Question

Consider the following project regarding the building of a large bridge between two major cities. The bridge will involve a ‘toll’ or monetary charge, where users of the bridge will pay an amount of money each time that they cross over the bridge.

The current date is 1 January 2019. The bridge is expected to take 2 years to build, and the first paid crossing of the bridge will occur in exactly 2 years from now.

The costs of the project are as follows:

Building costs

1 January 2019: $5 million

1 July 2019: $15 million

1 January 2020: $17.5 million

1 July 2020: $8 million

1 January 2021: $100,000

Maintenance and ongoing costs

Painting and repairs of $125,000 every quarter (ongoing), with the first cost incurred on 31 March 2021, and increasing by 1% every quarter thereafter

Road resealing: This occurs every 18 months with the first resealing occurring on 30 June 2022. The cost is $1.1m each time, increasing by 10% every 18 months.

Ongoing administration and staff costs: Assumed to be incurred monthly, of $75,000 per month with the first cost incurred on 1 February 2019, increasing by 2.5% (effective) every 12 months.

Income

The income from the monetary charges that apply to each bridge crossing is given by the following:

Cost per crossing: $2.80 per crossing over the bridge. This cost will apply throughout 2021. Every year thereafter, the cost increase by 5 cents per crossing.

Usage of the bridge

In 2021, it is anticipated that there will be 2 million crossings over the bridge over the year. This number of crossings is expected to increase by 7% per year, at the end of each year. Use of the bridge is not constant each month, but occurs in relation to the following breakdown per month:

Month	% of total annual bridge crossings that occur in this month
January	5%
February	12%
March	12%
April	9%
May	8%
June	7%
July	3%
August	8%
September	10%
October	12%
November	10%
December	4%

It can also be assumed that the income for each month, is earned on average half way through each month.

1. Assuming a time horizon of 20 years for this project, determine the Internal Rate of Return.
2. Assuming a time horizon of 20 years for this project, determine the PV of costs at a risk discount rate of 10% per annum (effective)
3. Assuming a time horizon of 20 years for this project, determine the PV of income at a risk discount rate of 10% per annum (effective)
4. Hence, using your answers to (b) and (c), determine the NPV of this project at a risk discount rate of 10% per annum (effective)

Answer 1

a)	IRR	17.01%
b)	Total Project Cost	($41.2 Mn + $19.80 Mn) = $61.04 Mn
c)	Total Income	$103.63 Mn
d)	NPV (c-d)	($103.63 Mn - $61.04 Mn)= $42.58 Mn

Workings	Total	D/f	Discouting
1 January 2019: $5 million	$5.0	1	$5.0
1 July 2019: $15 million	$15.0	0.909	$13.6
1 January 2020: $17.5 million	$17.5	0.909	$15.9
1 July 2020: $8 million	$8.0	0.826	$6.6
1 January 2021: $100,000	$0.1	0.826	$0.1
Project Cash Outflow			$41.2

Road Resealing	$1.1Million	Every 18 months		No of road sealings		13.33333333
Term	6/30/2022	12/31/2023	6/30/2025	12/31/2026	6/30/2028	12/31/2029	6/30/2031	12/31/2032	6/30/2034	12/31/2035	6/30/2037	12/31/2038	6/30/2040	Total
Total Cost	1.10	1.21	1.33	1.46	1.61	1.77	1.95	2.14	2.36	2.59	2.85	3.14	3.45	26.97

Income		2021	2022	2023	2024	2025	2026	2027	2028	2029	2030	2031	2032	2033	2034	2035	2036	2037	2038	2039	2040
Term		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	Total
Crossings	A	2.00	2.14	2.29	2.45	2.62	2.81	3.00	3.21	3.44	3.68	3.93	4.21	4.50	4.82	5.16	5.52	5.90	6.32	6.76	7.23	$81.99
Cost per Crossing	B	$2.80	$2.94	$3.09	$3.24	$3.40	$3.57	$3.75	$3.94	$4.14	$4.34	$4.56	$4.79	$5.03	$5.28	$5.54	$5.82	$6.11	$6.42	$6.74	$7.08	$92.58
Income / Mn	C	$5.60	$6.29	$7.07	$7.94	$8.92	$10.02	$11.26	$12.65	$14.22	$15.97	$17.94	$20.16	$22.65	$25.45	$28.59	$32.12	$36.09	$40.54	$45.55	$51.18	$420.22
Painting cost	D	$507,550	$528,159	$549,604	$571,920	$595,142	$619,308	$644,454	$670,621	$697,851	$726,187	$755,673	$786,356	$818,286	$851,511	$886,086	$922,065	$959,504	$998,464	$1,039,006	$1,081,193
Painting cost in Mn	E	$0.51	$0.53	$0.55	$0.57	$0.60	$0.62	$0.64	$0.67	$0.70	$0.73	$0.76	$0.79	$0.82	$0.85	$0.89	$0.92	$0.96	$1.00	$1.04	$1.08	$15.21
Road Reselling Cost	F		$1.10	$1.21		$1.33	$1.46		$1.61	$1.77		$1.95	$2.14		$2.36	$2.59		$2.85	$3.14		$3.45	$26.97
Administrative Cost	G	$0.83	$0.92	$0.95	$0.97	$0.99	$1.02	$1.04	$1.07	$1.10	$1.12	$1.15	$1.18	$1.21	$1.24	$1.27	$1.30	$1.34	$1.37	$1.40	$1.44	$22.92
Discounting Factor @ 10%	H	0.751	0.683	0.621	0.564	0.513	0.467	0.424	0.386	0.350	0.319	0.290	0.263	0.239	0.218	0.198	0.180	0.164	0.149	0.135	0.123	$7.04
b) Total Cost Discounted	I = (E + F + G) * H	$1.00	$1.74	$1.68	$0.87	$1.50	$1.45	$0.72	$1.29	$1.25	$0.59	$1.12	$1.08	$0.49	$0.97	$0.94	$0.40	$0.84	$0.82	$0.33	$0.73	$19.80
c) Total Income Discounted	J = (C * H)	$4.21	$4.30	$4.39	$4.48	$4.58	$4.68	$4.78	$4.88	$4.98	$5.09	$5.20	$5.31	$5.42	$5.54	$5.66	$5.78	$5.90	$6.03	$6.16	$6.29	$103.63