In: Finance
(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 
$ 
3,000 
$ 
3,000 
$ 
6,000 

2 

4,000 
3,000 
6,000 

3 

5,000 
3,000 
(6,000) 

4 

(6,000) 
3,000 
(6,000) 

5 

6,000 
5,000 

16,000 
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?
A  
Discount rate  0.08  
Year  0  1  2  3  4  5 
Cash flow stream  0  3000  4000  5000  6000  6000 
Discounting factor  1  1.08  1.1664  1.259712  1.360489  1.469328 
Discounted cash flows project  0  2777.778  3429.355  3969.161  4410.179  4083.499 
NPV = Sum of discounted cash flows  
NPV A =  9849.61  
Where  
Discounting factor =  (1 + discount rate)^(Corresponding period in years)  
Discounted Cashflow=  Cash flow stream/discounting factor  
B  
Discount rate  0.08  
Year  0  1  2  3  4  5 
Cash flow stream  0  3000  3000  3000  3000  5000 
Discounting factor  1  1.08  1.1664  1.259712  1.360489  1.469328 
Discounted cash flows project  0  2777.778  2572.016  2381.497  2205.0896  3402.916 
NPV = Sum of discounted cash flows  
NPV B =  13339.3  
Where  
Discounting factor =  (1 + discount rate)^(Corresponding period in years)  
Discounted Cashflow=  Cash flow stream/discounting factor  
C  
Discount rate  0.08  
Year  0.00%  1  2  3  4  5 
Cash flow stream  0  6000  6000  6000  6000  16000 
Discounting factor  1  1.08  1.1664  1.259712  1.360489  1.469328 
Discounted cash flows project  0  5555.556  5144.033  4762.99  4410.179  10889.33 
NPV = Sum of discounted cash flows  
NPV C =  12415.75  
Where  
Discounting factor =  (1 + discount rate)^(Corresponding period in years)  
Discounted Cashflow=  Cash flow stream/discounting factor  