A garage is comparing the cost of buying two different car hoists. Hoist A will cost $20 000, will require servicing of $1 000 every two years, and last ten years. Hoist B will cost $15 000, require servicing of $800 per year, and last eight years. If the cost of capital is 7%, which is the better option, given that the firm has an ongoing requirement for a hoist?
A)Hoist B, since it has a greater present value (PV).
B)Hoist B, since it has a greater equivalent annual annuity.
C)Hoist A, since it has a greater equivalent annual annuity.
D)Hoist A, since it has a greater present value (PV).

Question

Quizplus · Accepted Answer

To determine the better option, we need to calculate the present value of the total cost for each hoist, and then calculate the equivalent annual annuity (EAA) for each.

For Hoist A: 
- Initial cost = $20,000 
- Servicing cost every 2 years = $1,000, so the total servicing cost over 10 years is: $1,000 x 5 = $5,000 
- Total cost = $20,000 + $5,000 = $25,000 
- Present value at 7% = $25,000 / (1 + 0.07)^1 + $5,000 / (1 + 0.07)^3 = $25,000 / 1.07 + $5,000 / 1.225 = $22,429.91 
- EAA = $22,429.91 / annuity factor for 10 years at 7% = $3,574.53

For Hoist B: 
- Initial cost = $15,000 
- Annual servicing cost = $800 x 8 = $6,400 
- Total cost = $15,000 + $6,400 = $21,400 
- Present value at 7% = $21,400 / (1 + 0.07)^1 = $19,999.07 
- EAA = $19,999.07 / annuity factor for 8 years at 7% = $3,645.81

Since Hoist B has the higher EAA, it is the better option. Option B is correct.

A Garage Is Comparing the Cost of Buying Two Different