These are the forecasts of revenues over the lifetime of a project. Assume all c
ID: 2776934 • Letter: T
Question
These are the forecasts of revenues over the lifetime of a project. Assume all cash flows occur at the end of the year. Yearly expenses from year 1 to year 3: $30 Million Yearly revenues from year 1 to year 3: $0 Yearly expenses from year 4 to year 10: $55 Million Yearly expected revenues from year 4 to year 10: $105 Million The discount rate for the firm is 8.1% for all cash flows (net cash flows from projects, recovered NWC, salvage, etc.). In the first part of this question, you are asked to only calculate the present value of the discounted costs and revenues. What is this value? Part 2 is an annuity of $50 Million a year for 7 years, the first cash flow which will occur at the end of the 4th year, and the last one which will occur at the end of the 10th year. Now position yourself at the end of year 3. You should be able to use the annuity formula for the 7 cash flows which will occur from the end of year 4 to the end of year 10. However, you will have the value at the end of year 3 by using the annuity formula. You will have to use discounting again to find the present value, that is today. Once you have calculated the above, answer would be Part 1- Part 2= Discounted Net Cash Flows from year 4 to year 10- discounted costs from year 1 to year 3.
Explanation / Answer
Part 1
We need to discount all the cash flows to calculate their present value
Year
Revenue
Cost
Cash flow
PV factor 8.1%
PV
1
0
-30
-30
0.9251
-27.75
2
0
-30
-30
0.8558
-25.67
3
0
-30
-30
0.7916
-23.75
4
105
-55
50
0.7323
36.62
5
105
-55
50
0.6774
33.87
6
105
-55
50
0.6267
31.33
7
105
-55
50
0.5797
28.99
8
105
-55
50
0.5363
26.81
9
105
-55
50
0.4961
24.80
10
105
-55
50
0.4589
22.95
128.20
Hence net present value is 128.20 million.
Part 2
N= 7
R= 8.1%
Pmt = 50 million
We have following formula to calculate PV of annuity
PV = Pmt x PVIFA(n,r)
= 50 x PVIFA(7,8.10%)
= 50 x 5.1886
=259.43 million
This is the present value at the end of third year. We need to discount it further 3 years to get it’s present value:
PV = FV/ (1+r)^n
= 259.43 / (1+0.081)^3
= 205.37
Year
Revenue
Cost
Cash flow
PV factor 8.1%
PV
1
0
-30
-30
0.9251
-27.75
2
0
-30
-30
0.8558
-25.67
3
0
-30
-30
0.7916
-23.75
4
105
-55
50
0.7323
36.62
5
105
-55
50
0.6774
33.87
6
105
-55
50
0.6267
31.33
7
105
-55
50
0.5797
28.99
8
105
-55
50
0.5363
26.81
9
105
-55
50
0.4961
24.80
10
105
-55
50
0.4589
22.95
128.20
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