Question

You have been offered a unique investment opportunity. If you invest $9,800 ​today, you will receive $490 one year from​ now, $1470 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 5.9% per​ year? Should you take the​ opportunity?

b. What is the NPV of the opportunity if the cost of capital is 1.9% per​ year? Should you take it​ now?

Answer 1

Initail investment at year 0 = $9800

You will rreceive $490 in year 1, $1470 in year 2 and $9800 in year 10

a). Calculating the NPV of the opportunity if the cost of capital is 5.9% per​ year:-

Year	Cash Flow of Investment Opportunity ($) [(a)]	PV Factor @5.9% [(b)]	Present Value of Cash Flow of Investment Opportunity ($) [(a)*(b)]
0	(9,800.00)	1.00000	(9,800.000)
1	490.00	0.94429	462.701
2	1,470.00	0.89168	1,310.767
10	9,800.00	0.56369	5,524.163
			(2,502.37)

NPV of the opportunity is -$2502.37

As the NPV is negative, you should not take this opportunity.

Note- PV [email protected]% can be taken from PVAF Table or calculated using this formula which is = 1/(1+0.059)^n

where, n = Respective year.

For example, PV [email protected]% of 2nd year = 1/(1+0.059)^2 = 1/1.121481 = 0.89168

b). Calculating the NPV of the opportunity if the cost of capital is 1.9% per​ year:-

Year	Cash Flow of Investment Opportunity ($) [(a)]	PV Factor @1.9% [(b)]	Present Value of Cash Flow of Investment Opportunity ($) [(a)*(b)]
0	(9,800.00)	1.00000	(9,800.000)
1	490.00	0.98135	480.864
2	1,470.00	0.96306	1,415.693
10	9,800.00	0.82843	8,118.658
			215.21

NPV of the opportunity is $215.21

As the NPV is Positive, you should take this opportunity now.

Note- PV [email protected]% can be taken from PVAF Table or calculated using this formula which is = 1/(1+0.019)^n

where, n = Respective year.

For example, PV [email protected]% of 2nd year = 1/(1+0.019)^2 = 1/1.038361 = 0.96306

If you need any clarification, you can ask in comments.    

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