Help me with practice test questions

Question

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.

Answer 1

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 

Answer 2

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.

 

Answer 3

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