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Help me with practice test questions

1. A project proposal stated that it would provide at least $20,000 in annual returns for the next 3 years but requires an initial investment of $50,000. Will its approval be worthwhile if the cost of capital is 8%?
2. Find the net present value for a project that would yield $25,000, $35,000, $30,000, and $40,000 in the first 4 years of operation if the interest rate is 9.5% and the initial investment is $80,000.
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3 Answers

1. I feel that the Present Value method is best. If the PV of cashflows (including initial investment) is positive, the project is worthwhile.
 
PV = -50,000 + 20,000*1.08^-1 + 20,000*1.08^-2 + 20,000*1.08^-3 = $1,541.94
 
The project is worthwhile.
 
2. PV = -80,000 + 25,000*1.095^-1 + 35,000*1.095^-2 + 30,000*1.095^-3 + 40,000*1.095^-4
    PV = 22,694.02 
1. 20000 each year for 3 years is 60000.  which is a 10000 profit for the project.  but since there is an 8% cost tied in, then 8% of 50000 is 4000.  So it really costs and extra 4000 on top of the 50000 making it 54000.  **I am not sure if the cost of capital is an annual expense or not.  If it is 8% per year, then it's 4000 each year for 3 years making it an extra 12000, coming to a total cost of 62000 and a return of only 60000.
 
Depending on if the cost of capital is annual, they will have either a 6000 profit or a 2000 loss.
 
2. NPV: you take each of the yields and multiply them by (1/1.095)n, where is that particular yields time away from the beginning. 
25,000(1/1.095)1
35,000(1/1.095)2
30,000(1/1.095)3
40,000(1/1.095)4
Add each of your results and don't forget the take off the cost of the initial investment of 80,000.(subtract it)
 
**I got the 1.095 from 1 + 9.5%  = 1+.095 = 1.095
 
Your teacher might be having you use a crappy chart.  If that is the case, it is the same technique but instead use the chart values that correspond to the (1/1.095)n values.  I can't help you with reading the chart since I don't have it in front of me and I don't believe in it.  It gives you a imprecise answer.
 
The present value (PV) formula for a stream of income with annual payments A for n years and annual interest rate i is
 
PV= (A/i) (1 - (1+i)-n)
 
1. PV = 20,000/0.08 (1 - 1.08-3) = 51, 541 > 50,000
Since the present value is greater than the initial investment, the proposal is worthwhile.
 
2. Net present value = present value minus initial investment.
I'll just do the first:
PV = 25,000/0.095 (1-1.095-4) = 80,112, so net PV =80,112-80,000=112