Mathematics of finance

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...problem. The factors to be taken into account are: (1) The values of old and new machines, (2) the annual operating expenses of both machines for their lifetimes, not including repairs, (3) the annuities sufficient to accumulate funds for repairs, (4) the number of units of output of each machine. Let C = the first cost of new machine, N = lifetime of new machine, F = annual rent of annuity to amortize C in N years, 0 = annual operating expense of new machine exclud-ing repairs, R = annual rent of annuity for repairs on machine, Y = number of units of output per year. Let the corresponding lower case letters /, o, r, and y denote the corresponding quantities for the old machine, and let c be the value of the old machine at the time of making the valuation, and n the remaining lifetime of the old machine. Let i be the rate of interest. Then the cost per unit output of the new machine is 0 + R + F+Ci Y and of the old machine o + r + / + Ct. y From the basic principle that unit cost is to be the same for the two machines, we have O + R + F + Ci = o + r + f+ ci (8) Y y The annuity of annual rent F necessary to accumulate to C in N years is given by F = CX, (9) UNIT COST METHOD 121 When we have not only Y = y, but the annual operating expense equal so that 0--o, then (16) If when Y = y, we have 0 + R = o + r, then from (15), = Ccg (17) PROBLEMS 1. A machine with a remaining service life of 5 years turns out 20 units of work per year. Its operation costs $250 per year, and repairs $200 per year. A new machine that turns out 25 units costs $1200. It has a probable life of 12 years, will cost $300 per year for operation and $200 for repairs. Find the value of the old machine on the basis cf interest at 5 per cent. Solution: C = $1200, N = 12, 0 = $300, R = $200, Y ...