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]

Household Capital Budgeting

Financial mathematics is very useful to corporations for capital budgeting. In general, an investment is worthwhile if it has a net present value greater than zero. The tools of capital budget are equally useful to the household. Two types of common household decisions relate to non-human and human capital investments.

Example 5-20

Laura spends $5 per week at the laundramat. She can purchase a washer and dryer for a total of $800 and expects that they will last for 10 years. Ignoring her costs for utilities and repairs as well as the time she could save and inflation, what is the net present value of the investment if we use a discount rate of 8%?

Solution 5-20

Laura spends 52 times $5 = $260 per year at the laundramat. The present value of $260 per year for 10 years at 8% is $1,744.62. This exceeds the present value of the capital expenditure of $800 by $944.62 which is the net present value. Laura should buy the washer and dryer.

Example 5-21

Glenda is a 34 year old nurse earning $35,000 per year. She is thinking of taking an MBA degree in health systems management which would enable her to become a hospital administrator and earn $5,000 more per year than she is earning now, in today's dollars. The MBA requires 2 years of full time work and costs $30,000 per year. Using an inflation rate of 6% and a discount rate of 8%, is the MBA financially worthwhile if she plans to work to age 60?

Solution 5-21

If Glenda gets the MBA, she would be 36 when her salary resumes. In today's dollars it would be $40,000, but with two years of 6% inflation, it would be $40,000 x (1.06)2 = $44,944. She would have 24 remaining years of work at an inflation-adjusted discount rate of 1.08/1.06 = 1.0189. The present value of that income stream would be $952,618. Since this would begin in 2 years, we discount it to the present at $952,618/(1.0189)2 = $917,605.

If Glenda continues at her present work, she will have 26 remaining years at $35,000 discounted at the same rate of 1.0189. The present value of her income stream is $795,903. The cost of the MBA is the present value of $30,000 per year at 1.0189% for 2 years or $59,095. The net present value is $917,605 minus ($795,903 + $59,095 = $854,998) or $62,607. The MBA is financially worthwhile.

[Duration]

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