Using DCF

1. Comparing Investments
Using DCF to help with Management
Decisions

2. The Scenario
• You run an FM Department.
• For maintenance and cleaning of parts of the
building, you need to use a hydraulic lift (aka
cherry picker)
• Is it better to buy or rent?

3. What does it Cost?
• Hire Costs, say 500 Crowns per week
• Purchase Price, say 100,500 Crowns
• Other Costs:
• Insurance, Maintenance, Fuel.

4. Other Costs
• Fuel – diesel or electricity. Same whether hire
or rent.
• Maintenance, if we rent, no maintenance
costs to us. If we buy, say 500 Crowns per
year
• Insurance, if we rent, no insurance costs to us.
If we buy, say 200 Crowns per year

5. Time & Lifetime
• How much will we use it?
– Say 1 week per month
• How long will it last?
– Say 20 years.

6. COMPOUND INTEREST TABLES
5PER CENT
Yrs Amt of £1
(Amount to which a capital sum will accrue)
PV of £1
(Present Value of a Capital Sum)
Amt of £1 pa
(Amount to which an income stream will accrue at a given rate)
PV of £1 pa
(Present Value of a income or expenditure stream)
Annual Sinking Fund
1 1.050000 0.952381 1.000000 0.952381 1.000000
2 1.102500 0.907029 2.050000 1.859410 0.487805
3 1.157625 0.863838 3.152500 2.723248 0.317209
4 1.215506 0.822702 4.310125 3.545951 0.232012
5 1.276282 0.783526 5.525631 4.329477 0.180975
6 1.340096 0.746215 6.801913 5.075692 0.147017
7 1.407100 0.710681 8.142008 5.786373 0.122820
8 1.477455 0.676839 9.549109 6.463213 0.104722
9 1.551328 0.644609 11.026564 7.107822 0.090690
10 1.628895 0.613913 12.577893 7.721735 0.079505
11 1.710339 0.584679 14.206787 8.306414 0.070389
12 1.795856 0.556837 15.917127 8.863252 0.062825
13 1.885649 0.530321 17.712983 9.393573 0.056456
14 1.979932 0.505068 19.598632 9.898641 0.051024
15 2.078928 0.481017 21.578564 10.379658 0.046342
16 2.182875 0.458112 23.657492 10.837770 0.042270
17 2.292018 0.436297 25.840366 11.274066 0.038699
18 2.406619 0.415521 28.132385 11.689587 0.035546
19 2.526950 0.395734 30.539004 12.085321 0.032745
20 2.653298 0.376889 33.065954 12.462210 0.030243
21 2.785963 0.358942 35.719252 12.821153 0.027996
22 2.925261 0.341850 38.505214 13.163003 0.025971
23 3.071524 0.325571 41.430475 13.488574 0.024137
24 3.225100 0.310068 44.501999 13.798642 0.022471
25 3.386355 0.295303 47.727099 14.093945 0.020952
26 3.555673 0.281241 51.113454 14.375185 0.019564
27 3.733456 0.267848 54.669126 14.643034 0.018292
28 3.920129 0.255094 58.402583 14.898127 0.017123
29 4.116136 0.242946 62.322712 15.141074 0.016046
30 4.321942 0.231377 66.438848 15.372451 0.015051
35 5.516015 0.181290 90.320307 16.374194 0.011072
40 7.039989 0.142046 120.799774 17.159086 0.008278
45 8.985008 0.111297 159.700156 17.774070 0.006262
50 11.467400 0.087204 209.347996 18.255925 0.004777
55 14.635631 0.068326 272.712618 18.633472 0.003667
60 18.679186 0.053536 353.583718 18.929290 0.002828
65 23.839901 0.041946 456.798011 19.161070 0.002189
70 30.426426 0.032866 588.528511 19.342677 0.001699
75 38.832686 0.025752 756.653718 19.484970 0.001322
80 49.561441 0.020177 971.228821 19.596460 0.001030
85 63.254353 0.015809 1245.087069 19.683816 0.000803
90 80.730365 0.012387 1594.607301 19.752262 0.000627
95 103.034676 0.009705 2040.693529 19.805891 0.000490
100 131.501258 0.007604 2610.025157 19.847910 0.000383

7. Appraisal – Purchase
Purchase Lifetime 20years
Capital Cost K100,500
Insurance K200 pa
Maintenance K500 pa
Annual
Costs K700 pa
PV £1
20years @
5.00% 12.462 K8,723
NPV K109,223
SAY K110,000

8. Appraisal - Rent
Rent Lifetime Unlimited years
Hire Cost K500 pw
12weeks pa K6,000 pa
PV £1 pa
In perpetuity @
5.00% 19.84
NPV K119,040
Say K120,000

9. Further Considerations
• What happens after 20 years? Need to buy a
new one.
• Annual Sinking Fund to recover K100,500 in 20
years @ 5% =
• K100,500 * 0.04632 = K4,655 pa
• Might be able to sell the old cherry picker, say
K2,000, in 20 years time

10. Purchase Lifetime 20years
Capital Cost K100,500
Insurance K200 pa
Maintenance K500 pa
Sinking Fund K4,655 pa
Annual
Costs K5,355pa
PV £1
20years @
5.00% 12.462 K66,734
NPV K167,234
Add
Re-sale Value K2,000
Deferred 20years @
5.00% 0.37689
K754
NPV K167,988
SAY K170,000

11. More Considerations
• What if we are wrong about how much we will
use the Cherry Picker?
• What if we use it more than 1 week in 4?
– Properties getting older, need more maintenance
– Business expanding, more buildings.

12. Rent Lifetime Unlimited years
Hire Cost K500pw
18weeks pa K9,000pa
PV £1 pa
In perpetuity @
5.00% 19.84
NPV K178,560
Say K180,000

13. Allowing for different circumstances
• Create a spreadsheet
– Can apply different models
– Different costs
– Different timescales
– Different rates