**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

Formula is:

Solution:

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)

= $68.16

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.

Guidelines

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.

**Will Bolinger**

Alaysha Browning

Matt Cahill

Jason Meyers

Alaysha Browning

Matt Cahill

Jason Meyers

Example

Example

Example

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.