Question

Here are the net cash flows for a project your company is considering:

Year 0 = -1000

Year 1 = 250

Year 2 = 449

Year 3 = 800

Year 4 = 500

Year 5 = 500

If the payback period with interest is 3 years, for what range of interest rates is this project worth doing (start your analysis with an interest rate of 0%)?

** Kindly just don’t directly draw the table with values in it, it’ll be helpful to include explanation of how you get to fill the table . Already I posted this question earlier and noticed that someone had just randomly written someone else’s who has solved the question with no change in word format too.

Answer 1

We use the present worth method

PW (0%) = -1000 + 250(P/F, 0%, 1) + 449(P/F, 0%, 2) + 800(P/F, 0%, 3) + 500(P/F, 0%, 4) + 500(P/F, 0%, 5)

= -1000 + 250*(1 + 0%)^-1 + 449*(1 + 0%)^-2 + 800*(1 + 0%)^-3 + 500*(1 + 0%)^-4 + 500*(1 + 0%)^-5

= 1499

PW (5%) = -1000 + 250*(1 + 5%)^-1 + 449*(1 + 5%)^-2 + 800*(1 + 5%)^-3 + 500*(1 + 5%)^-4 + 500*(1 + 5%)^-5

= 1139.536

PW (10%) = -1000 + 250*(1 + 10%)^-1 + 449*(1 + 10%)^-2 + 800*(1 + 10%)^-3 + 500*(1 + 10%)^-4 + 500*(1 + 10%)^-5

= 851.37

PW (15%) = -1000 + 250*(1 + 15%)^-1 + 449*(1 + 15%)^-2 + 800*(1 + 15%)^-3 + 500*(1 + 15%)^-4 + 500*(1 + 15%)^-5

= 617.38

PW (20%) = -1000 + 250*(1 + 20%)^-1 + 449*(1 + 20%)^-2 + 800*(1 + 20%)^-3 + 500*(1 + 20%)^-4 + 500*(1 + 20%)^-5

= 425.17

PW (30%) = -1000 + 250*(1 + 30%)^-1 + 449*(1 + 30%)^-2 + 800*(1 + 30%)^-3 + 500*(1 + 30%)^-4 + 500*(1 + 30%)^-5

= 131.85

PW (35%) = -1000 + 250*(1 + 35%)^-1 + 449*(1 + 35%)^-2 + 800*(1 + 35%)^-3 + 500*(1 + 35%)^-4 + 500*(1 + 35%)^-5

= 18.74

It then appears that at i = 40%, PW should turn negative

PW (40%) = -1000 + 250*(1 + 40%)^-1 + 449*(1 + 40%)^-2 + 800*(1 + 40%)^-3 + 500*(1 + 40%)^-4 + 500*(1 + 40%)^-5

= -77.68

Now find the i* at which PW = 0

Use interpolation

i*% = 35% + (40% - 35%)*(18.74/(18.74+77.68)) = 35.97%

Hence the relevant range for the interest rate is from 0% to 35.97%.