Annual Worth Analysis

1
Chapter 6

• Annual Worth Analysis

2
Capitalized Cost (CR)

• Capitalized Cost (CR) is the equivalent annul
  cost of owning the asset plus the return on the
  initial investment.
• CR - P(A/P, i, n) S(A/F, i, n)

3
Example

• For an alternative that has a first cost of
  50,000 and a salvage value of 10,000 after its
  4-year life determine the capital recovery. The
  interest rate is 12 per year. Explain the
  meaning of this capital recovery amount.

4
Solution

• CR - P(A/P, i, n) S(A/F, i, n)
• -50,000(A/P,12,4) 10,000(A/F,12,4)
• -50,000(0.32923) 10,000(0.20923)
• -14,369.20
• Capital recovery is the equivalent annual amount
  that
• must be recovered by the alternative to return
  the initial
• cost and a 12 rate of return over the 4-year
  life.

5
Example (6.23, Page 235)

• A company that manufacturers magnetic membrane
• witches in investigating three production options
  that
• have the estimated cash flows below.
• In-house
  License Contract
• First Cost, -30
  -2 0
• Annual cost, /year -5 -0.2
  -2
• Annual income, /year 14 1.5
  2.5
• Salvage value, 7
  --- ---
• Life, years 10
  8 5
• (a) Determine which option is preferable at an
  interest rate of 15 per year.
• (b) If the options are independent, determine
  which are economically acceptable. (All dollar
  values are in millions.)

6
Solution

• (a) AWIn-house -30(A/P,15,10) 5 14
  7(A/F,15,10)
• -30(0.19925) 5 14
  7(0.04925)
• 3.37 ( millions)
• AWLicense -2(0.15) 0.2 1.5
• 1.0 ( millions)
• AWContract -2 2.5
• 0.5 ( millions)
• Select In-house option.
• (b) All three options are acceptable.

7
Example

• Compare the alternatives shown below on the
• basis of their capitalized costs using an
  interest
• rate 10 per year.
• Alternative V
  Alternative W
• First cost, -50,000
  -500,000
• Annual cost, /year -30,000
  -1,000
• Salvage value, 10,000
  500,000
• Life, years 10
  8

8
Solution

• AWV -50,000 (A/P, 10, 10) 30,000
• 10,000(A/F, 10, 10)
• -50,000(0.16275) -30,000
• 10,000(0.06275)
• -37,510
• CCv -37,510/0.1
• -375,100
• CCW -500,000 -1000/0.1
• -510,000

9
Example

• For the cash flow sequence shown below (in
• thousands), determine the amount of money that
• can be withdrawn annually for an infinite period
• of time, if the first withdrawal is to be made in
• year 10 and the interest rate is 15 per year.
• Year Cash Flow
• 0 60
• 1 50
• 2 40
• 3 30
• 4 20

10
Solution

• P-1 60(P/A, 15,5) 10 (P/G,15,5)
• 60(3.3522) 10(5.7751)
• 143,381
• F9 P-1(F/P, 15,10)
• 143,381(4.0456)
• 580,062
• CC A/i
• A (CC) . (i)
• A 580,000 (0.15)
• A 87,009