Question

1. You have plenty of cash to invest. You are considering an investment of $125,000 in a project which is expected to earn $14425 a year for ten years. Is it an attractive investment if your minimum expected annual rate of return is 5% (compound interest)? Calculate the expected annual rate of return (R) of the project. (6 points) NO TABLE

Answer 1

The project is attractive if the NPV of the project is positive at 5%

NPV = -125000 + 14425/1.05 + 14425/1.05^2 + ... + 14425/1.05^10

= -125000 + 14425/0.05* (1-1/1.05^10)

= - 13613.97

As the NPV is -$13613.97, the project is not attractive

The expected annual rate of return of the project (R) is the rate at which NPV = 0

=>  -125000 + 14425/1.05 + 14425/1.05^2 + ... + 14425/1.05^10 = 0

=> -125000 + 14425/R* (1-1/(1+R)^10) = 0

Using hit and trial method

If R = 0.04 , Left hand side of equation = -125000 + 14425/0.04* (1-1/1.04^10) = -8000.33

If R = 0.03 , Left hand side of equation = -125000 + 14425/0.03* (1-1/1.03^10) = -1951.82

If R = 0.02 , Left hand side of equation = -125000 + 14425/0.02* (1-1/1.02^10) = 4573.79

If R = 0.025 , Left hand side of equation = -125000 + 14425/0.025* (1-1/1.025^10) = 1248.52

So, somewhere between r =0.025 and r = 0.03, NPV = 0

Using Linear approximation

R = 0.025 + (1248.52-0)/(1248.52- (-1951.82))* (0.03-0.025) =0.02695 or 2.695%

If R = 0.02695 , Left hand side of equation = -125000 + 14425/0.02695* (1-1/1.02695^10) = -14.15

If R = 0.0269 , Left hand side of equation = -125000 + 14425/0.0269* (1-1/1.0269^10) = 17.99

Using Linear approximation

R = 0.0269 + (17.99-0)/(17.99- (-14.15))* (0.02695-0.0269) =0.026928 or 2.6928%

Expected Annual Rate of return of the project is 2.69% (rounded off to two decimal place)