Question

Question #1: Your company is considering the purchase of either machine A or machine B as shown in the following table: Initial cost Estimated life Salvage value Other costs Machine A $80,000 20 years $20,000 $18,000 per year Machine B $100,000 25 years $25,000 $15,000 per year for the first 15 years $20,000 per year for the next 10 years 1. If the interest rate is 10%, and all cash flows may be treated as end-of-year cash flows. Assume that equivalent annual cost is the value of the constant annuity equal to the total cost of a project. Calculate the equivalent annual cost of machine B. 2. If funds equal to the present worth of the cost of purchasing and using machine A over 20 years were invested at 10% per annum. Calculate the value of the investment at the end of 20 years. 3. How much money would have to be placed in a sinking fund each year to replace machine B at the end of 25 years if the fund yields 10% annual compound interest and if the first cost of the machine is assumed to increase at a 6% annual compound rate? (Assume the salvage value does not change.)

Answer 1

Sol? 1. i= 10%. i= 10%. n= 25 years Az= equivalent annual cost of machines. Present worth of B (pwle= $ 100000 + $15000 (NA,1,15)+ $20000 (PA, 1.10) X Cons)is] 2500 s (pulp = $ 1000+ fisarm Co hen - 2 1.10 - 1 = Pw 1$ = $21409).1926 +$27111.8103 Pule = $241203.co # Annual worth of B AB= pelo (Aſp. 764, 25) . = $241203* [ 0 1 1 25 1 ] Xr0.10X 1-10231 = AB = 26572.87] Any

2 value of investment at end of 20 years i= loy n=20 Fas = $80,000 (Flp, loy.,20) + $18000 (Fla, 104,20) - $20,000 = $8000 X (1-10)?# $18000 (1:02] - $20000 ? A) = $5381 99.9959+ $1030949.991- $20000 > |fra) = $1599149.987 value of investment at end of 20 years fa= $1549149-907