Question

For each example, calculate the present value, or net present value, of the future amount(s) to support your answer and show your work using either factors (pp. 219 & 221 in the text), an Excel spreadsheet with the Excel PV or NPV functions or the equations, such as PV = FV / (1+Interest Rate)^Time.

1. Suppose you have a project where you will invest $20,000 today and receive one payment $26,200 exactly 5 years in the future. If your opportunity cost rate (the return you could get on other investments of similar risk) were 5.0% per year, would you approve this project strictly from a financial standpoint, meaning is the PV of the future cash flow greater than the $20,000 initial investment? Explain why.
2. Change the example so that, rather than the $26,200 in in 5 years, you receive $4,600 at the end of each of the next 5 years. You still invest $20,000 at the beginning. What advantage does this offer have, relative to the first one? Would you approve this one? Explain why.
3. One more example. How about if you invest the same $20,000 but this time the offer is to pay you $1,900 per year to you (and your heirs) forever. Would you make that investment?
4. Based on the current unsettled economic conditions, your boss is not sure about the 5% opportunity cost. She wants you to also look at the possibility of a 3% rate and a 7% rate. What effect does changing the rates have on the acceptability of the projects?
5. From these examples, sum up what you have learned about the time value of money. Can you lay out some general rules about how changes in the inputs affect the output?

Answer 1

1. Initial cost=$20,000

Payments= 26200

Tenor= 5

Interest= 5%

Present value= future value/ (1+ interest rate)^time

= 26200/ (1+0.05)^5

=20528.39

As the present value of the future payment is higher than the present cost, he can accept the project.

2. If he receives $4600 for the next 5 years, we will calculate the NPV as the follow:

Year (n)	Cash Flow	working (r= 5%)	Discount factor = 1/(1+r)^n	Discounted cash Flow= Cash flow * discount value
1	4,600	1/ (1+0.05)^1	0.95	$                     4,380.95
2	4,600	1/ (1+0.05)^2	0.91	$                     4,172.34
3	4,600	1/ (1+0.05)^3	0.86	$                     3,973.65
4	4,600	1/ (1+0.05)^4	0.82	$                     3,784.43
5	5,500	1/ (1+0.05)^5	0.78	$                     4,309.39
			Total	$                   20,620.77

Net Present Value = Total Cash Inflows from Investments – Cost of Investments

PV= 20620.77 -20000

NPV= $ 620.77

Here also, the present value of the future payments,$ 20620, is greater than its initial cost. Nut this is a better offer than the above one because, firstly the return is more and here there is a constant inflow of cash which will be beneficial to the project.

3. Here, there is a payment of $1900 forever,

For infinite cash flow, present value = cash flow/ interest rate

= 1900/ 0.05

= 38000

So the present value of this infinite annual payments is $38000. Which is a much higher amount than $20000

They make a profit of $18000.

So he can accept this project.