Question

In the Chicago mayor's race, candidate A proposes a project that will cost $200,000 today (t=0), $100,000 next year (t=1) and $15,000 to destroy it after ten years of operation (t=12) when the project is discontinued. Once finished in three years (t=3), it will generate a flow of revenue of $40,000 per year until it is discontinued in (t=12) - ie in t=12 the project generates that flow of revenue too.

1. Set the discount rate as r and write the expected present value of the costs and benefits.

2. Calculate the present value of the project if the discount rate is r=.1

3. Candidate B considers that a discount rate r=.3 is more realistic. Calculate the present value of the project with this new discount rate proposed by Candidate B. Why do you think Candidate B has an interest in convincing the public that her discount rate is more realistic?

Answer 1

1.

t	Cash outflow	Cash inflo	Net flow
0	-2,00,000	-	-2,00,000
1	-1,00,000	-	-1,00,000
2		-	-
3		-	-
4		40,000	40,000
5		40,000	40,000
6		40,000	40,000
7		40,000	40,000
8		40,000	40,000
9		40,000	40,000
10		40,000	40,000
11		40,000	40,000
12	-15,000	40,000	25,000
IRR (r )			0.02

2.

t	Cash outflow	Cash inflow	Net flow	Discount factor @ 0.1	Net flow
0	-2,00,000	-	-2,00,000	1.0	-2,00,000
1	-1,00,000	-	-1,00,000	0.91	-90,909
2		-	-	0.83	-
3		-	-	0.75	-
4		40,000	40,000	0.68	27,321
5		40,000	40,000	0.62	24,837
6		40,000	40,000	0.56	22,579
7		40,000	40,000	0.51	20,526
8		40,000	40,000	0.47	18,660
9		40,000	40,000	0.42	16,964
10		40,000	40,000	0.39	15,422
11		40,000	40,000	0.35	14,020
12	-15,000	40,000	25,000	0.32	7,966
Present Value of Cash flow					-1,22,615

3.

t	Cash outflow	Cash inflow	Net flow	Discount factor @ 0.3	Net flow
0	-2,00,000	-	-2,00,000	1.0	-2,00,000
1	-1,00,000	-	-1,00,000	0.77	-76,923
2		-	-	0.59	-
3		-	-	0.46	-
4		40,000	40,000	0.35	14,005
5		40,000	40,000	0.27	10,773
6		40,000	40,000	0.21	8,287
7		40,000	40,000	0.16	6,375
8		40,000	40,000	0.12	4,904
9		40,000	40,000	0.09	3,772
10		40,000	40,000	0.07	2,902
11		40,000	40,000	0.06	2,232
12	-15,000	40,000	25,000	0.04	1,073
Present Value of Cash flow					-2,22,601