Question

You can purchase an optical scanner today for $460. The scanner provides benefits worth $80 a year. The expected life of the scanner is 10 years. Scanners are expected to decrease in price by 20% per year. Suppose the discount rate is 14%. When is the best time to purchase the scanner? (Round your answer to the nearest cent.)

                    

NPV is maximized when you wait  (Click to select)  0  1  2  3  4  6  5  7  8  9  10  years to purchase the scanner. At this date NPV will be equivalent to $---- today.

Answer 1

Solution :

It is given that the price of optical scanner is $460 today and it will decrease by 20% every year means 80% of previous year .

Hence price will be 80% *460 = 368 in year 1, 368*0.8 = 294.4 in year 2, 294.4*0.8 = 235.52 in year 3 and so on till year 10.

Cash flow is $80 every year and discount rate is 14%.

In order to find the best year to purchase the scanner , we need to find 10 NPV and select the best one. NPV is calculated. The calculation is done in below Excel and the maximum NPV is -3.96 and it is in year 3. Means we need to wait 3 years to purchase and NPV is -3.96

L10 0.8 N11 N B M Discounted CF 1 CF 24 -460.00 2 5 8 -460 6 10 0 1 4 7 3 9 70.18 B3/1.14 A3 61.56 B4/1.14^A4 54.00 B5/1.14 A5 -368.00 80 294.40 E3*0.8 80 2 61.56 5 80 235,52 F4*0.8 54.00 3 54.00 47.37-B6/1.14 A6 6 47.37 47.37 4 80 -188.42-G5 0.8 47.37 41.55B7/1.14^A7 36.45B8/1.14 A8 41.55 -150.73 | H6*0.8 5 80 41.55 41.55 41.55 120.5917 0.8 31.97-96.478 0.8 36.45 6 80 36.45 36.45 36.45 36.45 9 31.97 B9/1.14A9 28.04 B10/1.14 A10 24.60 B11/1.14^A11 21.58 B12/1.14^ A12 -42.71 -SUM(C2:C12) 7 31.97 31.97 31.97 80 31.97 31.97 -77.18- K9 0.8 24.60 61.74 L10 0.8 28.04 28.04 28.04 28.04 10 8 80 28.04 28.04 28.04 24.60 24.60 80 24.60 24.60 24.60 11 24.60 24.60 21.58 .-8.84 3.96 21.58 21.58 21.58 21.58 21.58 -27.81 12 10 80 21.58 21.58 21.58 13 Stanme -22.24 -14.39 -4.22 -8.09 -31.00 -40.16 -27.81 -20.89 14 CamS.canner 15 16