Question

In: Finance

​(Present value of an uneven stream of payments​) You are given three investment alternatives to analyze....

​(Present value of an uneven stream of payments​) You are given three investment alternatives to analyze. The cash flows from these three investments are as​ follows:

Investment

End of Year

    A

    B

    C

1

​$

1,000  

​$

1,000

​$

5,000  

2

  

2,000  

1,000

5,000  

3

  

3,000  

1,000

(5,000)

4

  

(4,000)

1,000

(5,000)

5

  

4,000  

5,000

  

15,000  

What is the present value of each of these three investments if the appropriate discount rate is 8 ​percent?

a.  What is the present value of investment A at an annual discount rate of 8 ​percent?

b.  What is the present value of investment B at an annual discount rate of 8 ​percent?

c.  What is the present value of investment C at an annual discount rate of 8 ​percent?

Solutions

Expert Solution

Ans a) 4804.31

b) 6715.04

c) 11480.76

a) Year Project Cash Flows (i) DF@ 8% DF@ 8% (ii) PV of Project A ( (i) * (ii) )
1 1000 1/((1+8%)^1) 0.926                           925.93
2 2000 1/((1+8%)^2) 0.857                       1,714.68
3 3000 1/((1+8%)^3) 0.794                       2,381.50
4 -4000 1/((1+8%)^2) 0.735                      (2,940.12)
5 4000 1/((1+8%)^3) 0.681                       2,722.33
PRESENT VALUE                       4,804.31
b) Year Project Cash Flows (i) DF@ 8% DF@ 8% (ii) PV of Project A ( (i) * (ii) )
1 1000 1/((1+8%)^1) 0.926                           925.93
2 1000 1/((1+8%)^2) 0.857                           857.34
3 1000 1/((1+8%)^3) 0.794                           793.83
4 1000 1/((1+8%)^2) 0.735                           735.03
5 5000 1/((1+8%)^3) 0.681                       3,402.92
PRESENT VALUE                       6,715.04
c) Year Project Cash Flows (i) DF@ 8% DF@ 8% (ii) PV of Project A ( (i) * (ii) )
1 5000 1/((1+8%)^1) 0.926                       4,629.63
2 5000 1/((1+8%)^2) 0.857                       4,286.69
3 -5000 1/((1+8%)^3) 0.794                      (3,969.16)
4 -5000 1/((1+8%)^2) 0.735                      (3,675.15)
5 15000 1/((1+8%)^3) 0.681                     10,208.75
PRESENT VALUE                     11,480.76

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