Question

Question 7 +250 The government of UK government is considering a series of toll roads which will be operated by companies in the private sector. Contracts to run the toll roads will be for five years at which time contracts will be put out to competitive tender again. As the finance director of Oval ple, a transport operator, you are interested in bidding for one of the first series of contracts. It is anticipated that you will need to pay the UK government an initial fee of $100m to acquire the right to operate the toll road plus an annual fee of $10m payable at the end of year 1, increasing by 10% per year thereafter. In addition, the government will take 20% of all revenues generated by the toll road. Operating costs to monitor traffic and collect tolls are expected to be $20m in year 1 and will increase by 5% per year. Based on current estimates of usage, there will be 112 million miles of vehicle travel per year for each of the five years. The UK government will allow Oval plc to set a toll fee which will be based on the number of miles a vehicle travels on the toll road. Once set, the toll per mile will remain constant for the duration of the contract. Given the risk profile of this project, the company will require a return of 12%. Assume all cash flows, apart from the initial fee, will occur at the end of each year concerned. Ignore taxation. Required: What is the minimum toll fee per mile you would be prepared to charge? (10 marks) (b) Assume the UK government is prepared to accept an alternative to the initial fee of $100m. The alternative is to pay five equal annual instalments to the government commencing immediately. What is the maximum Oval ple should be prepared to pay per year to avoid the initial $100m fee? (5 marks) (c) Assume that the government now states that the toll charge must fall by 5% per year from the end of year 1. How would this affect your recommendation in part (a) above? Show the appropriate calculation. (10 marks) All calculations should be expressed in millions and rounded to two decimal places.

Answer 1

1.

Year	Fees	Operating Costs	Total	Discount factor @ 12%	Discounted cashflow
0	(100,000,000.00)		(100,000,000.00)	1.0000	(100,000,000.00)
1	(10,000,000.00)	(20,000,000.00)	(30,000,000.00)	0.8929	(26,785,714.29)
2	(11,000,000.00)	(21,000,000.00)	(32,000,000.00)	0.7972	(25,510,204.08)
3	(12,100,000.00)	(22,050,000.00)	(34,150,000.00)	0.7118	(24,307,295.46)
4	(13,310,000.00)	(23,152,500.00)	(36,462,500.00)	0.6355	(23,172,577.93)
5	(14,641,000.00)	(24,310,125.00)	(38,951,125.00)	0.5674	(22,101,914.39)
				Total	(221,877,706.15)

Let the toll fee per mile be X,

We know that, 20% revenue goes to govt. So since Oval plc requires 12% returns,

ie, 0.8X * (12% for 5 years ie, 3.605) = 221877706.15. So, X = 76,938,793.73.

So, Per mile => 76938793.73/112000000 = 0.6870 or 0.69 $.

2.

Year	Fees	Operating Costs	Total	Discount factor @ 12%	Discounted cashflow
0	(20,000,000.00)		(20,000,000.00)	1.0000	(20,000,000.00)
1	10000000+20000000 = (30,000,000.00)	(20,000,000.00)	(50,000,000.00)	0.8929	(44,642,857.14)
2	11000000+20000000 = (31,000,000.00)	(21,000,000.00)	(52,000,000.00)	0.7972	(41,454,081.63)
3	(32,100,000.00)	(22,050,000.00)	(54,150,000.00)	0.7118	(38,542,900.42)
4	(33,310,000.00)	(23,152,500.00)	(56,462,500.00)	0.6355	(35,882,939.50)
5	(14,641,000.00)	(24,310,125.00)	(38,951,125.00)	0.5674	(22,101,914.39)
				Total	(202,624,693.08)

So, now

0.8X * (12% for 5 years ie, 3.605) = 202624693.08 . So, X = 70262577.24

So, Per mile => 70262577.24/112000000 = 0.6273 or 0.63 $.

3.

Since reduction of toll charges by 5% every year, we collect equivalent toll charges as follows;

1	1
2	1*95% = 0.9500
3	0.95*95% = 0.9025
4	0.9025*95% = 0.8574
5	0.8574*95% = 0.8145
Total	4.5244 years

So, to get 12% returns we have to icnrease the toll charges per mile. ie,

0.6870 $ * 5 years / 4.5244 years => 0.7592 or 0.76 $ per mile.

(please comment in case of any query regarding the solution)