CHAPTER 5

Mathematics of Individual Finance

[Mathematics of Individual Finance Page 1] [Time Value Of Money][Future Values] [More Frequent Compounding] [Effective Annual Interest Rate] [Present Value]
[Annuities] [Present Value Of An Annuity] [Annuities Due] [Future Value Of An Annuity] [Determining Payments] [Bond Valuation]
[Uneven Cash Flows] [Amortization Schedule] [Household Capital Budgeting] [Duration] [Summary] [Discussion Questions]
[Problems]

Uneven Cash Flows

Bond valuation is an example of taking the present value of uneven cash flows. However, because it is such a frequently done procedure, it is programmed into many calculators. There are many cases in finance where you must value a stream of uneven cash flows. The most basic approach is to treat each cash flow as a future lump sum and value it by dividing by (1 + r) raised to the number of periods before receipt.

You can save time, however, if the cash flows are similar for a consecutive number of times. In this case, they can be treated as an annuity.

Example 5-18

Tom has just taken early retirement at age 55. He will receive $25,000 per year in retirement benefits until he turns 62 and begins receiving Social Security, at which time the pension declines to only $18,000 for 20 years. What is the present value of his pension if he uses a discount rate of 7%?

Solution 5-18

For the next 7 years, until he turns 62, Tom will receive an annuity of $25,000 per year. At 7 percent, the annuity is worth $134,732.23. For the next 20 years, the reduced annuity will be worth $190,692.26, but we can't add the two annuities together since the latter figure is the value in 7 years. Dividing $190,692.26 by 1.077 gives us $190,692.26/1.6058 or $118,753.56. Adding the two streams together gives us $253,485.79.

In LOTUS, the solution would be given by the formula @PV(25000,.07,7)+(@PV(18000,.07,20))/1.07^7.

[Amortization Schedule]

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