Question

Consider a proposal to invest $8.55 million into a stretch of wild river preservation in Wyoming. The project would require periodic capital expenditures as well as annual maintenance expenditures. Benefits from river restoration range from current recreational use to flood prevention to potential future fishing and floating benefits as well as societal benefits from knowing wild stretches of river exist and will be passed on to future generations. Following current best practices for benefit estimation, the following set of costs and benefits are reported for the project.

Year	Time Period	Capital Costs	Maintenance Costs	Recreation Benefits	Flood Prevention Benefits	Reserve the right to fish the river benefits	Reserve the right to float the river benefits	Benefits from knowledge the stretch of river system is preserved	Benefits from leaving preserved river system to future generations
1	0	$550,000	$50,000	$5,000	$75,000	$80,000	$45,000	$175,000	$85,000
2	1	$550,000	$75,000	$7,500	$75,000	$82,500	$46,000	$180,000	$87,500
3	2	$0	$100,000	$10,000	$75,000	$85,000	$47,000	$185,000	$90,000
4	3	$0	$125,000	$12,500	$75,000	$87,500	$48,000	$190,000	$92,500
5	4	$0	$150,000	$15,000	$75,000	$90,000	$49,000	$195,000	$95,000
6	5	$350,000	$175,000	$17,500	$75,000	$92,500	$50,000	$200,000	$97,500
7	6	$350,000	$200,000	$20,000	$125,000	$95,000	$51,000	$205,000	$100,000
8	7	$0	$225,000	$20,000	$125,000	$97,500	$52,000	$210,000	$102,500
9	8	$0	$250,000	$20,000	$125,000	$100,000	$53,000	$215,000	$105,000
10	9	$0	$275,000	$20,000	$125,000	$102,500	$54,000	$220,000	$107,500
11	10	$250,000	$300,000	$20,000	$125,000	$105,000	$55,000	$225,000	$110,000
12	11	$250,000	$325,000	$20,000	$125,000	$107,500	$56,000	$230,000	$112,500
13	12	$0	$350,000	$30,000	$125,000	$110,000	$57,000	$235,000	$115,000
14	13	$0	$375,000	$30,000	$125,000	$112,500	$58,000	$240,000	$117,500
15	14	$0	$400,000	$30,000	$175,000	$115,000	$59,000	$245,000	$120,000
16	15	$250,000	$425,000	$30,000	$175,000	$117,500	$60,000	$250,000	$122,500
17	16	$250,000	$450,000	$30,000	$175,000	$120,000	$61,000	$255,000	$125,000
18	17	$0	$475,000	$30,000	$175,000	$122,500	$62,000	$260,000	$127,500
19	18	$0	$500,000	$50,000	$175,000	$125,000	$63,000	$265,000	$130,000
20	19	$0	$525,000	$50,000	$175,000	$127,500	$64,000	$270,000	$132,500

Assume the discount rate is 8%. Complete the following table using only "use" values (First 4 Benefit columns)

1. Discounted present value of net benefits

2. Discounted present value of costs

3. Discounted present value of benefits

4. Benefit-Cost Ratio

Answer 1

Year	Time Period	Total benefits	Present worth of the benefits	Total costs	Present worth of the costs	Net Benefits	Present value of net benefits
1	0	$465,000	$465,000	$600,000	$600,000	($135,000)	($135,000)
2	1	$478,500	$443,056	$625,000	$578,704	($146,500)	($135,648)
3	2	$492,000	$421,811	$100,000	$85,734	$392,000	$336,077
4	3	$505,500	$401,282	$125,000	$99,229	$380,500	$302,053
5	4	$519,000	$381,480	$150,000	$110,254	$369,000	$271,226
6	5	$532,500	$362,411	$525,000	$357,306	$7,500	$5,104
7	6	$596,000	$375,581	$550,000	$346,593	$46,000	$28,988
8	7	$607,000	$354,179	$225,000	$131,285	$382,000	$222,893
9	8	$618,000	$333,886	$250,000	$135,067	$368,000	$198,819
10	9	$629,000	$314,657	$275,000	$137,568	$354,000	$177,088
11	10	$640,000	$296,444	$550,000	$254,756	$90,000	$41,687
12	11	$651,000	$279,203	$575,000	$246,608	$76,000	$32,595
13	12	$672,000	$266,860	$350,000	$138,990	$322,000	$127,871
14	13	$683,000	$251,138	$375,000	$137,887	$308,000	$113,251
15	14	$744,000	$253,303	$400,000	$136,184	$344,000	$117,119
16	15	$755,000	$238,007	$675,000	$212,788	$80,000	$25,219
17	16	$766,000	$223,588	$700,000	$204,323	$66,000	$19,265
18	17	$777,000	$209,999	$475,000	$128,378	$302,000	$81,621
19	18	$808,000	$202,201	$500,000	$125,125	$308,000	$77,077
20	19	$819,000	$189,772	$525,000	$121,649	$294,000	$68,123
Total		$6,263,858		$4,288,429		$1,975,429

As we can see from the above table, the total costs, total benefits and net benefits have been calculated for the respective years.

Total benefits = sum of all benefits for the respective year

Total costs = sum of all costs for the respective year

Net benefits = sum of all benefits for the respective year - sum of all costs for the respective year

1.

Discounted present value of net benefits = sum of all entries in the present value of net benefits coloumn

Present value of net benefits = net benefits for the respective year / (1+0.08)^{time period}

Therefore, from the above table, we can see that Discounted present value of net benefits = $1,975,429

2.

Discounted present value of costs = sum of all entries in the present value of total costs coloumn

Present value of costs = total costs for the respective year / (1+0.08)^{time period}

Therefore, from the above table, we can see that Discounted present value of costs = $4,288,429

3.

Discounted present value of benefits = sum of all entries in the present value of total benefits coloumn

Present value of benefits = total benefits for the respective year / (1+0.08)^{time period}

Therefore, from the above table, we can see that Discounted present value of benefits= $6,263,858

4.

The benefit cost ratio is calculated by dividing the present value of the total benefits by that of total costs.

Therefore, BCR = present value of total benefits / present value of total costs

= $6,263,858 / $4,288,429

= 1.46