Question

You have been offered a unique investment opportunity. If you invest $9,800 today, you will receive $490 one year from now, $1,470 two years from now, and $9,800 ten years from now.

a. What is the NPV of the opportunity if the cost of capital is 6.9% per year? Should you take the opportunity?

b. What is the NPV of the opportunity if the cost of capital is 2.9% per year? Should you take it now?

Answer 1

Part (a) : NPV at cost of capital 6.9 %

NPV means Net Present Value
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

Present value factor = 1 / (1+r)^n

r - cost of capital = 6.9 %

n - no. of year of the cash flows

Year of cash flows	Cash flows	PVF @6.9 %	Disc. Cash flows
0	$         -9,800.00	1.0000	$         -9,800.00
1	$              490.00	0.9355	$              458.37
2	$          1,470.00	0.8751	$          1,286.36
10	$          9,800.00	0.5131	$          5,028.62
NPV			$         -3,026.65

Npv = - $ 3026.65

NPV < 0 , Opportunity will be rejected.  

Part (b) : NPV at cost of capital 2.9 %

Year of cash flows	Cash flows	PVF @6.9 %	Disc. Cash flows
0	$         -9,800.00	1.0000	$         -9,800.00
1	$              490.00	0.9718	$              476.19
2	$          1,470.00	0.9444	$          1,388.31
10	$          9,800.00	0.7514	$          7,363.30
NPV			$            -572.20

Npv = - $ 572.20

NPV < 0 , Opportunity will be rejected.