# Answer to Question #5615 in Finance for Hairolnezam

Question #5615

Under Topic/Chapter of Project appraisal from book of Public Sector Financial Management by Hugh Malcolm Coombs, D. E. Jenkins

Exhibit 9.4

Chilly County Council is considering installing a new central heating system in one of its older offices. As part of its long-term plan this office will be sold in three years’ time on 31/12/X3. The authority believes that installing the central heating system will make the building easier to sell and add £100 000 to the final selling price. Three systems are regarded as feasible and estimated capital costs of each are set out here:

£

Gas 170 000

Oil 150 000

Solid fuel 140 000

Annual fuel costs are dependent on the severity of the winter each year and the rate of increase in fuel price. At the prices expected to be in force during 19X1 the annual fuel costs are estimated at:

Severe Winter ( £ ) Mild Winter ( £ )

Gas 40 000 24 000

Oil 53 000 37 000

Solid fuel 45 000 36 000

The authority estimates that in each year there is a 70% chance of a severe winter and a 30% chance of a mild winter. The chance of a mild or severe winter in any year in considered to be independent of the chance of a mild or severe winter in the previous year.

Fuel prices are expected during 19X2 and 19X3 to increase by either 8% (probability equal to 0.4) or 10% (probability equal to 0.6%). Whichever rate of increase applies in 19X2 will be repeated the following year. Maintenance costs (payable at the end of year) are expected to be:

£

Gas 2 500

Oil 2 000

Solid fuel 10 000 (in 19X2)

Maintenance costs are fixed.

There is no difference in performance between the systems.

The authority uses the monetary cost of capital as its hurdle rate. This rate is currently 12%.

Which system should be purchased by the authority?

The following solution uses expected value to calculate risk, and expresses project costs in monetary terms, permitting discounting using the monetary cost of capital.

Gas heating

Expected value of fuel costs, based upon the probabilities of a mild (0.3) or severe (0.7) winter:

= (0.7 x £40 000) + (0.3 x £24 000)

= £35 200

Annual fuel costs

8% inflation 10% inflation

Year 12% discount factor Cash flow PV Cash flow PV

£ £ £ £

1 0.893 35 200 31 433 35 200 31 433

2 0.797 38 016 30 298 38 720 30 860

3 0.712 41 057 29 234 42 592 30 326

£90 965 £92 619

Expected value of discounted fuel costs, allowing for probabilities of 8% inflation (0.4) and 10% inflation (0.6): (0.4 x £90 965) + (0.6 x £92 619)

£

Expected value 91 960

Capital costs 170 000

Maintenance (£2 000 per annum for 3 years)

= £2 500 x 2.402 6 005

NPV of gas option £-267 965

Oil heating

Expected value of fuel costs, based upon the probabilities of a mild (0.3) or severe (0.7) winter:

= (0.7 x £53 000) + (0.3 x £37 000)

= 48 200

Annual fuel costs

8% inflation 10% inflation

Year 12% discount factor Cash flow PV Cash flow PV

£ £ £ £

1 0.893 48 200 43 043 48 200 43 043

2 0.797 52 056 41 489 53 020 42 257

3 0.712 56 220 40 029 58 322 41 525

£124 561 £126 825

Expected value of discounted fuel costs, allowing for probabilities of 8% inflation (0.4) and 10% inflation (0.6): (0.4 x £124 561) + (0.6 x £126 825).

£

Expected value 125 920

Capital costs 150 000

Maintenance (£2 000 per annum for 3 years)

= £2 000 x 2.402 4 804

NPV of oil option £280 724

Solid fuel heating

Expected value of fuel costs, based upon the probabilities of a mild (0.3) or severe (0.7) winter:

= (0.7 x £45 000) + (0.3 x £36 000)

= £42 300

Annual fuel costs

8% inflation 10% inflation

Year 12% discount factor Cash flow PV Cash flow PV

£ £ £ £

1 0.893 42 300 37 774 42 300 37 774

2 0.797 45 684 36 410 46 530 37 084

3 0.712 49 339 35 129 51 183 36 442

£109 313 £111 300

Expected value of discounted fuel costs, allowing for probabilities of 8% inflation (0.4) and 10% inflation (0.6): (0.4 x £109 313) + (0.6 x £111 300)

£

Expected value 110 505

Capital costs 140 000

Maintenance (£10 000 in 2 years time)

= £10 000 x 0.797 7 970

NPV of solid fuel option £258 475

Based on these calculations, the solid fuel option has the lowest NPV of costs and on financial grounds would appear to be the favoured option. It also requires less capital investment than the other two options, which may be important if there are severe constraints on capital expenditure.

The main limitations on this type of analysis are that the expected value will never occur and we are ignoring the decision maker’s attitude to risk. A possible alternative would be to attempt to redefine the problem in terms of utility but clearly this is difficult ground to read. A decision must be made and therefore we have to take into account uncertainty whatever decision-making technique is used and there is inevitable compromise. The comparison between the three systems must also take into account both financial and so-called non-financial factors. Selections of these are now set out:

1. How reliable are the estimates of cost, the probabilities of fuel price inflation and the chances of a mild or severe winter.

2. Is there a legal obligation to install a new system?

3. While the increase in the selling price has been ignored since it is common to all three systems the question must arise as to the validity of this assumption due to the possible views of potential buyers.

4. There is no mention of storage problems or extra employees to check deliveries of the appropriate systems.

5. Gas may be an environmentally cleaner fuel.

Exhibit 9.4

Chilly County Council is considering installing a new central heating system in one of its older offices. As part of its long-term plan this office will be sold in three years’ time on 31/12/X3. The authority believes that installing the central heating system will make the building easier to sell and add £100 000 to the final selling price. Three systems are regarded as feasible and estimated capital costs of each are set out here:

£

Gas 170 000

Oil 150 000

Solid fuel 140 000

Annual fuel costs are dependent on the severity of the winter each year and the rate of increase in fuel price. At the prices expected to be in force during 19X1 the annual fuel costs are estimated at:

Severe Winter ( £ ) Mild Winter ( £ )

Gas 40 000 24 000

Oil 53 000 37 000

Solid fuel 45 000 36 000

The authority estimates that in each year there is a 70% chance of a severe winter and a 30% chance of a mild winter. The chance of a mild or severe winter in any year in considered to be independent of the chance of a mild or severe winter in the previous year.

Fuel prices are expected during 19X2 and 19X3 to increase by either 8% (probability equal to 0.4) or 10% (probability equal to 0.6%). Whichever rate of increase applies in 19X2 will be repeated the following year. Maintenance costs (payable at the end of year) are expected to be:

£

Gas 2 500

Oil 2 000

Solid fuel 10 000 (in 19X2)

Maintenance costs are fixed.

There is no difference in performance between the systems.

The authority uses the monetary cost of capital as its hurdle rate. This rate is currently 12%.

Which system should be purchased by the authority?

The following solution uses expected value to calculate risk, and expresses project costs in monetary terms, permitting discounting using the monetary cost of capital.

Gas heating

Expected value of fuel costs, based upon the probabilities of a mild (0.3) or severe (0.7) winter:

= (0.7 x £40 000) + (0.3 x £24 000)

= £35 200

Annual fuel costs

8% inflation 10% inflation

Year 12% discount factor Cash flow PV Cash flow PV

£ £ £ £

1 0.893 35 200 31 433 35 200 31 433

2 0.797 38 016 30 298 38 720 30 860

3 0.712 41 057 29 234 42 592 30 326

£90 965 £92 619

Expected value of discounted fuel costs, allowing for probabilities of 8% inflation (0.4) and 10% inflation (0.6): (0.4 x £90 965) + (0.6 x £92 619)

£

Expected value 91 960

Capital costs 170 000

Maintenance (£2 000 per annum for 3 years)

= £2 500 x 2.402 6 005

NPV of gas option £-267 965

Oil heating

Expected value of fuel costs, based upon the probabilities of a mild (0.3) or severe (0.7) winter:

= (0.7 x £53 000) + (0.3 x £37 000)

= 48 200

Annual fuel costs

8% inflation 10% inflation

Year 12% discount factor Cash flow PV Cash flow PV

£ £ £ £

1 0.893 48 200 43 043 48 200 43 043

2 0.797 52 056 41 489 53 020 42 257

3 0.712 56 220 40 029 58 322 41 525

£124 561 £126 825

Expected value of discounted fuel costs, allowing for probabilities of 8% inflation (0.4) and 10% inflation (0.6): (0.4 x £124 561) + (0.6 x £126 825).

£

Expected value 125 920

Capital costs 150 000

Maintenance (£2 000 per annum for 3 years)

= £2 000 x 2.402 4 804

NPV of oil option £280 724

Solid fuel heating

Expected value of fuel costs, based upon the probabilities of a mild (0.3) or severe (0.7) winter:

= (0.7 x £45 000) + (0.3 x £36 000)

= £42 300

Annual fuel costs

8% inflation 10% inflation

Year 12% discount factor Cash flow PV Cash flow PV

£ £ £ £

1 0.893 42 300 37 774 42 300 37 774

2 0.797 45 684 36 410 46 530 37 084

3 0.712 49 339 35 129 51 183 36 442

£109 313 £111 300

Expected value of discounted fuel costs, allowing for probabilities of 8% inflation (0.4) and 10% inflation (0.6): (0.4 x £109 313) + (0.6 x £111 300)

£

Expected value 110 505

Capital costs 140 000

Maintenance (£10 000 in 2 years time)

= £10 000 x 0.797 7 970

NPV of solid fuel option £258 475

Based on these calculations, the solid fuel option has the lowest NPV of costs and on financial grounds would appear to be the favoured option. It also requires less capital investment than the other two options, which may be important if there are severe constraints on capital expenditure.

The main limitations on this type of analysis are that the expected value will never occur and we are ignoring the decision maker’s attitude to risk. A possible alternative would be to attempt to redefine the problem in terms of utility but clearly this is difficult ground to read. A decision must be made and therefore we have to take into account uncertainty whatever decision-making technique is used and there is inevitable compromise. The comparison between the three systems must also take into account both financial and so-called non-financial factors. Selections of these are now set out:

1. How reliable are the estimates of cost, the probabilities of fuel price inflation and the chances of a mild or severe winter.

2. Is there a legal obligation to install a new system?

3. While the increase in the selling price has been ignored since it is common to all three systems the question must arise as to the validity of this assumption due to the possible views of potential buyers.

4. There is no mention of storage problems or extra employees to check deliveries of the appropriate systems.

5. Gas may be an environmentally cleaner fuel.

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