Question

Part B: New Location

1. Rhonda has found a location for the next store she plans to open. The store front will require $30,000 in renovations before it is ready to open. She would like the initial investment to be paid off in 5 years. Assuming a discount rate of 4.5%, what will her annual profits for the store need to be if she wishes to recover the $30,000 in 5 years (assuming equal profits each year)?
2. What if the discount rate increased to 7.75%? What would her annual profits need to be to recover the $30,000 in 5 years?

If Rhonda expects profits from the new location in Part B to be $7,250 annually, should she open the new location? First, if the discount rate is 4.5%? Then, if the discount rate is 7.75%?

Please show your work so I can understand how you get to the answers.  

Thank you!

Answer 1

Rhonda aims at recovering the initial investment of $ 30000 in 5 years time. This implies that the present value of the annual profits over the 5 years of the project should sum up to equal the initial investment, thereby giving an NPV of zero.

Discount Rate = 4.5 % and let the annual profits be $ P

Therefore, 30000 = P x (1/0.045) x [1-{1/(1.045)^(5)}] = P x 4.3899767

P = 30000 / 4.3899767 = $ 6833.7492 ~ $ 6833.75

New Discount rate = 7.75 % and the new required profit be P'

Therefore, 30000 = P' x (1/0.0775) x [1-{1/(1.0775)^(5)}] = P' x 4.0191572

P' = 30000 / 4.0191572 = $ 7464.25

Now if Expected profit is $ 7250, then Rhonda should take up the project when the discount rate is 4.5 % as the required minimum profit in that case is lower at $ 6833.75 as compared to the expected profit of $ 7250

However, a discount rate of 7.75% requires a minimum profit of $ 7464.25, therby impliying that the expected profit of $ 7250 will not be sufficient to recoup Rhonda's initial investment of $ 30000 in 5 years. Hence, Rhonda should take up the project when the discount rate is 4.5 % but not when it is 7.75 %.