Question

The Western Railway Company (WRC) has been offered a 50-year contract to haul a fixed amount of coal each year from Wyoming to Illinois. Under the terms of the agreement, WRC will receive $2,800,000 now in exchange for its hauling services valued at $380,000 per year through end of year 50. If Western Railway Company’s cost of capital is 15% per year is this a profitable agreement for WRC?

A) Draw the Cash Flow Diagram

B) Calculate the answer

C) What is the minimum equivalent uniform for this contract?

Answer 1

Annual revenue A = $380000

R = 15%

Time, t = 50 years

Year	Value of service	Present Value of corresponding amount at i=15%	Remarks
1	380000	3,30,434.78	380000*1((1+.15)^1)
2	380000	2,87,334.59	380000*1((1+.15)^2)
3	380000	2,49,856.17	380000*1((1+.15)^3)
4	380000	2,17,266.23	380000*1((1+.15)^4)
5	380000	1,88,927.16	Formula continues
6	380000	1,64,284.49
7	380000	1,42,856.08
8	380000	1,24,222.67
9	380000	1,08,019.72
10	380000	93,930.19
11	380000	81,678.42
12	380000	71,024.72
13	380000	61,760.62
14	380000	53,704.89
15	380000	46,699.90
16	380000	40,608.61
17	380000	35,311.84
18	380000	30,705.95
19	380000	26,700.82
20	380000	23,218.11
21	380000	20,189.66
22	380000	17,556.22
23	380000	15,266.28
24	380000	13,275.03
25	380000	11,543.50
26	380000	10,037.83
27	380000	8,728.55
28	380000	7,590.04
29	380000	6,600.03
30	380000	5,739.16
31	380000	4,990.57
32	380000	4,339.63
33	380000	3,773.59
34	380000	3,281.38
35	380000	2,853.38
36	380000	2,481.20
37	380000	2,157.56
38	380000	1,876.14
39	380000	1,631.43
40	380000	1,418.63
41	380000	1,233.59
42	380000	1,072.69
43	380000	932.77
44	380000	811.11
45	380000	705.31
46	380000	613.31
47	380000	533.32
48	380000	463.75
49	380000	403.26
50	380000	350.66
	Total PV for 50 yrs	25,30,995.57
	Amount received today	28,00,000.00
	profit	2,69,004.43

Since the lump-sum payment of $2800000 is more than the $2530995.57, then it is a profitable agreement. WRC should receive $2800000.

Let, minimum equivalent amount = P

Then, 2800000 = P*(1- 1/1.15^50)/.15

2800000 = P*6.6604

P = 2800000/6.6604

P = $420395 approx.

So, annual value for 50 years should be $420395 approx

Assuming WRC receives 2800000 now spends 380000 for next 50 years cash flow will be