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Present Worth Method
Transcript of Present Worth Method
Problem: A parent wishes to establish a college account for a newborn child. The parent estimates the education will cost $40,000 18 years from now. If the interest rate on the account is guaranteed at 8 percent indefinitely, how much must be invested today to have $40,000 on the child's 18th birthday?
Solution: Here, Fn = $40,000 i = 0.08, and n = 18
Material A: PV = $2M / (1.10)^15 = $2M (0.2394) = $478,800
Material B: PV = $2.8M (0.1228) = $343,840
Material B is least cost. Replacement cost is less than material A.
Problem: An installation needs to reroof a large building. Roof material A will last 15 years and cost $2M to replace at that time. Material B will last 22 years with a replacement cost of $2.8M. An interest rate of 10 percent is used to compare the materials. Which is the least cost with respect to replacement cost?
Investment Cost $5000
Annual Receipts 1,300
Annual Expenses 350
Expected Life 8 yrs
If your MARR is 10%, is this project profitable?
To find the PW at the MARR, we need to find the present equivalent of all the cash flows involved:
PW(MARR) = -$5000 + (1,300 - 350)(P/A,MARR, 8)
PW(10%)= -$5000 + 950(P/A, 10%, 8)
= -$5000 + 950 (5.3349)
Since PW(10%) > 0, the project is profitable.
Explanation for same life-alternatives
Present worth analysis is calculated at the MARR for each alternative. It is used to convert future cash flows into the present.
One alternative: calculate PW at the MARR, if PW ≥ 0, it is a viable option.
Two alternatives: calculate the PW of each at the MARR, select the alternative with the PW value that is less negative or more positive.
Explanation for different - life alternatives
If same life alternatives are not present, shorter-lived alternatives will be favored based on lower, PW of total costs.
Two ways to use PW analysis : (1) evaluate over a specific study period (2) use the least common multiple of lives for each pair of alternatives.
In both these cases, the PW is calculated at the MARR, and the selection guidelines are applied.