Title 96 Capitalized Cost, Annual Cost, and BC Ratio.pdf ✅

MSTC 95: Capitalized Cost, Annual Cost, and B-C Ratio 1. Present Worth and Equivalent Annual Cost (EAC) The total present worth of a property is the sum of all present values. The lifespan may or may not be indefinite. The following formulas may be useful. P = F (1 + i) n (Present value of a single payment at year n) P = A[(1 + i) n − 1] i(1 + i) n (Present value of an annuity starting from year 1) P = A i (Present value of perpetuity starting from year 1) P = A (1 + i) n − 1 ( Present value of perpetuity starting from year n and skipping by n years ) The equivalent annual cost is the annuity with the same present value as the original payment structure. For example, Calculate the annual cost for a highway project with the following benefits and costs. The project life is 40 years, the interest rate is 10 %, and the project’s right of way is worth PHP 5 M in 40 years. Construction cost = PHP 20 M (includes R.O.W.) Annual maintenance = PHP 350 K Repaving every 8 years = PHP 3 M Annual lives saved = PHP 1 M (1 life per year) Time savings for commercial traffic = PHP 1.25 M Time savings for recreational traffic = PHP 1 M Drawing the cash flow diagram, Finding the annual cost, Present value = 20M + 350K(1.1 40 − 1) 0.1(1.1 40) + 3M(1.1 8(4) − 1) (1.1 8 − 1)(1.1 32) − 5 M 1.1 40 = PHP 25.811 M EAC = 25.811M(1.1 40)(0.1) 1.1 40 − 1 = PHP 2. 639 M