Ford Motor Company was able to reduce by 64% the cost required for installing data acquisition instrumentation on test vehicles by using MTS-developed spinning wheel force transducers. The cost this year (.e. end of year 1) is expected to be $2500.

Question

If the costs are expected to increase by $250 each year for the next 4 years, what is the equivalent annual worth of the costs (years 1- 5) at an interest rate of 7% per year?
The equivalent annual worth is $

Answer 1

To calculate the equivalent annual worth of the costs (years 1-5), we need to determine the present value of the costs over that period.

First, we calculate the present value (PV) of the costs in year 1 using the formula:
PV = CF / (1 + r)^n
Where CF is the cash flow in year 1, r is the interest rate, and n is the number of years.

PV1 = $2500 / (1 + 0.07)^1
PV1 = $2500 / 1.07
PV1 ≈ $2336.45

Next, we calculate the present value of the increasing costs in years 2-5 using the same formula. The cash flow for each year is $250, and the number of years increases by 1 each year:

PV2 = $250 / (1 + 0.07)^2
PV2 ≈ $232.48

PV3 = $250 / (1 + 0.07)^3
PV3 ≈ $217.61

PV4 = $250 / (1 + 0.07)^4
PV4 ≈ $203.90

PV5 = $250 / (1 + 0.07)^5
PV5 ≈ $191.15

Finally, we calculate the equivalent annual worth (EAW) of the costs by summing the present values and dividing by the annuity factor of the cash flows over 5 years. The annuity factor can be calculated using the formula:
annuity factor = (1 - (1 + r)^-n) / r

EAW = (PV1 + PV2 + PV3 + PV4 + PV5) / annuity factor
EAW = ($2336.45 + $232.48 + $217.61 + $203.90 + $191.15) / [(1 - (1 + 0.07)^-5) / 0.07]
EAW ≈ $612.73

Therefore, the equivalent annual worth of the costs (years 1-5) at an interest rate of 7% per year is approximately $612.73.