.27902
3% 47595.84379 12726.55374
4% 42985.56513 11637.56509
5% 38803.86406 10605.35504
6% 35004.32759 9626.265575
7% 31546.12427 8696.912998
8% 28393.27554 7814.164732
9% 25514.02895 6975.118262
10% 22880.31821 6177.082041
11% 20467.2972 5417.558156
12% 18252.93725 4694.226566
13% 16217.67848 4004.930769
14% 14344.12756 3347.664747
15% 12616.79527 2720.561069
16% 11021.86822 2121.880038
17% 9547.010112 1549.99978
18% 8181.188414 1003.407191
19% 6914.522913 480.6896548
20% 5738.153313 -19.47254048
21% 4644.123258 -498.3131437
22% 3625.278605 -956.9863097
23% 2675.178096 -1396.572442
24% 1788.0148 -1818.083555
25% 958.5469361 -2222.468211
26% 182.0368843 -2610.616044
27% -545.8026586 -2983.361944
28% -1228.856274 -3341.489893
29% -1870.647943 -3685.736511
30% -2474.378377 -4016.794324

E.

Since, both NPV and IRR of Machine A is higher than Machine B, Machine A should always be selected as long as the MARR < 26.24%

jeff jeffy answered 1 year ago
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